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1
By Jason Neil / Kristin Calhoun
© 2009
Table of Contents
#1 Numbers in Physics…………………
3
#2 Converting Units …………………...
7
#3 Speed and Velocity …………………
10
#4 Acceleration ………………………...
13
#5 Free Fall …………………………….
15
#6 More Acceleration ………………….
18
#7 Motion Graphs ……………………...
21
#8 Triangle Review ……………………
25
#9 Vectors ……………………………...
28
#10 1st and 2nd Laws of Motion ……….
32
#11 3rd Law of Motion …………………
35
#12 Mass, Weight, and Friction ……….
38
#13 More Friction ……………………...
41
#14 Two-Dimensional Motion ………..
45
#15 Projectile Motion ………………….
47
#16 Momentum…………………………
51
#17 Conservation of Momentum ………
54
#18 Collisions ………………………….
56
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Table of Contents (continued)
#19 Work and Power ………………………
59
#20 Energy …………………………………
62
#21 Thermodynamics ………….…………...
65
#22 Specific Heat . …………………………
68
#23 Energy and State Changes……………..
71
#24 Temperature Scales ……………………
74
#25 Gas Laws ……………………………...
77
#26 Fluids …………………………………..
81
#27 Intro. to Waves ………………………....
83
#28 More Waves ……………………………
86
#29 Sound ……………………………………
90
#30 Light …………………………………….
93
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Physics Fix 1
Name: ______________________________
Date: _____________
Hour: _____
Information: Units
The following tables contain common metric (SI) units and their prefixes.
Table 1: metric base units
Quantity
Length
Mass
Time
Temperature
Volume
Amount of substance
Unit
meter
kilogram
second
Kelvin
Liter
mole
Table 2: prefixes for metric base units.
Prefix
Symbol
Mega
M
Kilo
k
Deci
d
Centi
c
Milli
m
Micro

Nano
n
Pico
p
Unit Symbol
m
kg
s
K
L
mol
Meaning in Words
million
thousand
tenth
hundredth
thousandth
millionth
billionth
trillionth
Meaning in Numbers
1,000,000
1,000
0.1
0.01
0.001
0.000001
0.000000001
0.000000000001
Note the following examples:
 “Mega” means million so “Megagram” (Mg) means one million grams NOT one
millionth of a gram. One millionth of a gram would be represented by the microgram
(g). It takes one million micrograms to equal one gram and it takes one million
grams to equal one Megagram.
 One cm is equal to 0.01 m because one cm is “one hundredth of a meter” and 0.01 m
is the expression for “one hundredth of a meter”
Critical Thinking Questions
1. “Milli” means “thousandth” so a milliliter (symbol: mL) is one thousandth of a Liter.
Therefore, it takes _____________ mL to make one L
how many?
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2. “Kilo” means “thousand” so a kiloliter contains ____________ Liters?
how many?
3. How many milligrams are there in one kilogram?
4. How many meters are in 21.5 km?
5. Is it possible to answer this question: How many mg are in one km? Explain.
6. Which is larger one Mm or one mm?
Information: Scientific Notation
“Scientific notation” is used to make very large or very small numbers easier to handle. For
example the number 45,000,000,000,000,000 can be written as “4.5 x 1016 ”. The “16” tells you
that there are sixteen decimal places between the right side of the four and the end of the number.
Another example: 2.641 x 1012 = 2,641,000,000,000  the “12” tells you that there are
12 decimal places between the right side of the 2 and the end of the number.
Very small numbers are written with negative exponents. For example, 0.00000000000000378
can be written as 3.78 x 10-15. The “-15” tells you that there are 15 decimal places between the
right side of the 3 and the end of the number.
Another example: 7.45 x 10-8 = 0.0000000745  the “-8” tells you that there are 8
decimal places between the right side of the 7 and the end of the number.
In both very large and very small numbers, the exponent tells you how many decimal points are
between the right side of the first digit and the end of the number. If the exponent is positive, the
decimal places are to the right of the number. If the exponent is negative, the decimal places are
to the left of the number.
Critical Thinking Questions
7. Two of the following six numbers are written incorrectly. Circle the two that are incorrect.
a)
3.57 x 10-8
104
b)
4.23 x 10-2
c)
75.3 x 102
d)
2.92 x 109
e)
0.000354 x 104
f)
9.1 x
What do you think is wrong about the two numbers you circled?
8. Write the following numbers in scientific notation:
a) 25,310,000,000,000,000 = _____________
b) 0.000000003018 = ____________
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9. Write the following scientific numbers in regular notation:
a) 8.41 x 10-7 = ________________
b) 3.215 x 108 = _____________________
Information: Multiplying and Dividing Using Scientific Notation
When you multiply two numbers in scientific notation, you must add their exponents. Here are
two examples. Make sure you understand each step:
(4.5x1012) x (3.2x1036) = (4.5)(3.2) x 1012+36 = 14.4x1048  1.44x1049
(5.9x109) x (6.3x10-5) = (5.9)(6.3) x 109+(-5) = 37.17x104  3.717x105
When you divide two numbers, you must subtract denominator’s exponent from the numerator’s
exponent. Here are two examples. Make sure you understand each step:
2.8 x1014 2.8

x10147  0.875 x107  8.75 x106
7
3.2 x10
3.2
5.7 x1019 5.7

x1019  ( 9 )  1.84 x1019  9  1.84 x10 28
3.1x10 9 3.1
Critical Thinking Questions
11. Solve the following problems.
a) (4.6x1034)(7.9x10-21) =
b) (1.24x1012)(3.31x1020) =
12. Solve the following problems.
8.4 x10 5

a)
4.1x1017
b)
5.4 x10 32

7.3 x1014
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Information: Adding and Subtracting Using Scientific Notation
Whenever you add or subtract two numbers in scientific notation, you must make sure that they
have the same exponents. Your answer will them have the same exponent as the numbers you
add or subtract. Here are some examples. Make sure you understand each step:
4.2x106 + 3.1x105  make exponents the same, either a 5 or 6  42x105 + 3.1x105 = 45.1x105 =
4.51x106
7.3x10-7 - 2.0x10-8  make exponents the same, either -7 or -8  73x10-8 – 2.0x10-8 = 71x10-8 =
7.1x10-7
Critical Thinking Questions
13. Solve the following problems.
a) 4.25x1013 + 2.10x1014 =
b) 6.4x10-18 – 3x10-19 =
c) 3.1x10-34 + 2.2x10-33 =
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Physics Fix 2
Name: ______________________________
Date: _____________
Hour: _____
Information: Dimensional Analysis
“Dimensional Analysis” is a big scary term that doesn’t really need to be scary. It’s simple. The
basis for dimensional analysis is this: if you multiply something by 1 you do not change its
value! Pretty easy, eh? Here’s an example:
1 3 3
 
2 3 6
Notice that the value of ½ didn’t really change because 3/3 is the same as 1. Again, in
mathematics, multiplying by 1 doesn’t change the real value of anything.
100 cm
3
3
100 cm
is a fraction t hat behaves just like because 100cm  1 meter! Therefore, neither nor
1 meter
3
3
1 meter
will change the real value of a number.
Here’s an example problem of a conversion:
Convert 3.75 cm into meters. All you need to do is multiply by a fraction.
Always begin by
putting the number
you are given in a
fraction over 1.
Find a fraction that contains both
units that you are working with.
Here we have cm and m.
Notice that 1 m and 100 cm equal each other. THIS IS A
MUST. You could also have “0.01 m” and “1 cm”
because 0.01 m = 1 cm.
3.75 cm
1m
3.75 cm  1m 3.75 cm  1m



 0.0375 m
1
100 cm
1  100 cm
1  100 cm
We put cm on the bottom
here so that it cancels here.
m is the only
unit left and it’s
the unit we
want
Notice in the above example that cm was on the bottom in the conversion factor fraction. This is
very important. “Tops and bottoms cancel each other.” We need cm on the bottom so that it
cancels out the one on the top!
Critical Thinking Questions
1. If you were converting 42 grams into kilograms, which fraction would you use as a
converting factor?
A)
1000 g
1 kg
B)
1000 kg
1g
C)
1 kg
1000 g
D)
1g
1000 kg
Explain your reasoning:
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2. How many meters are in 32.5 kilometers? (You are converting km to m.)
The problem is started for you:
32.5 km


1
3. How many L are there in 32.5 L?
Information: Non-base unit  non-base unit
So far we have been converting a prefixed unit into a base unit or vice versa. It gets a little more
complex when we want to convert a prefixed unit into another prefixed unit. Whenever such is
the case, convert to the base unit first and then finish the problem.
For example, if you needed to convert centimeters into kilometers, first convert to the base
unit—meters. Then convert meters into kilometers.
Critical Thinking Questions
4. How many cm are there in 40 km? Let’s break it into two steps…
a) First, convert to the base unit, which for this problem is meters. Fill in the blanks.
40 km

1
m
 ______________________
km
km is on the bottom to cancel out the
other km, which is on the top.
m and km are chosen because we are
converting from km to m
b) Now convert your answer to part a (which is in meters) into centimeters.
m
1
5. How many kL are there in 34,500 mL?

km

m
a) First, convert mL to L.
b) Now convert your answer to part a (in L) to kL.
6. How many m are there in 0.0035 km?
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Information: Quantities containing two units at once
It gets a bit more complicated if we have to convert a quantity containing two units. For
example, speed has two units. “Miles per hour” contains two units. “Meters per second”
contains two units. When you need to do a conversion on such a quantity, do one unit at a time.
Here’s an example.
Convert 50 km/hr to m/s.
hr is on the top here so that it cancels
with the hr on the bottom. “Tops and
bottoms cancel.”
50 km 1000 m
1 hr
1 min 50 km  1000 m  1 hr  1 min




 13.89 m/s
1 hr
1 km
60 min 60 s
1 hr  1km  60 min  60 s
First we converted
km then we’ll work
on the hr.
Critical Thinking Questions
7. Convert 25 m/s to km/hr.
8. The speed of sound is approximately 340 m/s. How many km/hr is that?
9. The maximum highway speed in Michigan is 70 miles/hr. How many km/hr is this? (Note:
1 mile is equal to 1609 m.)
10. The flow of water in our kitchen tap is 3.2 L/min. How many mL/s is this?
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Physics Fix 3
Name: ______________________________
Date: _____________
Hour: _____
Information: Speed is Relative
Speed is a measure of how fast distance changes. Distance must change or there is no speed.
Right now as you are reading this, you are probably sitting still. If you were asked how fast you
are moving you would probably reply that your speed is zero. However, the Earth is currently
traveling around the sun at a speed of about 30,000 meters per second (m/s)! So, your speed
relative to the sun would be about 30,000 meters per second (m/s) but your speed relative to the
ground of the Earth is zero. Speed is always “relative” to something; usually we assume that
speed is relative to the ground unless specified otherwise.
Critical Thinking Questions
1. Consider the diagram below.
Speedometer reads: 60 km/hr
Speedometer reads: 35 km/hr
a) How fast is the van traveling relative to the ground?
b) How fast is the van traveling relative to the car? (This is how fast it looks like the van
is traveling to someone riding in the car.)
Information: Units
So far you probably realized that the units for speed involve some measure of distance (meters,
kilometers, miles, etc.) and time (seconds, hours, etc.). Consider the table below:
Distance Units
Meters
Miles
Kilometers
Time Units
Seconds
Minutes
Hours
Speed Units
Meters per second
Miles per minute
Kilometers per hour
Symbol for Speed Units
m/s
mi/min
km/hr
Critical Thinking Questions
2. If distance is measured in units of centimeters and time is measured in seconds, what would
be the units for speed?
3. A kilogram is equal to one thousand grams. How many meters are in a kilometer?
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4. To find the correct units for the speed of a car we must…
A) Multiply the distance the car travels by the time it takes to travel.
B) Add the distance the car travels and the time it takes to travel.
C) Divide the distance the car travels by the time it travels.
5. Which one of the following is an equation that you can use to calculate speed. (Note the
following symbols: s=speed; d=distance; t=time; =change in)
d
A) s = d + t
B) s 
C) s = d – t
D) s = d  t
t
**Note: the symbol “” is necessary because for an object to have speed, its distance
must change as the time ticks (the time is changing too!).
6. Use the correct equation from the previous question to answer the following…
a) A car was at a 30 km marker and began to drive as someone else started the stopwatch.
The car passed the 90 km marker when the stopwatch read 30.00 minutes. What was the
average speed of the car during the time interval?
b) A man rowed a boat at a speed of 12 mi/hr. He rowed for 2 hours. How many miles did
he travel?
7. Given your answer to question 5 and the fact that units for speed are something like
kilometers per hour or meters per second, what does the word “per” signify?
A) addition
B) subtraction
C) division
D) multiplying
8. When you are in a car, what is the easiest way to find out how fast you are going in any
instant, or moment, of time? (You don’t need a calculator, right?)
Information: Average vs. Instantaneous
Hopefully, your answer to question 8 involved looking at the speedometer.  At any moment
(in any instant) you can find your speed by looking at a speedometer. A police officer can find
your speed at any instant if he uses his radar gun. The speed on the speedometer or the speed
that the police officer finds using a radar gun is called instantaneous speed because it is the speed
at an instant or moment of time. In question 6a you calculated the average speed, not the
instantaneous speed.
Critical Thinking Questions
9. What is the difference between average and instantaneous speed?
10. A snail was traveling across a sidewalk. A brilliant physics student decided to find the
snail’s speed and so she found a ruler and a stopwatch. Is the student going to find the snail’s
average speed or instantaneous speed? Explain.
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11. Is it possible to find instantaneous speed by measuring distance and time? Explain.
12. During a certain trip, a car traveled at an average speed of 75 km/hr. Would it be possible to
attain such an average speed if the car never had an instantaneous speed of more than 75
km/hr? Explain.
Information: Velocity
Consider this picture again, but this time notice that both vehicles are traveling at the same
speed:
Speedometer reads 80 km/hr
Speedometer reads 80 km/hr
In normal, everyday speech we would use the words “velocity” and “speed” interchangeably to
mean the same thing. But in physics, velocity and speed are different from one another. The
two vehicles in the picture above have the same speed, but not the same velocity. Weird, eh?
Critical Thinking Questions
13. Velocity includes speed AND something else. What do you think makes velocity different
from speed?
14. Why do the two vehicles pictured above have different velocities?
15. The following vehicle has the cruise control set to 20 km/hr. The speed is remaining
constant, but the velocity is not constant—it is changing. Explain why.
16. What is the average velocity of an airplane that flies…
a) … 420 km due north in 1 hour?
b) … 210 km due north in ½ hour?
c) … 105 km due north in 15 minutes?
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Physics Fix 4
Name: ______________________________
Date: _____________
Hour: _____
Information: What is Acceleration?
You just learned a bit about velocity. If the velocity doesn’t change, we say that it is constant.
Sometimes, however, the velocity is not constant. We would like to now consider how to
describe changes in velocity. Acceleration is a measure of how fast the velocity changes.
Critical Thinking Questions
1. In which of the following situations does the car undergo acceleration? (There may be more
than one correct answer to circle.)
A)
B)
C)
D)
A car maintains a speed of 15 km/hr as it drives in a circle.
A car travels south at 50 km/hr.
A car slows from 45 km/hr to 35 km/hr.
A car speeds up from 50 km/hr to 75 km/hr.
2. Why is the gas pedal on a car sometimes called the “accelerator”?
3. A vehicle may accelerate or decelerate—what do you think is the difference between
acceleration and deceleration?
Information: Calculating Acceleration
Hopefully for question 1 (check your answer now!), you realized that the car in part (A) was
undergoing acceleration even though the speed wasn’t changing. The velocity changed because
velocity includes the idea of direction as well as speed. For now, we will focus on just the
changing speed aspect. (For question 1, C and D also described acceleration.)
It’s no big deal if a car can go from “zero to sixty”—any car can do that! We want to know how
quickly the car can go from “zero to sixty”. Can it go from “zero to sixty” in 20 seconds or in 4
seconds? There’s a big difference. We don’t merely want to know that the speed of a vehicle
changes. We want to know how fast the speed changes—that’s acceleration.
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Critical Thinking Questions
4. A car’s speed changed gradually and evenly from 15 m/s to 35 m/s. It took the car 10
seconds to accomplish the change in speed.
On average, the car’s speed increased by __________ each second. Therefore the
2 m/s or 4 m/s or 10 m/s
acceleration is _____ m/s-s (“meters per second-second”—the units are a little strange, eh?)
2, 4, or 10
5. It took an airplane 3 seconds to increase in speed from 50 m/s to 65 m/s.
a) Calculate the net change in speed? (This is just the final minus the beginning speed.)
b) Verify that the average acceleration was 5 m/s-s.
6. Which one of the following equations is the equation for average acceleration, a? (Note: vf =
final speed or velocity and vi = initial speed or velocity and t = time elapsed.)
A) a = (vf – vi )(t)
B) a 
vf  vi
t
C) a 
t
vf  vi
D) a 
(v f  v i )
2
7. A van increased in speed from 20 km/hr to 30 km/hr in 5 seconds. A truck increased in
speed from 40 km/hr to 60 km/hr in 15 seconds. Calculate the acceleration of each. Include
units.
*Note: The units for acceleration in question 7 should be km/hr-s, pronounced “kilometers per
hour-second”. For questions 4 and 5, the units were m/s-s. When the units for time are the
same, the units are usually expressed as time squared. Instead of writing “m/s-s” we would write
“m/s2” and say, “meters per second squared”.
8. A car has an initial speed of 7 m/s. Its speed increases to 21 m/s. It took 2.1 seconds for the
speed to change. Calculate the acceleration.
9. A car starts with a speed of 20 km/hr and accelerates at a rate of 3.4 m/s for 20 seconds.
What is the final speed of the car in km/hr? (Be careful of units!)
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Physics Fix 5
Name: ______________________________
Date: _____________
Hour: _____
Information: Free Fall
When a skydiver is falling a couple things are happening. 1) Gravity is pulling the skydiver
downward. 2) Air resistance is slowing down the skydiver. When the skydiver opens his
parachute, the air resistance slows him down a lot! The reason a feather doesn’t fall straight
down is because of air resistance. Air resistance has a big affect on light objects like feathers.
For now, we are going to ignore air resistance and pretend it doesn’t exist. Then we can examine
just the pull of gravity on an object without getting too confused. Free fall is when an object
falls and gravity is the only thing affecting the object; there is no air resistance.
Critical Thinking Questions
1. Of course, perfect “free fall” does not exist since there is always air resistance. But which of
the following objects behaves most similarly to an object in free fall?
a) confetti at a party
b) a vase falling off a table
c) a feather falling off a bird
Information: Speed and Gravity
Gravity is constantly pulling
downward. If you throw a ball
up, it will be decelerated by
gravity. As the ball moves
upward, gravity will cause its
speed to decrease by 9.8m/s each
second.
If an object is moving downward,
it will be accelerated by gravity.
Its speed, v, will increase by 9.8
m/s each second.
Figure 1: Gravity
affecting the horizontal
velocity of a ball
t=2s
v = 9.8 m/s
t=1s
v = 19.6 m/s
t=0s
v = 29.4 m/s
t=3s
v = 0 m/s
t=4s
v = 9.8 m/s
t=5s
v = 19.6 m/s
t=6s
v = 29.4 m/s
The strength of the acceleration
due to gravity is given the
symbol, g, and it is equal to 9.8
m/s2.
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t=7s
v = 39.2 m/s
16
Critical Thinking Questions
2. The picture doesn’t show us what happens after 7 seconds. At a time of 8 seconds, how fast
would the ball be going?
3. The ball in figure one started out at a speed of 29.4 m/s and took 3 seconds to reach its
maximum height. At a time of 3 seconds the speed of the ball was 0 m/s. If the beginning
speed had been 39.2 m/s (instead of 29.4 m/s), how many seconds would it have taken to
reach a speed of 0 m/s?
4. If a rock fell off of a cliff, how fast would the rock be going after 2 seconds?
5. If a rock fell off a cliff, how fast would it be traveling after 8 seconds?
6. Which equation could be used to answer questions 4 and 5?
a) v = g ∙ t
b) v = g + t
c) v = g ∙ t2 + 2
d) v = 2( t + g )
7. If a ball is thrown upward at an initial velocity of 45.6 m/s, how many seconds will it take for
the ball to reach it’s maximum height? (Hint: use the equation from question 6; you know v
and g, so you can solve for t!)
8. Considering the same ball from question 7, how long will it take for the ball to come back
down for you to catch it? (Hint: the ball will take the same amount of time to come down as
it took to go up.)
Information: Gravity and How Far A Rock Falls
The following information was gathered by scientists observing a rock falling down a cliff. The
rock was initially at rest with no speed and then began to fall:
Time (seconds)
0
1
2
3
4
Distance Fallen (meters)
0
4.9
19.6
44.1
78.4
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Critical Thinking Questions
9. Which one of the following equations fits the data? (Note: d stands for distance fallen.)
a) d = g ∙ t
b) d = 2(g ∙ t)
c) d = ½ g ∙ t2
d) d = t2 + 2g
10. A boy dropped a penny off a cliff. How many meters did the penny fall in 7 seconds?
11. Considering the penny from the previous question, how fast was the penny going after 7
seconds? (Hint: the equation from question 6 might help.)
12. How long would it take a rock to fall down a cliff that is 109 m tall? (Hint: use the equation
from question 9 and solve for t.)
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Physics Fix 6
Name: ______________________________
Date: _____________
Hour: _____
Information: Constant Acceleration
In the previous Physics Fix we looked at the acceleration due to gravity, which had the symbol g.
It was a constant or uniform acceleration, always equal to 9.8 m/s2. We discovered a couple
equations also. I will rewrite them here using “a” instead of “g”. The equations work for the
acceleration due to gravity and any other acceleration that is constant. (Recall that d=distance
and t=time.)
v = a t and d = ½ a t2
Review Question
1. A ball is resting atop a cliff. Suddenly it begins to fall. It lands on the ground after exactly
3.5 seconds.
a) What was the velocity of the ball when it hit the ground?
b) How high was the cliff? (Hint: the height of the cliff equals the distance fallen.)
Information: Initial Velocity
In question 1 and in other similar questions that you have done the object is not moving initially.
How could you find the velocity of a ball that was thrown down a cliff instead of one that merely
falls of the cliff with no starting velocity? Fortunately, it’s not difficult. Simply add the initial
velocity (vi) to the equation you already know in order to find the final velocity (vf):
Equation 1: vf = vi + a t
But how would you calculate the distance fallen? Again, we need to modify the equation you
already know.
Equation 2: d = vi t + ½ a t2
A final equation that is helpful:
Equation 3: vf =
v i2  2 a d
Critical Thinking Questions
2. A ball rolls down a ramp and experiences a constant acceleration of 3.2 m/s2. At a certain
instant its velocity was 0.65 m/s.
a) What is the velocity of the ball 9 seconds later?
b) What distance did the ball travel during the 9 seconds?
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3. A car is traveling at 20 m/s. The car accelerates at a constant rate of 3.5 m/s2 for 10 seconds.
What was the final speed of the car?
4. A penny was thrown downward off of the top of a 100 m building. The initial velocity of the
penny was 15 m/s. How fast was the penny traveling when it his the ground? (Remember
that because this problem involves gravity, the acceleration is 9.8 m/s2.)
5. A penny was thrown off a different building given an initial velocity of 10 m/s. It hit the
ground 3.9 seconds later. How tall was the building?
Information: Remembering Direction
In the previous problems the velocity of the object and the acceleration were in the same
direction. If the velocity and acceleration are in opposite directions, you must make one of them
negative. It is common to make the acceleration negative. In the next problem note that it is
talking about deceleration, which is acting in the opposite direction from velocity. Therefore, in
the following problem make the deceleration a negative number when you use Equation 2.
Critical Thinking Questions
6. A car initially traveling at 30 m/s decelerated at a rate of 7 m/s2. It took 4.3 seconds in order
to stop. What distance did the car travel while stopping?
7. A toy rocket was launched with an initial velocity of 200 m/s. How high did it go? (Hints:
use Equation 3 and solve for d. Remember that the acceleration is in the opposite direction
as the initial velocity. Also, the final velocity is zero when it reaches its maximum height.)
8. Considering the hint from question 7, why is the final velocity of the toy rocket equal to
zero?
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9. A truck traveling at 70 km/hr decelerate at 6.5 m/s2. Note: km/hr and m/s2 don’t match up.
You must convert 70 km/hr into m/s before proceeding! Also, is the acceleration negative or
positive? Think!
v  vi
a) How many seconds will it take to stop the truck? (Hint: use a  f
and remember
t
that vf is zero here because the truck will be stopped.)
b) How far will the truck travel after the brakes are applied?
10. A car traveling at 30 m/s notices an accident about 65m up the road. The car’s breaks are
capable of decelerating at a rate of 6.4 m/s2. Can the car stop before hitting the accident?
11. A motorcycle moves at an initial velocity of 40 km/hr and accelerates at a constant rate of 8.3
m/s2 for a distance of 120m. How fast is the motorcycle then moving? (Note: the units must
match up!!!)
12. A bullet is fired straight up into the air. The initial speed of the bullet is 425 m/s. How long
will it take the bullet to reach its highest point?
13. Given your answer to question 12, how high did the bullet go?
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Physics Fix 7
Name: ______________________________
Date: _____________
Hour: _____
Information: Speed Graphs
Recall that speed is a measure of how fast an object’s distance changes. By graphing distance
vs. time we can investigate an object’s speed graphically.
Critical Thinking Questions
1. Consider the following graph of a car driving. Use the graph to answer the following
questions:
Distance in meters
0
5
10
15 20
Time in seconds
25
a) How long did it take the car to travel 10 meters?
b) Consider the time interval between 0 and 10 seconds.
i) How far did the car travel during that time?
ii) What was the car’s average speed during that time?
c) Consider the time interval between 5 and 15 seconds. What was the car’s average
speed during that time?
d) From this graph we can conclude that between 0 and 15 seconds…
A) the speed was constant
B) the velocity was constant
C) both speed and velocity was constant
D) we can’t conclude for sure that the speed or velocity was constant.
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2. The following graphs represent two different cars—car A and car B.
Distance in meters
0
5
10
15 20
Time in seconds
25
a) What is the average speed of Car A during the time interval of 0-10 seconds?
b) What was the average speed of Car B during the time interval of 0-10 seconds?
c) What was the average speed of Car A during the time interval of 10-20 seconds?
d) What was the average speed of Car B during the time interval of 10-20 seconds?
3. Only one of the cars from the previous question had a constant speed. Which one?
Justify your answer.
4. Given a graph of distance vs. time, how can you tell if the object had constant speed?
Information: Acceleration Graphs
Since acceleration is a measure of how fast speed changes, we can graphically examine
acceleration by graphing speed vs. time.
Critical Thinking Questions
5. Consider the graph from question 2. Which car had an acceleration of zero?
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6. Consider the following graph of Cars A, B, and C:
Speed (km/hr)
0
5
10
15 20
Time in seconds
25
a) Which car(s) is/are accelerating?
b) Car D is driving at 60 km/hr at time zero seconds. The acceleration of Car D between
0 and 25 seconds is 0 km/hr-s. Draw the graph for Car D on the graph above.
c) What is the average acceleration for Car A between the time of 0 and 5 seconds?
d) Draw a graph for Car E on the graph above. Car E is traveling at 40 km/hr at time 0.
The car’s average acceleration is 2 km/hr-s during the entire time interval of 0-25
seconds.
7. Label each of the graphs with the following labels. You may use some more than once or
not at all. (1) Constant Speed, (2) Constant Acceleration, (3) Not Moving, (4)
Acceleration (not constant)
_____a)
_____ b)
S
p
e
e
d
Time
_____ d)
_____ e)
d
i
s
t
a
n
c
e
d
i
s
t
a
n
c
e
S
p
e
e
dS
p
e
e
d
_____ c)
S
p
e
e
d
Time
Time
_____ f)
Time
d
i
s
t
a
n
c
e
Time
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Time
24
8. Consider the graph of speed vs. time for Car A as it accelerates constantly at 32 m/s2.
Graph 1: Speed (m/s) vs. Time (s)
Speed (m/s)
0
1
2
3
4
Time in seconds
5
Graph 2: Distance (m) vs. Time (s) for the same car during the same time period.
Distance in meters
0
1
2
3
4
Time in seconds
5
a) Calculate the area under the line for Graph 1. Hint: this is like finding the area of a
triangle using the formula area=1/2 base x height. The height is about 160 and the
length of the base is about 5.
b) Using Graph 2, find the distance the car traveled during the 5 second time span?
c) Given your answer to parts a and b, fill in the blank: If you have a graph of speed vs.
time, the area under the graph is equal to the __________________ the car traveled.
d) Find the slope of the line in Graph 1. How does the value for the slope relate to the
acceleration of Car A (as stated at the beginning of question 8)?
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Physics Fix 8
Name: ______________________________
Date: _____________
Hour: _____
Information: Vocabulary
Figure 1: A Right Triangle (any triangle with a 90o angle)
Side C
Side A
Angle X
A “right angle”: a
square corner
measuring 90o
Side B
Application Questions
1. The hypotenuse is the longest side in a right triangle. Which side is the hypotenuse?
2. The word “adjacent” means “next to”. Which side is adjacent to Angle X? (Note: this
cannot be the hypotenuse.)
3. Which side is “opposite” Angle X?
Information: Trigonometry Equations
There are three main equations involving the angles of a right triangle. They are as follows:
sine 
opposite
hypotenuse
cosine 
adjacent
hypotenuse
tangent 
opposite
adjacent
For example, if we wanted to find the sine of Angle X we would divide the length of Side A by
Side C.
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Application Questions
4. How would you find the tangent for Angle X in Figure 1?
5. Use the following triangle to answer the questions:
Angle Y
25.1
10.5
Angle X
22.8
a) Calculate the sine, cosine and tangent for Angle Y.
sine = _____________
cosine = ______________
tangent = ______________
b) Given your answers to part a, you should be able to find out the value of Angle Y.
For example, use your answer for the sine. On your calculator take the sin-1 of the
sine. Usually this is done by hitting the “2nd key” and then the “sin” button.
c) Your answer to part b should be about 65.3o. Use cosine in the same way and see if
you get the same answer.
d) What is the value of Angle X? (Hint: you’ll need to first use one of the three
trigonometry equations—it doesn’t matter which!)
6. Use the following triangle to answer the questions:
Side Y
61.1o
20.1
Side X
a) Calculate Side X. Note that Side X is opposite the angle of 61.1o. We can use this
equation:
sine 
opposite
hypotenuse
Sin(61.1) = 0.875
0.875 
opposite
20.1
Therefore, Side X has a length of __________________
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b) Calculate the length of Side Y:
7. All of the triangles in the previous questions follow an equation.
Note the following symbols:
c = hypotenuse
a = any side of the triangle other than the hypotenuse
b = any side of the triangle other than the hypotenuse
Which of the following equations is true for all right triangles?
B) a2 + b2 = c2
A) a + b = c
C) a2 – b2 = c2
D) all of these
8. Given the equation in question 7, find the length of the missing side of each triangle
below.
a)
b)
42.9
18.7
X
23.1
X
12.9
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Physics Fix 9
Name: ______________________________
Date: _____________
Hour: _____
Information: Vector vs. Scalar
We have seen that velocity and speed are technically different. Velocity includes the idea of
direction and speed does not. Speed only requires a magnitude, but not a direction. Quantities
that only require magnitude are called scalar quantities. How much something weighs is a scalar
quantity—obviously, no direction is needed. Measurements that require both magnitude and
direction are called vector quantities.
Critical Thinking Questions
1. Indicate whether each of the following are vector (V) or scalar (S) quantities.
_____ Mass
_____ Acceleration
_____ Time
_____ Volume
Information: A Picture is Worth 1000 Words
Sometimes a picture can add meaning that words cannot. A convenient way to describe velocity
is with arrows. Since velocity is a vector quantity, we call the arrows vectors. Both the length of
the arrow and the direction of the arrow have meaning.
Vectors can be added: A car drives 30 km east then turns right and heads 10 km south. Then the
car turns left heading 10 km east, then 20 km north, and finally turns and heads 30 km west.
Pictures help!
When adding vectors, they are always
drawn “head to tail”—where one arrow
ends, the other starts. The “resultant”
vector is the sum of all the other
vectors. Here, it is the actual real
displacement as shown with a dotted
arrow.
“resultant”
Vectors can be subtracted: Vectors can be added and subtracted too. Here’s an example: An
airplane flying east at 200 km/hr encounters a wind blowing west at 20 km/hr. The airplanes
“resultant” velocity is 180 km/hr west.
200 km/hr
20 km/hr
Wind
Resultant: 180 km/hr
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Critical Thinking Questions
2. Consider the following diagram. Explain TWO things about the diagram: Explain how
the diagram conveys that the race car and the limousine are driving in opposite directions
AND the race car is going approximately twice as fast as the limousine.
3. If an airplane were flying west at 100 km/hr and encountered a strong gale blowing east
at 100 km/hr, what would be the plane’s velocity relative to the ground?
4. Air traffic controllers are responsible for guiding airplanes to their proper destinations.
An air traffic controller needs to use vectors all the time to keep a plan on course. As an
example, consider an airplane traveling east at 120 km/hr encounters a southern
crosswind blowing at 30 km/hr. What is the plane’s resultant velocity?
120 km/hr
30 km/hr
We’ll break it into a couple steps…
120 km/hr
a) Draw the vectors “head to tail” so that where one
vector ends, the next one starts. This is done for you:
30 km/hr
b) Then complete the triangle with a third vector (this is the resultant vector) and find
the length of this resultant vector. [Hint: use (a2 + b2) = c2]
120 km/hr
30 km/hr
c) Next, find the angle. Use trigonometry! (Hint: 30 120 = 0.25 = tangent of the
angle. On your calculator, then, take the inverse tangent of 0.25.)
d)
120 km/hr
Find this angle
30 km/hr
123.7 km/hr
should be your answer to part b
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e) Hopefully in part c you found that the angle was about 14.0o. Therefore the resultant
vector can be described like this:
The airplane was traveling at _________ km/hr at an angle of ________ south of east.
answer to part b
answer to part c
5. An airplane was flying north at 245 km/hr. There was a strong west wind of 60 km/hr.
What is the resultant velocity of the airplane? (Your final answer should be a description
like that in part 4d, including both the amplitude and the angle.)
6. What affect does a crosswind (like in questions 4 and 5) have on the speed of an
airplane? Does it speed it up or slow it down?
7. Use the following axes, a ruler and a protractor to draw vectors. Each centimeter stands
for 10 km/hr.
35 km/hr at 20o east of north
40 km/hr at 35o north of east
Information: Components of Vectors
In questions 4 and 5 you took a horizontal and vertical vector and found the resultant vector.
Next we will start with a vector that is at an angle and break it up into its horizontal and
vertical parts. These horizontal and vertical parts are called the components of the vector.
Finding the components is called resolution. Let’s start resolving vectors!
Draw a rectangle,
making sure all
angles are 90o
The sides of the rectangle
form the components!
Given this vector
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Critical Thinking Questions
8. Resolve the following vector into its horizontal and vertical components by drawing a
rectangle as done in the previous information section.
9. Resolve the following vectors into their components. Calculate the velocity and specify
the direction of each component.
a) 65 km/hr at 30o north of east
b) 45 km/hr, 20o west of north
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Physics Fix 10
Name: ______________________________
Date: _____________
Hour: _____
Information: Newton’s 1st Law of Motion
In the 1600’s, Isaac Newton changed the way motion was viewed. He said that for an object to
change its state of motion a force needs to act on the object. A force, scientifically speaking, is
any push or pull. So without a force, an objects motion will not change. An object that is
already in motion will stay in motion (in a straight line path)… an object at rest will stay at
rest… unless a force acts on the object. This law is sometimes called the law of inertia. Inertia
is simply the tendency of an object to remain in the same state of motion.
Critical Thinking Questions
1. If someone isn’t wearing her seatbelt during a high speed car accident it is possible that she
may fly forward through the windshield.
a) Using the first law of motion, explain why this happens?
b) Using the first law of motion, explain the role of the seat belt.
2. If you are driving straight, and the car turns quickly to the right, you probably feel a force
acting on your body. Think about the force for a minute. The force happens because your
body wants to move in one direction but the car pulls you in another direction.
a) Which of the following black arrows best represents the direction that your body wants to
move? (A, B, or C)
A
B
C
turning
to the right
b) Which of the above black arrows indicates the direction that the car is pulling you?
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3. Using the first law of motion, is there a force acting on the object in each of the following
scenarios? In the blanks, write “Yes” or “No” and also explain your answer. (Ignore the
force of gravity for now.)
_____ a) A hockey puck slides across the ice.
_____ b) A car accelerates from 30 km/hr to 40 km/hr.
_____ c) A car travels at a constant speed of 15 km/hr as it turns a corner.
4. You are probably starting to realize that to change an object’s velocity, a force is needed. If
the object’s velocity is 0 km/hr, it will stay that way unless something pushes or pulls it.
Which of the following objects would be most difficult to accelerate?
A) a rock with a mass of 20 kg
B) a rock with a mass of 2000 kg
C) a 200,000 kg rock
5. True or False: the more mass an object has, the less force is required to accelerate it.
6. If you kick a ball (this would be a force), which ball would accelerate the most?
A) a 0.5 kg ball
B) a 10 kg ball
C) a 25 kg ball
7. True of False: the more mass an object has the greater the acceleration when a force is
applied.
8. As you may have guessed by now, there is a relationship between force (F), mass (m) and
acceleration (a). Given the previous 4 questions, which of the following equations makes the
most sense:
m
F
A) a 
B) a = Fm
C) a 
F
m
Information: Newton’s 2nd Law of Motion
The relationship you discovered in question 8 is known as Newton’s second law of motion.
F
a
m
If “F” is big, acceleration will be
big too
If “m” is big, acceleration will be small
The above equation usually rewritten as F = ma. The units for force are made up from the units
for mass and for acceleration. Mass is measured in kg. Acceleration is measured in m/s2.
Therefore, force is measured in kg-m/s2. One kg-m/s2 is given the special name “Newton”. So
force is measured in Newtons (N), which is the same thing as kg-m/s2.
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Critical Thinking Questions
9. What force (in units of Newtons) is needed to give a 3.5 m/s2 acceleration to a 1200 kg car?
10. A force of 24 N was required to accelerate an object at a rate of 4 m/s2. What was the
object’s mass?
11. It took 2.3 seconds for a car’s velocity to change from 20 m/s to 35 m/s. The mass of the car
was 1370 kg. What force was required to cause the acceleration? (Hint: First calculate the
acceleration.)
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Physics Fix 11
Name: ______________________________
Date: _____________
Hour: _____
Information: Combining the 2nd Law With Equations We Already Know
In previous lessons we have looked at the following equations:
Equation 1: vf = vi + a t
Equation 2: d = vi t + ½ a t2
Equation 3: vf =
v i2  2 a d
It is important to keep in mind that if an object is ever initially at rest, then the initial velocity (vi)
is equal to zero.
Critical Thinking Questions
1. A ball with a mass of 2 kg resting on the grass was suddenly kicked. In a split second (0.328
s), the ball moved 1.7m. What force was exerted on the ball? (Hint: we will break this
question into steps.)
a) Why is vi equal to zero?
b) Calculate the acceleration using Equation 2 above. (You are given d and t, so all you have
to do is solve for a.)
c) Use the acceleration from part b to calculate the force, remembering that F=ma.
2. A 30 kg rocket leaves a rocket launcher traveling at a velocity of 750 m/s. What was the
force during the rocket’s launch?
a) First, find the acceleration. The initial velocity was zero. Use the final velocity (vf),
the distance (d) along with Equation 3 and solve for the acceleration (a).
b) Using Newton’s second law, calculate the force.
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Information: Two Forces Acting on an Object
Balanced forces: when two or more equal forces act on an object in an opposite directions so that
the forces cancel each other.
Example:
20 N Force
20 N Force
Because both men pull with equal force in the opposite direction, the object
(which is the rope) does not move.
Unbalanced forces: when a force or more than one force is not cancelled by an opposing force.
Critical Thinking Questions
3. A football player is about to be tackled by three defensive players at the same time. On the
diagram below, you can see the forces of each tackle. Explain why the player accelerates in
the direction of the 60 N force.
20 N
60 N
20 N
4. Another tackle is about to occur by three defensive players at the same time. Explain why the
tackled player does not accelerate in any direction.
20 N
20 N
20 N
5. In which question—3 or 4—were the forces “unbalanced”?
6. If only one force acts on an object, is the force balanced or unbalanced?
7. For an object to accelerate, the forces must be ___________________.
balanced or unbalanced?
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Information: Newton’s 3rd Law of Motion
The third law of motion you have probably heard before: “For every action there is an equal and
opposite reaction.” Forces always come in pairs.
Action force: ball pushes on cannon (recoil)
Reaction force: ball shoots out
Action force: Rocket pushes out gas
Reaction force: Gas pushes rocket up
It doesn’t matter which force we call the “action force” or which we call the “reaction force”.
The important thing is that the forces come in pairs.
Critical Thinking Questions
8. In the cannonball picture above we can imagine that the ball gets accelerated forward much
faster than the cannon’s recoil acceleration backward. If the forces are “equal and opposite”
F
why are the accelerations not the same? (Hint remember that a 
and consider the mass
m
of the cannonball and the cannon itself.)
9. If your foot kicks a football, your foot exerts a force on the football and the football exerts a
force on your foot.
a) How many forces are involved in this scenario?
b) How many of the forces act on the football?
c) Therefore, the forces acting on the football are ______________ and it _____ accelerate.
balanced or unbalanced
will or won’t
d) True or false: Action/reaction forces are equal and opposite but they do not “cancel” like
the balanced forces did in question 4.
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Physics Fix 12
Name: ______________________________
Date: _____________
Hour: _____
Information: Mass and Weight
Imagine a box on the ground. If you apply a force to it by kicking it, then the box will
accelerate. The box’s mass, force, and acceleration are all related according to the equation that
you have already learned about: F=ma.
Critical Thinking Questions
1. If you kick the box and it accelerates rapidly, what does that tell you about the mass? (For
example, does the box have a big mass or little mass?)
2. If you kick the box and it accelerates very slowly, what does that tell you about the mass?
3. Suppose you come upon 3 different boxes. Suppose also that you are very skilled at kicking
boxes with a force of exactly 35 N. You kick each box the same way.
 Box A accelerates at 4.5 m/s2.
 Box B accelerates at 3.1 m/s2.
 Box C accelerates at 6.2 m/s2.
Arrange the boxes in order from the highest to the lowest mass.
4. Arrange the same boxes in question 3 from highest to lowest inertia.
5. Come up with a scientific description/definition of “mass” using the following terms: force,
acceleration, and inertia. Give it your best shot!
6. Which of the boxes from question 3, has the greatest weight?
7. Consider a box with a mass of 25 kg. On earth, where the acceleration of gravity is 9.8 m/s2
the box weighs 245 N. On the moon, where the acceleration due to gravity is 1.6 m/s2 the
box weights 40 N. Which equation can be used to calculate weight? (Note: “g” is a symbol
for the acceleration due to gravity and “W” is the wieght.)
A) W = m g
B)W = m + g
C) W = m g
D) W = m – g
8. What is the difference between an object’s mass and its weight?
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9. Consider a box that has a mass of 35 kg.
a) Calculate the weight of the box on Earth. (Use information from question 7)
b) Calculate the weight of the box on the moon. (Use information from question 7)
10. Again, consider the box from question 9. Let’s say you saw the box in the street as you were
walking by one day. You decide to kick the box to move it off the street. If you kicked the
box with a force of 70 N, how fast would the box accelerate?
11. What if the box were on the moon? Would your answer to question 10 change? (Do the
calculation and then explain.)
12. True or False:
_____ a) An object will have the same mass on the moon as it does on Earth.
_____ b) An object will weigh more on the moon than on Earth.
_____ c) If you tried to kick a bowling ball across the surface of the moon, it would be just as
hard to accelerate it on the moon as it would on Earth.
_____ d) A bowling ball would fall faster on Earth than on the moon.
Information: Friction
Friction is what we call the force that acts between two objects touching as they move past each
other. It opposes the motion of two objects that are in contact with each other.
There is a low amount of friction between a hockey puck and the ice as the puck slips across the
surface of the ice.
There is a large amount of friction between brake pad and the wheel rim when a rider is applying
the brakes to his bicycle.
Critical Thinking Questions
13. Recall that Newton’s first law of motion stated that an object in motion will stay in motion
until an outside force acts on the object. However, we normally don’t see any objects staying
in motion. What we witness is that an object will gradually slow down. For example, if the
driver of a car takes his foot of the gas, the car gradually slows down. Roll a ball across the
floor and it will soon stop. Newton’s law is not wrong, so there must be another force acting
on these objects. What force is it?
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14. Imagine that you are about to attempt to slide a very heavy box full of books across the floor.
You push against the box and finally it starts to move and you slide it across the floor. There
are two different kinds of friction forces that you would feel:
 Static friction: the force that opposes the start of motion. This is the force you must
overcome to get the box to begin moving.
 Sliding friction: the force that opposes the motion once the box is already moving.
This is the force you must overcome to keep the box moving.
In your experiences, you have probably had to push a heavy object. Which frictional force is
stronger: the static or the sliding friction?
15. The driver of a car is pressing the accelerator pedal causing a constant force of 390 N to be
acting on the car. The car, however, is not accelerating. What must be the magnitude of the
frictional force?
16. There is a 0.5 kg hockey puck hit with a force of 16.4 N. The acceleration is 27.8 m/s2. What
is the frictional force (Ff) between the puck and the ice? Use the following steps…
a) First, find the total force using Newton’s second law, F=ma. Multiply the given mass
times the given acceleration. (Ignore the number 16.4 N for now.)
b) Now, realize that your answer to part a is the total force on the puck. 16.4 N of the force
is from the hockey stick. Now you can find the frictional force (Ff).
Solve for Ff: 16.4 N + Ff = __________
answer to part a
c) Your answer to part b should be a negative number. The negative sign indicates the
direction of the force. What can you conclude about the direction of the friction force
and the direction of the force exerted by the hockey stick?
17. A 1.8 kg textbook is slid across a desk with a force of 3.1 N. The initial acceleration of the
book was 0.67 m/s2. What is the force of friction between the book and the desk? (Hint: this
is just like the previous question.)
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Physics Fix 13
Name: ______________________________
Date: _____________
Hour: _____
Information: The Normal Force
Recall that each force has an equal and opposite force. If you use your hand to push on a wall,
the wall pushes on you with exactly the same force—thus, neither you nor the wall will
accelerate.
There is a force that is exactly the opposite of weight. It is called the “normal force”. Consider a
5 kg book at rest on a table. You can find its weight as follows:
W = m  g = 5 kg  9.8 m/s2 = 49 N
The normal force is the same magnitude as the weight: 49 N. It’s direction, however, is not
downward. Its direction is perpendicular to the surface. Since the surface is flat (horizontal), the
normal force is upward. Observe the diagram below of a book resting on the table:
The normal force points upwards and
is 49 N.
5 kg book
The weight force
points downwards
and is 49 N.
Critical Thinking Questions
1. Calculate the normal force of a 1200 kg boulder resting on the ground.
2. Calculate the normal force of a 3 kg bowling ball setting on the ground at the bowling alley.
Information: The Normal Force on Slanted Surfaces
So far, we have only calculated the normal force on a flat surface. Now we are going to look at
slanted surfaces. For a flat surface, the weight and the normal forces were opposite each other.
But with a slanted surface, this is not the case because the normal force always is perpendicular
to the surface!
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In the diagram below, we have our same 5 kg book, but this time it is on a slanted surface with a
30o incline:
The normal force is not exactly opposite the
weight so it is NOT 49 N.
30o
Weight is 49 N
For the 5 kg book, the weight force is 49 N (as calculated earlier). This force points directly
downward because it is due to gravity (which always points downward).
To find the normal force, we are going to change the diagram and do a little triangle
trigonometry.  Notice in the diagram below, the Weight arrow is flipped upside down:
90o
#1: Flip the
Weight arrow
upside down
#2: Erase
everything except
the arrows
#3: Use the
arrows to make a
new triangle
30o
Now, we have this (enlarged) right triangle and we want to solve for the normal, which is the
white arrow:
90o
49 N
30o
Critical Thinking Questions
3. In the above enlarged triangle, which is the normal force?
A) the white arrow
B) the gray arrow
C) the line
4. In the above enlarged triangle, which is the hypotenuse?
A) the white arrow
B) the gray arrow
C) the line
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30o given
by the
original
incline
angle.
43
5. Why is the gray arrow equal to 49N?
6. The normal force (equal to the length of the white arrow) can be found by using which of the
following formulas? (Remember your triangle trigonometry!)
A) 49  sin 30o
B) 49  cos 30o
C) 49  tan 30o
7. Using your answer to question 6, calculate the normal force.
8. OK, now you are ready to do the whole process yourself, including flipping the weight arrow
and drawing some pictures. Draw the pictures; they help. I’ve drawn the first one for you. 
Question: Calculate the normal force of a 53 kg rock resting on a 20o incline.
20o
9. There is a 75 kg rock resting on a 28o incline. Calculate the normal force.
Information: The Coefficient of Friction
Every substance has a different “coefficient of friction.” The coefficient of friction is a constant
that depends on the surface properties of the substance. Because of its rough surface sand paper
has a much larger coefficient of friction than ice—the frictional force is stronger when something
slides on sand paper than on ice.
The following equation relates the force friction (Ff), the normal force (FN), and the coefficient of
friction ():
Ff = FN
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Critical Thinking Questions
10. A 2.3 kg book is setting on a flat table. Calculate the frictional force between the book and
the table if the coefficient of friction is 0.38. (Hint: first calculate the normal force, then use
the equation above.)
11. A 7.5 kg cardboard box is setting on the ramp of a moving truck. The ramp makes an angle
of 15o with the ground. The coefficient of friction between the ramp and the box is 0.49.
Calculate the frictional force between the box and the ramp.
12. A 64.8 kg rock rests on a 38o incline. If the coefficient of friction is 0.44, what is the
frictional force?
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Physics Fix 14
Name: ______________________________
Date: _____________
Hour: _____
Information: Components of Motion
Here’s an important rule: the horizontal and vertical components of motion are completely
independent of each other. What this means is that we can consider the horizontal motion and
vertical motion separately.
Critical Thinking Questions
1. Answer true or false to the following:
a) A ball rolling on a flat table has a horizontal but no vertical component of motion.
b) A rock falling straight downward with no wind blowing has no horizontal component
of motion.
c) A baseball hit into the air toward right field has vertical but no horizontal component
of motion.
d) A basketball bounced straight up and down has vertical but no horizontal component
of motion.
2. If there was no friction, a ball rolling on a perfectly horizontal floor would never stop
unless it struck something. It would keep on going and going and going even though
gravity is still acting on it. Why won’t gravity stop the rolling ball? [Hint: consider the
direction of the ball and the direction of gravity’s action.]
3. A cannonball is shot horizontally at the exact same time that a bowling ball is dropped.
The bowling ball is dropped from the same height as the cannonball. Consider the
horizontal and vertical parts of the motion separately to answer the following questions.
a) Why doesn’t the bowling ball move at all horizontally?
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b) Both balls move vertically. The cannonball and the bowling ball both will hit the
ground sometime. What influences the vertical motion of each ball?
Bowling ball:
Cannonball:
c) The horizontal distance is not the same for each ball, but is the vertical distance?
Explain.
d) Both the cannonball and the bowling ball will hit the ground at the same time!
Explain why this is so, using your answers to parts b and c.
Information: Calculations Involving the Components of Motion
When a cannonball is shot it travels both horizontally and vertically. Horizontal motion is along
the x axis and vertical motion is along the y axis. We will use x and y labels to distinguish
between horizontal and vertical motion. To describe the distance an object travels horizontally
(x) and the distance an object travels vertically (y) we can use the following two equations.
Horizontal Distance
Vertical Distance
x = vx t
y = vyt + ½ g t2
Critical Thinking Questions
4. A cannonball is shot horizontally at a speed of 25 m/s, as shown by the following
diagram:
1.2 m
a) The initial velocity in the y direction (vy) is equal to zero. Why?
b) Recalling the g equals 9.8 m/s2, find the time (t) that it takes for the cannonball to hit
the ground.
c) Using your answer to part b, calculate the distance that the ball travels in the x
direction.
5. A bowling ball is dropped from a height of 1.2m off the ground. How long will it take
for the ball to hit the ground? (Note: the initial velocity in the y direction (vy) is equal to
zero because it was at rest just before it was dropped.)
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NOTICE: Your answers to 4c and 5 should be the same and that’s a proof of question 3d.
6. A rock is thrown horizontally at a speed of 4.2 m/s from the top of a cliff 65 m high.
a) How long does it take the stone to reach the bottom of the cliff?
b) The stone strikes the ground how far from the base of the cliff?
c) Use x = vxt to calculate the horizontal component of the velocity (vx) when it hits the
ground. (Hint: t = your answer to part a; x = your answer to part b.)
7. Consider the previous question again. Instead of throwing the stone at a speed of 4.2 m/s,
let’s assume that the stone was thrown at twice that speed (still horizontally).
a) How long does it take the stone to reach the bottom of the cliff?
b) The stone strikes the ground how far from the base of the cliff?
c) Use x = vxt to calculate the horizontal component of the velocity (vx) when it hits the
ground. (Hint: t = your answer to part a; x = your answer to part b.)
d) Calculate the vertical component of the velocity upon impact. (Recall the equation
vf = vi + at. Again, vi was zero. Part a gives you t and a is equal to 9.8 m/s2.)
NOTICE: For 6c and 7c you should have got the same value as the initial velocity given in
the problem. This shouldn’t be surprising since the velocity is constant in the x direction and
there is no force acting in that direction to either slow or speed up that component.
8. A ball rolls with constant velocity off of a tabletop 0.92 m high. It hits the ground 0.51 m
from the edge of the table. How fast was the ball initially rolling?
0.92 m
0.51 m
9. A ball rolls with constant speed of 1.5 m/s off a ledge. It hits the ground 2.25 m from the
base of the ledge. How high is the ledge?
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Physics Fix 15
Name: ______________________________
Date: _____________
Hour: _____
Information: Projectiles
A projectile is a word that we will use to describe an object that is in motion. A baseball thrown
into the air, a bowling ball rolling, and a bullet fired from a gun—all of these are projectiles.
Many projectiles, such as the baseball, move in an arc-like shape and therefore there is both a
horizontal and vertical part, or component, to their motion.
So far we have considered projectiles that are initially rolling horizontally. Now we will
consider those that are launched at an angle. We will continue to use the two basic equations
from the previous Physics Fix:
Horizontal Distance
Vertical Distance
x = vx t
y = vyt + ½ g t2
Consider the following diagram:
C
Figure 1: A cannonball is
launched at an angle.
B
A
D
E
F
40o
G
This dashed line
represents a height
of y = 0
Critical Thinking Questions
1. At which position on the above figure is the vertical (y) component of velocity equal to zero?
2. The cannonball in Figure 1 is fired at an initial velocity of 8.2 m/s at an angle of 40o above
the horizontal.
a) Calculate the initial vertical (vy) and horizontal (vx) components of the velocity. Use the
following picture to help. It’s like solving the sides of a triangle using trigonometry!
8.2 m/s
vy
40o
vx
b) How long did it take the ball to land? (Hint: when it lands, y = 0. You can use the vertical
distance equation above along with vy from part a to solve for t.)
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c) Calculate the maximum height the ball reached.
i. The ball reached maximum height at half the flight time, which is half of your
answer to part b. Calculate this.
ii. Use the value from part (i) as t. Use vy from part a. Then use the vertical distance
equation given in the information section to find y. The value for y = the maximum
height.
d) How far did the ball go? (Hint: use the horizontal distance equation. You know vx from
part a and t from part b.)
3. This question is just like the previous one, except without all the hints. A cannonball was
fired with a velocity of 12.4 m/s at an angle of 60o above the horizontal.
a) Calculate the initial vertical (vy) and horizontal (vx) components of the velocity.
b) How long did it take the ball to land?
c) Calculate the maximum height the ball reached.
d) How far did the ball go?
4. A football was kicked at 22.5 m/s at an angle of 35o above the horizontal.
a) What was the ball’s hangtime? (This is the total time in the air.)
b) How far was the ball kicked?
5. The same kicker kicked the football again at a speed of 22.5 m/s. This time the angle was
45o above the horizontal. How far did the ball go?
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6. Again, the kicker kicked the football at the same speed, but this time the angle was 55o. Find
the distance the ball traveled.
7. Given your answers to questions 4-6, if a football kicker wants to kick the ball as far as
possible, what advice could you give him?
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Physics Fix 16
Name: ______________________________
Date: _____________
Hour: _____
Critical Thinking Questions
1. We have previously learned about inertia. Give a definition for inertia.
2. Obviously, a boulder is more difficult to move than a bowling ball. Which substance has a
greater rest inertia?
3. A semi truck will be more difficult to stop than a motor cycle if they are both going at the
same speed. Which vehicle has the greater motion inertia?
4. Now consider two very similar semi trucks. One travels at 40 km/hr and another travels at 75
km/hr. Which truck will have the greater motion inertia?
5. Which two of the following characteristics affect the “motion inertia”?
A) Direction
B) Velocity
C) Acceleration
D) Mass
Information: Momentum
“Motion inertia” is the tendency of an object to continue in motion. Momentum is the word most
often used when speaking of an object continuing in motion. There is a mathematical equation
that describes momentum which is based on your answer to question 5. The equation is:
momentum = mass x velocity OR
momentum = mv
The units for momentum are simply the mass units times the velocity units. Kg m/s and g km/hr
are examples of momentum units.
Critical Thinking Questions
6. Calculate the momentum of a 25,000 kg truck traveling at a speed of 20 m/s. (Include units.)
7. Is it possible for a truck and a motorcycle to have the same momentum? Explain.
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8. What is the momentum of a 1900 kg car that is sitting in the driveway?
Information: Changing Momentum
As Newton’s 1st Law states, an object’s velocity will not change unless a force acts on the object.
Since momentum involves velocity, a force will change an object’s momentum. The force that
causes a change in momentum is called an impulse.
An impulse may be a very quick push or a push that lasts for a long time. To calculate how
much the momentum changes you need to know how long the force lasts.
“” means “change in”
Ft = m(v)
Impulse Force
Change in momentum
F = force of impact in Newtons
m = mass of the object in kg
t = the time of impact, how long the impact force acts on the object
v = change in velocity of the object
Before proceeding to the questions, please notice the difference between “force of impact” and
“impulse force”. The impulse force is actually the force of impact multiplied by the time of
impact.
Critical Thinking Questions
9. Some men were trying to push a car that had run out of gas. They applied a total force of 400
N for 220 seconds.
a) Calculate the impulse force. (The units should be N-s.)
b) If the car’s velocity changed from 0 m/s to 1.75 m/s, calculate the mass of the car.
10. A plate with a mass of 0.375 kg is dropped and has a speed of 3 m/s when it suddenly hits the
hard kitchen floor. Calculate the change in momentum. (Note: the final speed of the plate is,
of course, zero when it hits the floor.)
11. Consider the plate from the previous question. The floor provided an impact force that acted
on the plate. It acted on the plate very suddenly—it was a mere fraction of a second. If the
force acted on the plate for 0.00024 s, calculate the force of impact.
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12. The change in momentum for the plate in this situation is fixed—1.125 kg m/s (your answer
to question 10). The force of impact is very large, thereby breaking the plate. If the time
were larger than 0.00024 s, would the force of impact be larger or smaller than your answer
to question 11.
13. Increasing the time of impact will _________________ the force of impact.
increase of decrease?
14. Consider again the plate in questions 10 and 11. If the plate hits a pillow instead of the floor
it might not break. This question will examine the physics that explains why the plate may
not break.
a) If the plate falls onto a pillow instead of the floor will the time of impact be greater or
smaller? Explain.
b) Hopefully for part a, you answered that the time would be greater. It will be greater
because the pillow causes a gradual slowing of the plate instead of a sudden slowing as it
hits the floor. Go on to part c.
c) The time of impact when the plate hits the pillow is 0.0085 s. Now calculate the force of
impact. (The change in momentum is the same as it was in question 10. Only the time
has changed; the time is no longer 0.00024 s as it was in question 11.)
15. Calculate the impulse force with the pillow and then without the pillow for the plate in
questions 10-14.
16. Explain the physics of why an air bag works. Your explanation should include the terms
“force of impact”, “time of impact”, and “change in momentum”.
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Physics Fix 17
Name: ______________________________
Date: _____________
Hour: _____
Information: Newton’s Second Law and External Forces
We usually talk about an object, but now we are going to use the word “system”. A system is
sometimes one object and sometimes a group of objects. For example, a car is a group of several
objects including wheels, an engine, and passengers.
Remember that Newton’s Second Law says that to change the motion of a system (including
momentum), a force must act on the system. This force must be external and not internal. For
example, a passenger of a car pushing really hard on the dashboard will NOT cause a change in
the car’s motion because the force is internal. A truck striking the car will cause a change in the
car’s motion because the force is external.
Critical Thinking Questions
1. A certain man was having a hard time sailing on a day
with very little wind. He suddenly thought of bringing out
his fan and setting it up on the boat. Using what you
know about internal and external forces, is this a good
way to propel a sailboat? Explain.
Information: Conservation of Momentum
If no external force acts on a system, then the system’s motion cannot change. Its momentum
cannot change. We say that the momentum of the system is conserved because the momentum
remains the same unless an external force acts on it.
Critical Thinking Questions
2. A cannon (with a cannonball inside) is ready to be fired. The mass of the cannon is 300 kg
and the mass of the cannonball is 3 kg. What is the momentum of the system? (This should
be easy since the system is at rest.)
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3. Once the cannon fires, the ball is shot out at a speed of 120 m/s. The cannon moves too, but
in the opposite direction. The speed of the cannon is 1.2 m/s. Using the masses given in the
previous question, calculate the momentum of both the cannonball and the cannon.
4. Is the force that moves the cannonball external or internal to the system?
5. a) Using the concept of internal and external forces, explain why the total momentum of the
system equals zero in question 3.
b) Using the concept of the direction of momentum, explain why the total momentum of the
system equals zero in question 3.
6. Our friend is having a hard time getting started on a skateboard. If he
throws a ball while he is standing on the skateboard, he will move in the
opposite direction of the ball. Keep this in mind: Just like with the cannon
in the previous questions, the man and the cannonball will have the same
momentum, except in opposite directions.
a) The ball has a mass of 7.5 kg and the man throws it at a speed of
5.2 m/s. What is the momentum of the ball?
b) Using your answer to part a, calculate the speed of the man if he has a mass of 100
kg.
c) Would a heavier ball cause the man to go faster or slower, assuming the ball was
thrown at the same speed?
7. The same man from question 6 decides to use a 9 kg ball and does his best to heave it at a
speed of 12 m/s. Calculate his speed. (His mass is still 100 kg.)
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Physics Fix 18
Name: ______________________________
Date: _____________
Hour: _____
Information: Elastic Collisions
When two objects collide in the absence of any external forces, then the total momentum after
the collision must equal the total momentum before the collision. An example of an elastic
collision is two rubber balls bouncing off each other:
Remember that opposite directions of velocity get opposite signs. An object traveling to the
right will have a positive velocity and an object traveling to the left will be negative.
Critical Thinking Questions
1. Consider the two balls above. The white ball is travelling at 4 m/s and the black ball is
traveling at 3 m/s. The white ball has a mass of 6 kg and the black ball has a mass of 5 kg.
a) One of the balls has a “negative” velocity. Which one and why is it negative?
b) What is the momentum of the white ball?
c) What is the momentum of the black ball? (Because of the negative velocity of the black
ball, your answer should be negative.)
d) What is the total momentum of the balls? (Add parts b and c.)
e) After the balls collide, what will be the total momentum? (Same as d!)
f) After the balls collide, the velocity of the black ball will be positive. Why?
g) Using your answer to part e, calculate the velocity of the black ball after the collision.
The velocity of the black ball after the collision is 3.5 m/s. (Use the masses of each ball
given in the question.)
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2. Consider two balls colliding again. This time both balls are going in the same direction. A
white ball (mass = 4 kg) with a speed of 7.5 m/s is approaching a black ball (mass = 3.5 kg)
that has a speed of 4.5 m/s.
a) Calculate the total momentum of the balls before and after collision.
b) After collision the white ball is moving at a speed of 3.2 m/s. Calculate the speed of the
black ball.
3. A red ball that has a mass of 12 kg and a blue ball with a mass of 20 kg collide in an elastic
collision. The red ball is initially moving to the left with a velocity of 14 m/s. The blue ball
is moving to the right with a velocity of 18 m/s. If the final velocity of the blue ball is 12.8
m/s, what is the final velocity of the red ball?
4. A 10 kg red ball travels with a velocity of 8 m/s toward a 6 kg blue ball that is at rest. What
is the velocity of the blue ball after collision if the velocity of the red ball after collision is 3
m/s?
Information: Inelastic Collisions
Not all collisions are elastic. Some of them are “inelastic”, which means that the two objects
colliding stick together after the collision. For example, two railroad cars might stick together
after collision.
Before Collision:
After Collision:
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Critical Thinking Questions
5. Two railroad cars collide in an inelastic collision. The coal car has a mass of 12,300 kg. The
steel car has a mass of 15,000 kg. The coal car’s initial velocity is westward at 21 m/s. The
steel car is at rest.
a) Calculate the momentum of the coal car and the steel car. Then add them together to get
the total momentum of the system. (The system includes both cars.)
b) Again, the total momentum before collision equals the total momentum after collision.
After collision, the two cars stick together to become one. Find the total mass.
c) How fast are the two cars moving after collision? (Hint: Use the momentum from part a
and the mass from part b; solve for the velocity.)
6. Consider two cars that crash in an inelastic collision. The collision is so bad that the cars
stick together on impact. A brown car with a mass of 2100 kg is moving east at 45 km/hr. A
white car with a mass of 2300 kg is moving west at 65 km/hr. Calculate the speed and
direction of the combined cars just after impact. We’ll break it into a few steps:
a) Find the momentum of the brown car and the momentum of the white car. Then add them
together to get the total momentum. (The sign needs to indicate direction. If east is
positive and west is negative, then your total momentum will be a negative number.)
b) Find the total mass of the cars after they stick together.
c) Divide the momentum (part a) by the mass (part b). The negative sign gives you the
direction.
7. Once again, two cars collide in an inelastic collision. A red car (mass = 2800 kg) traveling
north at 50 km/hr strikes a blue car (mass = 1900 kg) traveling south at 70 km/hr. Find the
speed and direction of the cars as they stick together just after impact.
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Physics Fix 19
Name: ______________________________
Date: _____________
Hour: _____
Information: What is Work?
To change momentum, we learned that we need an “impulse force”, which is a force acting on an
object for a certain amount of time. For example, if a car ran out of gas and you had to push it
for 5 minutes you are changing the momentum. What if instead of time, we used “distance”?
Instead of talking about pushing the car for 5 minutes, we could talk about pushing the car for
200 meters.
Work is defined as a force applied over a distance and the equation is: W = F x d
The units for work (W) is the Joule (J). The unit for force (F) is, of course, the Newton (N). The
unit for distance is the meter. If you lift an apple over your head you are doing about one Joule
worth of work. Of course, work causes a change in motion and momentum.
Critical Thinking Questions
1. A man exerted a force of 200 N to push a car a distance of 10 m. How much work did he do?
2. A woman lifted a 5 kg box two meters of the ground. How much work did she do? (Hint:
first find weight of the box by multiplying by 9.8 m/s2—the acceleration due to gravity. This
weight is equal to the force that the woman applies.)
3. A boy pulls a sled with a 21 N force for 30 m. How much work did he do?
Information: Work and Direction of Force
In question 3, a boy was pulling a sled. Rarely does someone pull a sled straight, there is usually
an angle in the rope. Consider the diagram of a man pulling a sled. Notice that he is pulling the
sled at an angle. This angle changes the actual force that does work.
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The man is pulling at an
angle of . (The symbol,
, is like using x for an
unknown angle.)
The man pulls on the rope
with a force F.
F
But not all of the force F
causes the work because
of the angle.
This dotted arrow is the force
that does the work because it is
in the direction of motion.

To calculate the force you
multiply F times cos.
Critical Thinking Questions
4. The man in the diagram is pulling the sled with a force of 90 N at an angle of 55o for a
distance of 40 m.
a) Calculate the force that actually contributes to the work being done.
b) Use the force obtained in part a to calculate the work done. (You should get an answer of
about 2065 J.)
5. A child pulls a wagon with a force of 20 N. The handle of the wagon is at an angle of about
27o relative to the ground. If the child pulls the wagon 15 m, how much work did she do?
Information: Power
Power is a measure of the speed at which work is done. A high-power engine does work
quickly. The unit for power is the watt (W). One watt is on Joule per second, so work must be
measured in Joules and time in seconds, The equation for power is:
Power 
work done
time interval
OR
P
W
t
Critical Thinking Questions
6. A woman performed 278 J of work in 40 seconds. Calculate her power.
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7. A pulley is used to lift a 620 N box of construction equipment 24 m straight up into the air.
The pulley system accomplishes this in 18 seconds. Calculate the power of the pulley system.
(Hint: first calculate the work.)
8. Consider a box that is slid 12 m across the room. Two people apply a force of 19 N each. It
takes them a total of 11 seconds to accomplish the feat. What is the power of the people?
9. A certain generator performs 4506.3 kJ of work in 2.3 hours. How much power does the
generator have? (Pay close attention to units!)
10. A man pulled a sled at an angle of 32o. The force he exerted was 106 N until he had moved
the sled 95 m. It took him 312 s to accomplish this feat. Calculate his power.
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Physics Fix 20
Name: ______________________________
Date: _____________
Hour: _____
Information: Potential Energy
What is energy? In a loose sense, energy is the ability to do work. There are many types of
energy. For now, we will look at mechanical energy, of which there are two types. The two
types of mechanical energy are potential and kinetic.
Potential energy is a kind of energy that is stored or held ready. A common example of potential
energy is gravitational potential energy. For example, on the ground, a rock has no real potential
to do anything. But if the rock is lifted a meter off the ground it has the potential to fall and do
some damage to someone’s toe. If the rock is lifted 30 meters off the ground, it will have even
more potential energy and could potentially hurt someone if it fell.
Gravitational potential energy, then, depends on the height of an object off the ground. The
equation is:
PE = mgh
PE is potential energy, “m” stands for the mass of the object in kg, g is the constant 9.8 m/s2, and
h is the height in meters. Please note that m times g equals the weight of the object in Newtons
(N) so that the equation is sometimes PE = Wh, where W is weight.
Critical Thinking Questions
1. A 24 kg rock is resting on the floor. How much potential energy does it have? Explain.
2. Calculate the potential energy of a 1200 kg boulder on a cliff 45 m about the ground.
Information: Kinetic Energy
Kinetic energy is the energy of motion. For an object to have kinetic energy it must be moving.
An object that is moving has the potential to cause work to be done. The equation for kinetic
energy is:
KE = ½ mv2
KE stands for kinetic energy and is measured in Joules, v is velocity in m/s and m is mass in kg.
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Critical Thinking Questions
3. A young man heaves a 6.5 kg rock at a velocity of 6.9 m/s. What is the kinetic energy of the
rock?
4. An object was thrown with a velocity of 4.3 m/s. If the kinetic energy of the object was 225
J, what was the mass of the object?
For questions 5-9, consider the following scenario. A 145-g ball was thrown into the air at an
initial velocity of 7.2 m/s. (Assume the ball started at ground level.) The ball reached a
maximum height of 13 m.
5. What was the kinetic energy immediately after it was thrown?
6. What was the kinetic energy when the ball reached the maximum height (before it started
traveling downward)?
7. What was the potential energy when the ball reached the maximum height?
8. What was the kinetic energy of the ball just before it hit the ground (on its return)?
9. What was the potential energy when the ball landed on the ground?
10. The total energy of a substance is the sum of its potential and kinetic energy. The sum of
your answers to questions 6 and 7 will give you the total energy of the ball when it was at its
peak. Find this sum.
11. Just as question 10 gave you the total energy at the ball’s peak, so the sums of questions 8
and 9 will give you the energy of the ball at the end of its journey. Find the sum of questions
8 and 9.
12. Compare your answers to questions 10 and 11.
13. Hopefully in question 12 you noted that questions 10 and 11 were the same. Which of the
following statements are true. (There may be more than one.)
a) An object’s kinetic energy remains the same.
b) An object’s potential energy remains the same.
c) An object’s total energy remains the same.
d) An object’s potential energy is sometimes transformed into kinetic energy.
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Information: Conservation of Energy
The law of conservation of energy states that within a closed, isolated system the total amount of
energy is constant. In the last few questions you saw that the total amount of potential and
kinetic energy remained the same. We can summarize our results with an equation:
KEi + PEi = KEf +PEf
Critical Thinking Questions
13. Consider a 4.0 kg piece of ice that falls from a roof 4 m above the ground.
a) Calculate the initial kinetic energy, KEi, just before the ice fell. (Use KE = ½ mv2 and ask
yourself, “what is the velocity right now?”)
b) Calculate the initial potential energy, PEi, just before the ice fell. (Use the equation PE =
mgh)
14. We are now going to find the speed of the ice at the very moment it reaches the ground.
Because the total kinetic and potential energy remains the same, we can use the following
equation:
_________________ = KEf + PEf
add answers from 13a and 13b
a) Why does PEf equal zero? (Hint: use PE = mgh)
b) Calculate KEf. using the equation given in question 14.
c) Finally, find the speed of the ice as it hits the ground using the equation KEf = ½ mv2.
15. A 3.5 kg ball is rolling toward a hill at a speed of 12 m/s. The ball reaches the hill and rolls
up the hill to a certain height. How high up the hill will the ball go? (Use the approach from
questions 13 and 14.)
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Physics Fix 21
Name: ______________________________
Date: _____________
Hour: _____
Information: Internal Energy
Thermodynamics involves the study of the energy and disorder of a system. Every system has
“internal energy”. Internal energy is the total amount of all the potential and kinetic energy that
a system has. For an example of a “system” let’s take a car. A car has kinetic energy (the
energy of motion) if it is moving and it has potential energy (chemical energy of the gasoline) if
it has gas in the tank. A car always has a certain amount of energy associated with it. A car has
more total energy (chemical potential energy) with a full tank of gas than with a half full tank.
Therefore, after driving a car for a while the total amount of energy (called the internal energy)
that the car has decreases.
Critical Thinking Questions
1. If we use KE to symbolize kinetic energy and PE to symbolize potential energy, and U to
symbolize internal energy, then write an equation for internal energy.
2. Consider a car as described in the table below. Fill in the blanks in the table with the
hypothetical values for kinetic energy, potential energy, and internal energy. (Assume that
the overall mass of the car stays the same even though the amount of gasoline in the tank
decreases.)
A car is setting in
the driveway
before a long road
trip. The gas tank
is full.
Kinetic
Energy
Potential
Energy
Internal
Energy
The car has set out on
the trip and has been
driving for a while.
Cruise control is set
for a constant speed.
20
100
The car is still
driving at the
same speed.
The car ran out
of gas and is
parked along
the highway.
30
90
3. The Law of the Conservation of Energy states that energy isn’t created or destroyed. The car
in question 2, lost energy. If the energy was not destroyed, hypothesize what happened to it.
4. What would be the internal energy of the car in question 2 if someone brought enough gas to
fill the tank back up completely while the car was stranded at the side of the highway?
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Information: First Law of Thermodynamics
As you saw in question 2 above, the internal energy of a system can change. What happens to
the energy? The energy merely changes form. In the car example, the internal energy was
changed into heat energy as the gasoline burned. Also, some of the internal energy was used to
do work by moving the car. The First Law of Thermodynamics states that the change in internal
energy of a system equals the sum of the heat and the work. Internal energy of a system can
increase or decrease. If a system is heated, it gains internal energy, but if the system loses heat
then it decreases in internal energy. If a system does work it loses internal energy, but if work is
done on the system then it gains internal energy.
Critical Thinking Questions
5. For each of the following, state what the “system” is and also state whether the internal
energy of the system would increase or decrease in each situation.
a) Lifting a ball from the ground and holding it six feet off the ground.
b) Heating up a piece of pizza in the microwave.
c) The logs in the fireplace are burning.
d) An ice cube is melting while it sets on the kitchen counter.
e) Two molecules bond together and heat energy is released (exothermic).
Information: Spontaneity
It is often desirable to know if a process will occur all by itself or if you need to supply energy
for a process to occur. If a process occurs naturally, all by itself without outside help, it is said to
be spontaneous. Examples of spontaneous processes include iron rusting and a ball rolling down
a hill.
Critical Thinking Questions
6. Which of the following processes are spontaneous?
a) a rock rolling uphill
b) a leaf falling
c) water boiling at 100oC
Information: Entropy
It is important to consider the amount of disorder in a system when determining whether a
reaction will occur spontaneously. The change in the amount disorder or randomness is given a
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special name, “change in entropy”. Entropy is a measure of the amount of disorder in a system.
The Second Law of Thermodynamics states that for a process to be natural or spontaneous the
entropy of the universe must increase. Disorder is always on the increase.
Critical Thinking Questions
7. Indicate whether for each of the following processes will have a positive or negative change
in entropy. Explain each answer. (Hint: think in terms of the disorder or randomness of
molecules and molecular motion.)
a) an ice cube melting
b) water vaporizing
c) cleaning your room
d) folding paper into a paper airplane
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Physics Fix 22
Name: ______________________________
Date: _____________
Hour: _____
Information: Heat and Temperature
When a substance absorbs heat energy, the temperature of the substance increases. There are a
number of factors (such as mass of the substance) that affect how much the temperature of a
substance changes.
Critical Thinking Questions
1. Consider two pots of water. Each pot has the same diameter, but pot A is deeper than pot B
and so there is more water in pot A. If both of the pots are exposed to exactly the same
amount of heat for five minutes on a stove, which pot will contain the hottest water after
heating?
2. Considering question 1, propose an explanation for the fact that even though both pots were
exposed to the same amount of heat, one got hotter.
3. Fill in the blank: The greater the mass of a substance (like water in questions 1 and 2), the
____________________ the temperature change when heat is applied.
greater or lower
4. Consider the metal hood of a car on a warm sunny day. Next to the car is a large puddle of
water. The puddle of water is so large that it has the same mass as the hood of the car.
Assume that the hood of the car and the puddle are exposed to the same amount of sunlight.
Which will be hotter after two hours—the hood of the car or the puddle?
5. Propose an explanation for the fact that even though both the hood and the puddle were
exposed to the same amount of heat energy and their masses were the same, one still got
much warmer than the other.
6. In general is it harder to change the temperature of metal (like on a car hood) or of water? In
other words, would it require more heat energy to change the temperature of metal or of
water?
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7. In one of the following blanks you will need to write “400” and in the other blank you will
need to write “200”.
If we wanted to change the temperature of water by 4 oC, then _______ Joules of heat energy
are required, but to change the temperature of metal by 4oC, then ________ Joules of heat
energy are required.(Note: a Joule is the standard unit of energy.)
Information: Specific Heat
In questions 1 and 2 above you probably recognized that the temperature change of a substance
depends on the mass of the substance. You also have probably experienced the fact that different
substances heat at different rates as was discussed in questions 3 and 4 above. Each substance
has its own specific heat capacity, or just “specific heat”. The specific heat capacity is a measure
of the amount of energy needed to change the temperature of the substance. The higher the
specific heat, the more energy is required to change the temperature of the substance.
Critical Thinking Questions
8. Which substance has a higher specific heat—water or a metal like the aluminum in a car
hood?
9.
Consider 200 Joules (J) of heat energy applied to several objects and fill in the blank: The
higher the specific heat of the object, the __________________ the temperature change of
lower or higher
the object.
10. Given the following symbols and your answers to the above questions, which of the
following equations is correct. Make sure you have the correct answer before proceeding to
the next questions!
T = temperature change of a substance
Cp = specific heat capacity
m = mass of the substance
q = amount of heat energy applied to the substance
(C p )( m)
q
(q)(m)
A) T = qmCp
B) T 
C) T =
D) T =
q
(m)(C p )
Cp
HINT: Equation D is not correct because according to that equation, a large mass (m) will
lead to a large temperature change (T), but this is not consistent with question 3. Apply
this same reasoning to the other equations to see if which equation is logical.
11. If T is measured in oC, m is measured in grams (g), and q is measured in Joules (J), what
are the units for specific heat capacity?
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12. What is the temperature change of a 120 g piece of aluminum whose specific heat is 1.89
J/goC after 1800 J of heat energy is applied?
13. A beaker containing 250.0 g of water is heated with 1500.0 J of heat energy. If the
temperature of the water changed from 22.0000oC to 23.4354oC, what is the specific heat of
water?
14. Heat energy equal to 25,000 J is applied to a 1200 g brick whose specific heat is 2.45 J/goC.
a) What is the change in temperature of the brick?
b) If the brick was initially at a temperature of 25.0oC, what is the final temperature
of the brick?
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Physics Fix 23
Name: ______________________________
Date: _____________
Hour: _____
Information: Specific Heat Constants Depend on the State of Matter
Recall that specific heat is the energy necessary to raise the temperature of one gram of a
substance by one degree Celsius. The specific heat of liquid water is a constant equal to 4.18
J/(g-oC). This means that it takes 4.18 Joules (J) of heat energy to raise the temperature of each
gram of water by one degree Celsius. For ice, the specific heat is 2.06 J/goC. Steam’s specific
heat is 2.02 J/goC. You will want to remember the three different specific heat values for H2O.
Critical Thinking Questions
1. How much energy is required to heat 32.5g of water from 34oC to 75oC?
2. How many J of energy are needed to heat 45.0g of steam from 130oC to 245oC? Why don’t
you use 4.18 J/goC in this calculation?
3. Why is it impossible for you to answer the following question right now: How much energy
is required to heat 35g of H2O from 25oC to 150oC?
Information: Energy Involved in Changing State
Obviously, it takes energy to heat a substance such as water. There is also an energy change
when a substance changes state. For example, when water freezes, energy is taken away from
the water and when water boils, energy is being added to the water.
When water is heated up to 100oC, it will NOT automatically boil unless more energy is added.
Once water is at the correct temperature (100oC), it will boil IF you add energy to change it from
a liquid to a gas. The extra energy is needed to separate the molecules from one another. Note:
at the boiling point of a liquid energy is added to the liquid, but the temperature of the
liquid does NOT change. The temperature of H2O will increase above 100oC only after all of
the water has been changed to steam. After the phase change, if more energy is applied, the
temperature will go up.
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Figure 1: Graph of the temperature of H2O vs. energy added to the water.
Temperature of
H2O (oC)
0
25
50
75 100 125 150 175 200 225 250 275 300
Energy added to water in kilojoules (kJ)
Critical Thinking Questions
4. What is the significance of the horizontal portions of the graph? What is going on during
those times?
5. Label the temperature scale on the graph.
6. Does it require more energy to “vaporize” water at the boiling point or to melt water at the
melting point? Explain.
Information: Mathematics of Changes of State
Recall the equation: q = (m)(Cp)(T) where q is the heat energy, Cp is the specific heat of the
substance, m is the mass of the substance, and T is the change in the temperature. This
equation works ONLY when there is no phase change. You use it to find how much energy is
required to change the temperature of a certain substance as long as you know the specific heat
of the substance and as long as no change in state occurs.
Now for when there is a change in state: The energy required for a change of state is given a
special name called enthalpy. So the “enthalpy of vaporization” (symbolized by Hvap) of water
is the energy needed to vaporize (or boil) one gram of water when the water is already at its
boiling point. The Hvap of water is 2260 J/g. So for each gram of hot (100oC) water, 2260 J are
required to vaporize it. Similarly, the enthalpy of fusion (Hfus) of H2O is 334 J/g. So each
gram of ice at 0oC there are 334 J of energy required to melt it. (Fusion is melting.)
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Critical Thinking Questions
7. Verify that it takes 4140.7 J of energy to heat 12.7 g of water from room temperature (22oC)
to the boiling point (100oC). Recall that the specific heat (Cp) of water is 4.18 J/(g-oC).
8. Given the fact that the Hvap of water is 2260 J/g we know that 2260 J of energy is required
to vaporize 1 gram of water. To vaporize 2 grams of water it requires 4520 J. For 3 grams,
6780 J are needed. Verify that it takes 28,702 J of energy to vaporize 12.7 g of water, when
the water is already at its boiling point.
9. Verify that it takes 1513.6 J of energy to heat 12.7 g of steam from 100oC to 159oC. Note:
the specific heat of steam (Cp) is 2.02 J/(g-oC).
10. Using only your answers to questions 7-9, calculate how many Joules of energy it takes to
change 12.7 g of water at 22oC to steam at 159oC.
11. Calculate how many Joules of energy would be required to change 32.9 g of water at 35oC to
steam at 120oC. You will need to break this problem into four steps.
a) Find the Joules needed to heat the water to the boiling point.
b) Find the Joules needed to vaporize the water.
c) Find the Joules needed to heat the vapor (steam) from the boiling point to 120oC.
d) Add your answers to steps a, b, and c.
12. How much heat energy would be required to change the temperature of 125g of ice from
-32.9oC to liquid water at 75oC?
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Physics Fix 24
Name: ______________________________
Date: _____________
Hour: _____
Introductory Questions
1. Use what you have learned about gases to consider the following question: As the
temperature of a gas decreases, what happens to its volume?
2. Which of the following graphs correctly depicts the relationship between a gas’s volume and
the temperature?
Graph A
Graph B
Volume
mL
Volume
mL
Temperature
o
C
Temperature
o
C
Information: Extrapolating Data
30
Volume
mL
Figure 1: The graph of the
volume of several gases as
the temperature is lowered.
Gas A
25
Gas B
20
Gas C
15
10
Gas D
5
0
-280
-270
-260
-250
-240
-230
Temperature oC
-220
-210
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Notice in Figure 1 that none of the gases has a volume depicted on the graph below a
temperature of around –257 oC. The reason is because it is very hard to cool substances to
extremely cold temperatures. It can be done, but it takes a lot of technology.
For a graph such as Figure 1 you could extrapolate to graphically depict what would happen to
the volume of the gases if you cooled them further. All you need to do it continue the graphs into
regions of colder temperature. Use a ruler or another straight edge and continue the straight lines
to the left until they hit the x axis (the temperature axis). Go ahead and do this.
Critical Thinking Questions
3. In the information section you were asked to extrapolate the lines on the graph. Did they all
intersect at one point?
4. Hopefully you answered “yes” to question three. You should have found that they all
intersect at the x axis. At approximately what temperature do they intersect?
5. What is the volume when the gas lines intersect?
Information: Absolute Zero
What you have found by extrapolating the graph is a theoretical temperature called “Absolute
Zero”. Absolute zero occurs at –273oC (hopefully that is close to your answer for question 4). It
is the temperature at which all gases will have a volume of zero. No one has ever reached
absolute zero although they have been close.
There is a temperature scale based on absolute zero called the Kelvin scale. Zero Kelvin is the
coldest temperature believed to exist. 0 K = -273 oC
Critical Thinking Questions
6. No one has ever reached absolute zero. Why do we believe that absolute zero exists? Why do
we think there is no colder temperature? (Use reasoning from your graph extrapolation.)
7. Given the relationship between Kelvin and Celsius (0 K = -273oC), perform the following
temperature conversions:
a) 135oC = _____________ K
b) 42 K = _____________ oC
c) –50oC = _____________ K
d) 400 K = ____________ oC
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Information: Fahrenheit
Fahrenheit (F) is the temperature units used in the United States. Most of the rest of the world
uses Celsius. And, as we have seen, scientists will often use Kelvin. Because of the diversity of
units, it is necessary to know how to convert between units.
You already know how to convert between Celsius and Kelvin:
o
C + 273 = K
C = K – 273
o
OR
Here is how you convert between Celsius and Fahrenheit:
o
F = (oC x 9/5) + 32
C = (oF – 32) x 5/9
o
OR
Critical Thinking Questions
8. Water boils at 100oC. What Fahrenheit temperature is this?
9. Water freezes at 32oF. What Celsius temperature is this?
10. On the Celsius scale, there are 100 degrees between water’s freezing to its boiling because it
freezes at 0oC and boils at 100oC. How many degrees are there between water’s freezing and
boiling points on the Fahrenheit scale? (Subtract freezing point from the boiling point.)
11. Where does the 5/9 or the 9/5 come from? Question 10 gives you a big clue. Hopefully you
got 180 as your answer for question 10. Water has a 180 degree range in Fahrenheit and a
100 degree range in Celsius. For every 100 degrees Celsius, there are 180 degrees
Fahrenheit. Reduce the following fractions:
a)
100

180
b)
180

100
12. Perform the following unit conversions:
a) 75oF = _________ oC
b) 15oC = ________oF
c) 220oC = ___________ K
d) 125oF = _________ oC
b) 85oF = ________ K
c) 90oC = ___________ K
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Physics Fix 25
Name: ______________________________
Date: _____________
Hour: _____
Information: Gas Pressure
Figure 1: Two containers of gas molecules
Container 1
Container 2
Gas molecules move randomly in their containers, colliding with the walls of their containers
causing “gas pressure.” Pressure can be defined as the force pushing on an area. It can be
described with the equation:
F
2
P
A where P is pressure (in kPa), F is force (in N) and A is area (in m ).
The more molecules collide with the wall and the faster the molecules are going when they strike
the wall, the greater the force on the wall and therefore, the higher the pressure.
Critical Thinking Questions
1. Use the pressure equation to explain why it would be more likely for an ice skater to fall
through the ice on a lake than it would be for someone walking across the lake with regular
shoes on.
2. Which container in Figure 1 has the highest pressure? Explain.
3. If I heated container 1 and did not heat container 2, could I get the pressure in container 1 to
equal container 2? Explain.
4. If container 2 was made of an elastic material and if I expanded container 2, could I make the
two containers have equal gas pressures? Explain.
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Information: Gas Laws
Observe the following experimental data concerning a container of gas. The pressure, volume
and temperature of a gas are all related. The table of data was obtained by making measurements
of the pressure, volume and temperature of a sample of a gas. Several different kinds of gases
were used and all had identical results. The variable that was not changed was the amount of gas
present. The number of moles of gas always remained the same during these trials.
Table 1: Experimental Data for Gases
Trial
A
B
C
D
E
F
G
H
Pressure (P)
Units: kPa
120
135
195
150
135
100
225
262
Volume (V)
Units: L
3.2
2.5
2.3
2.0
4.2
3.0
3.2
2.8
Temperature (T)
Units: K
324.3
285.0
378.7
254.4
480.8
254.4
608.0
620.4
Critical Thinking Questions
P1 P2

5. Verify that this equation is true when the volume is unchanged:T1 T2
(Hint: You must use two sets of data where the volume does not change like in trials A and
G. Note: the subscript 1 refers to the pressure and temperature for the first trial you select and
the subscript 2 refers to the pressure and temperature for the second trial you select.)
6. Scientists often look for relationships between variables. If you wanted to see how the
volume and pressure are related you would need to compare data from different trials when
the temperature does not change. Why?
7. Find two sets of data in the table that have constant temperature. Which of the following
mathematical relationships is true (there may be more than one) when the temperature
remains unchanged? This relationship is known as “Boyle’s Law”, named after the person
who first discovered it.
a) P1 P2
b) (P1)(V1) = (P2)(V2)
c) P1 + V1 = P2 + V2
d) P1 V1


V1 V2
P2 V2
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8. At constant pressure, which of the following equations is/are true? This relationship is known
as “Charles’ Law”, named after the person who first discovered it.
a) V1 V2
b) (T1)(V1) = (T2)(V2)
c) P1 + V1 = P2 - V2

T1 T2
9. Complete the following. You may want to consider the equations from questions 5, 7 and 8.
a) At constant volume, as the temperature increases, the pressure always _______________.
b) At constant temperature, as the volume increases, the pressure always _______________.
c) At constant pressure, as the temperature increases, the volume always _______________.
10. If the volume is not constant, is the statement you completed in 9a always true? Justify your
answer by citing experimental data from the data table.
11. If the temperature or pressure is not constant are your statements in 9b and 9c correct?
Justify your answer.
12. Would the equations you discovered still be true if the temperature was measured in degrees
Celsius (oC) instead of Kelvin (K)? Recall that K = oC + 273 or oC = K – 273.
13. Which of the following quantities is a constant?
a) PV
b) PV + T
c) PT
T
V
P1 V1 P2 V2

14. Based on your answer to question 13, verify that this equation is true:
T1
T2 This
equation is called the “Combined Gas Law”. Notice that it contains all of the equations
combined into one!
15. What needs to remain constant in order for equation 14 to be true? (You may need to refer
to the information section.)
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16. Prove that when the temperature remains constant, the combined gas law becomes Boyle’s
Law.
17. Prove that when the pressure remains constant, the combined gas law becomes Charles’s
Law.
18. You have discovered several new mathematical relationships among gases. Now is your
chance to practice using these equations!
a) At constant temperature, the volume of a gas expands from 4.0 L to 8.0 L. If the initial
pressure was 120 kPa, what is the final pressure?
b) At constant pressure, a gas is heated from 250 K to 500 K. After heating, the volume of
the gas was 12.0 L. What was the initial volume of the gas? Notice: as the temperature
doubled, what happened to the volume?
c) The volume of a gas was originally 2.5 L; its pressure was 104 kPa and its temperature
was 270K. The volume of the gas expanded to 5.3 L and its pressure decreased to 95
kPa. What is the temperature of the gas?
19. At constant temperature, if you increase the volume by a factor of two (doubling the
volume), the
pressure _______________ by a factor of ______________. (Refer to 18a for a hint.)
increases or decreases
what number
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Physics Fix 26
Name: ______________________________
Date: _____________
Hour: _____
Information: Pascal’s Principle
Consider the diagram below. Please note the steps, 1-4, and go in order so that you understand
what is happening.
1. Push the
plunger
down
2. When you push the
plunger down, higher
pressure is created here
because the plunger is
squeezing the air at the
bottom of the cylinder.
4. The weight lifts
because of the pressure.
Heavy
Weight
(rubber disk that can
move up and down and
also provide an airtight
seal.)
3. The increased pressure is transferred uniformly
throughout the air that is trapped in these two cylinders.
The even transfer of pressure is called Pascal’s principle.
A contraption like the one above can be used to lift heavy objects. The plunger is called a
“piston”. Pushing a piston down a smaller cylinder will actually multiply the force so that a
heavier object can be lifted in a cylinder with a larger diameter. The following questions will
explain how it works!
Critical Thinking Questions
F
1. You have previously learned the relationship between force, pressure and area: P  . Let’s
say that someone pushes down the plunger with a force of 100 N. And the area of A
the head of the plunger is .5 m2. What is the pressure that is exerted by pushing the plunger?
2. Given your answer to question one and recalling Pascal’s principle, how much pressure
(units are kilopascals—kPa) will there be in the wider cylinder? Explain your answer.
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3. Now that you know the pressure in the wide cylinder (question 2). Find the upward force in
the wide cylinder if the disc in the cylinder has an area of .85 m2.
4. Now consider another plunger/cylinder system. Let’s say the plunger has an area of 0.10 m2.
The larger cylinder has an area of 0.18 m2. How much force do you need to use to push
down the plunger if you want to lift a weight of 240 N?
5. What if the plunger from question 4 had an area of 0.2 m2 instead of 0.10, how much force
would you need to push down the plunger then?
Information: Units
So far, we haven’t had to worry about units. Force must be in Newtons (N), area in meters (m),
and pressure in kilopascals (kPa). It is common, however, that area may be expressed in cm2
instead of m2. If you are even given cm2 you must divide by 10,000 to get m2.
Critical Thinking Questions
6. The chair in a dentist’s office is an example of a hydraulic lift system. The chair with a
person sitting in it weighs 1850 N and it rests on a piston with an area of 1270 cm2. What
force must be applied to the small piston with a cross-sectional area of 63 cm2 in order to lift
the person?
7. Consider yet another plunger/cylinder system. Let’s say the plunger has an area of 30 cm2.
The larger cylinder has an area of 78 cm2. How much force do you need to use to push down
the plunger if you want to lift a weight of 1290 N?
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Physics Fix 27
Name: ______________________________
Date: _____________
Hour: _____
Information: Waves and Jumping Rope
Figure 1: Three girls playing jump rope. When the girls shake the rope in an up and down
motion, the rope takes the shape of a wave.
Wavelength
“Wavelength
”
“Rest
Position”
B
Amplitude
A
Critical Thinking Questions
1. Based on Figure 1, define the following terms:
a) rest position:
b) amplitude:
c) wavelength:
2. In Figure 1, there are two arrows (A and B). One of the arrows is pointing to a “crest” and
the other is pointing to a “trough”. Indicate which arrow is the crest and which is the trough.
3. Obviously, if the girls in Figure 1 did not shake the rope up and down, then there would be
no wave. If they move the rope up and down faster, what will happen to the wavelength?
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4. Moving the rope up and down faster does not affect the amplitude. How could the girls
change the amplitude of their wave?
Information: Frequency of Waves
How fast the girls shake or vibrate the rope will be the frequency of the wave. If one of the girls
lifts the rope and brings it back to the rest position once each second, then the frequency is 1
hertz (Hz). The unit of hertz measures the number of complete cycles (back and forth) per
second. A frequency of 2 Hz means that the wave vibrates back and forth twice each second.
Critical Thinking Questions
5. Which rope would have the longest wavelength—one with a frequency of 2 Hz or one with a
frequency of 3 Hz? Explain.
6. If a wave has a frequency of 2 Hz (two complete cycles per second), how long does it take
for the wave to make one complete cycle?
7. If a wave has a frequency of 3 Hz, how long does it take for the wave to make one complete
cycle?
8. If a wave has a frequency of 4 Hz, how long does it take for the wave to make one complete
cycle?
9. In questions 6-8 you calculated the period of a wave. The period is the time it takes for a
wave to make one complete cycle. Which of the following is an equation that can be used to
calculate the period of a wave?
1
C) period = (frequency)2
frequency
10. True or false: When the girls make a wave, the rope moves up and down only; the rope does
not move left to right.
A) period  frequency
B) period 
Information: Motion of Waves
The correct answer for question 10 was TRUE. The rope is simply moving up and down. A
disturbance in the rope moves left to right, but the rope itself is only moving up and down.
Although the rope itself doesn’t move from left to right, we can calculate how fast the
disturbance moves in that direction.
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Critical Thinking Questions
11. A certain wave has a wavelength of 4 m. If the frequency of the wave was 3 Hz, then 3
complete wavelengths pass by a given point in one second. How many meters of waves pass
by a given point in one second?
A) 4 m
B) 7 m
C) 12 m
D) 1.25 m
12. Given your answer to question 11, what is the speed of the wave? (Remember that speed
equals distance traveled divided by time and the time was one second.)
13. Consider a wave that has a wavelength of 5 m. If the frequency was 4 Hz, then calculate the
speed of the wave.
14. Given your answers to questions 12 and 13, which of the following is the equation that
relates speed (v), wavelength (), and frequency (f).
f

A) v = f  
B) v 
C) v 

f
15. If a water wave vibrates up and down 3 times each second and the distance between wave
crests is 2.5 m…
a) What is the frequency of the wave?
b) What is the wavelength of the wave?
c) What is the speed of the wave?
16. Sounds travel to our ears in the form of waves. Sounds that have a high pitch are waves with
high frequencies. Sounds that have a low pitch are waves with low frequencies. When you
listen to a concert, high notes and low notes both reach your ears at the same time. What can
you conclude, therefore, about the speed of waves that have different frequencies?
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Physics Fix 28
Name: ______________________________
Date: _____________
Hour: _____
Information: Longitudinal Waves
The waves in the last lesson are called transverse waves. A transverse wave is often what
someone thinks of when they think of a wave. Such a wave may be produced by shaking a rope
and will look like this:
Figure 1: A Transverse Wave
Another kind of wave is called a longitudinal wave. A spring will produce a longitudinal wave if
you follow these steps:
Figure 2: Forming a Longitudinal Wave in a Spring.
Step 1: Obtain a coiled spring
Step 2: Compress some of the spring
Step 3: Release the compression. The compression will travel down the spring
The compression moves from here ……………………. To here
Longitudinal waves are formed from a series of compressions and rarefactions, as shown below:
Figure 3: Longitudinal Waves in a Spring.
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Critical Thinking Questions
1. In the information section it says that longitudinal waves are formed from a series of
compressions and rarefactions. Describe what you think a “rarefaction” is.
2. In Figure 3 there are 4 compressions and 3 rarefactions. Label the compressions and
rarefactions in Figure 3.
3. Recall that the wavelength of a wave is the distance between two identical points on a wave.
Label a wavelength of the transverse wave in Figure 1 and the longitudinal wave in Figure 3.
4. Most waves need a medium in which to travel. In the transverse in Figure 1, the medium was
a rope that was being shaken. In the longitudinal waves from Figures 2 and 3, the medium
was the spring. Think about the motion of the medium and then fill in the blanks:
In a transverse wave the medium moves ___________________________.
up and down OR side to side
In a longitudinal wave the medium moves __________________________.
up and down OR side to side
5. Consider if you had a world-famous Slinky® toy.
Slinky® to make a transverse and a longitudinal wave.
Describe how you could use a
a) To make a transverse wave…
b) To make a longitudinal wave…
Information: Interference
If you drop two stones into a pond, the waves produced will interfere with each other. The waves
we’ve been talking about can interfere with each other also. Let’s use transverse waves to
illustrate two types of interference:
Figure 4
Wave A
Wave B
Figure 5
Wave A
Wave B
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Critical Thinking Questions
6. Look at Figures 4 and 5 and imagine what it would look like if you put Wave A on top of
Wave B and fill in the blanks:
In __________________ the crests of Wave A and Wave B would cancel each other.
Figure 4 OR Figure 5
In __________________ the crests of Wave A and Wave B would add together.
Figure 4 OR Figure 5
7. There are two kinds of interference—constructive interference and destructive interference.
By the question marks in Figures 4 and 5, label each as either constructive or destructive.
Information: Periodic Motion
Periodic motion is a motion that is repetitive at regular intervals. A drumbeat in a song is
periodic—the drummer hits the drum at regular intervals, or periods. Wave motion is also
periodic because the motion involves a back and forth repetition. In transverse waves, there is a
repetition of crests and troughs. In longitudinal waves, there is a repetition of compressions and
rarefactions. You have learned that a period is the time it takes for a wave to make a complete
back and forth cycle.
A pendulum is a device that exhibits periodic motion. If you tie a rock to the end of a piece of
string, you will have a simple pendulum that will swing back and forth with a regular motion.
Pendulums swing so regularly that they are used to control the time in many clocks:
The “period” of a pendulum is the time it takes to make a complete back and forth motion. You
could probably imagine that a longer pendulum will take longer to swing back and forth. The
period, T, of a pendulum only depends on its length and on gravity:
T  2
L
g
T = Period of the pendulum in seconds
L = Length of pendulum in meters
g = Acceleration due to gravity, 9.8 m/s2
(Recall that  is 3.14)
Critical Thinking Questions
8. Why do you think that the length of a pendulum must have units of meters to be used in the
equation?
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9. Recall what you know about the acceleration due to gravity: If dropped from a height of 3
meters, will a bowling ball and a golf ball hit the ground at the same time? Explain.
10. The mass of a bowling ball and a golf ball are quite different and yet, they hit the ground at
the same time. (Hopefully you got question 9 correct!) Look again at the equation for the
period, T, of a pendulum. The mass of the pendulum is not in the equation. Why?
11. Find the period of a pendulum that has a length of 30 cm. (Be careful of units!)
12. How long does a pendulum need to be in order to have a period of 1 second?
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Physics Fix 29
Name: ______________________________
Date: _____________
Hour: _____
Information: Sound Waves
Sound is transmitted via sound waves. Look at the diagrams below:
Figure 1: The diagram below shows how a stereo speaker vibrates the air molecules near the
speaker. Notice how the air molecules are pushed close together near the speaker.
Figure 2: The Molecules that were pushed close together in turn push the air molecules right next
to them. The “clump” of compressed air molecules travels away from the speaker and toward the
ear.
Figure 3: Sound waves travel to our ears in a sort of compression and rarefaction of air
molecules:
Critical Thinking Questions
1. Are sound waves transverse or longitudinal? Explain.
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2. What medium do sound waves travel through?
3. On the diagram in Figure 3, label the compressions, rarefactions, and the wavelength.
Information: Characteristics of Sound Waves
All waves have a frequency and amplitude. We refer to the frequency of a sound wave as the
“pitch” of the sound. A “high pitch” sound has a high frequency—more waves hit the ear per
second. The amplitude tells us the loudness or intensity of the sound. A sound wave with a high
amplitude is causing a lot of air molecules to vibrate. A higher amplitude means that the sound
wave would sound louder. Below, there are three diagrams of waves. Compare them and then
answer the following questions.
Figure 4: Several different waves with differing pitch or amplitude.
Wave A
Wave B
Wave C
Critical Thinking Questions
4. Which wave—A, B, or C—is probably the loudest? Explain.
5. Which wave—A, B, or C—has the highest pitch? Explain.
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6. Consider Figure 3, where the speaker is producing sound waves. If the speaker were moving
toward the ear, which of the following do you think would happen? (circle the letter)
A) The molecules would get compressed like Wave C in Figure 4 and have a higher pitch.
OR
B) The molecules would spread out like Wave A in Figure 4 and have a lower pitch.
Information: The Doppler Shift
Hopefully you chose A for question 6. If the speaker travels toward the person’s ear, the sound
waves would get compressed and the pitch would sound higher than it normally would if the
speaker weren’t moving at all. Consider the two pictures of a car below.
Figure 5: A Car and the Sound Waves It Produces
A car is running, but not moving. The
sound that the car makes is
represented by the circles surrounding
the car.
The car is moving fast. The sound waves
in front of the car get compressed and the
pitch sounds higher. Behind the car, the
pitch sounds lower. If you’ve ever heard
the changing pitch of a race car as it passes
you, now you know why the pitch
changes.
Critical Thinking Questions
7. If a plane is flying toward you will the frequency of the sound waves you hear be higher or
lower than if it were still?
8. As a race car zooms toward you, compare the frequencies of the sound you hear before and
after the car reaches you.
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Physics Fix 30
Name: ______________________________
Date: _____________
Hour: _____
Information: The Electromagnetic Spectrum
Some energy travels in a wave that is partly electric and partly magnetic. We call these waves
“electromagnetic”. You have heard of many kinds of electromagnetic waves: Gamma () rays, X
rays, ultraviolet (UV), infrared (IR), microwaves, and many others. Visible light is also a kind of
electromagnetic wave. Like other waves, electromagnetic waves have frequency and
wavelength. A graphical depiction of these waves along with their wavelengths and frequencies
is called the electromagnetic spectrum.
Figure 1: The Electromagnetic Spectrum
violet
indigo
blue
green
yellow orange
red
Critical Thinking Questions
1. What are the units used for frequency in Figure 1?
2. The visible spectrum of electromagnetic waves is enlarged for clarification.
a) What units are used for wavelength in this enlarged visible spectrum portion?
b) What units are used for wavelength on the main portion of the diagram?
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3. Recalling that it takes one billion nanometers to equal one meter, perform the following
conversions. (Use scientific notation where appropriate.)
a) 6.25x10-7 m = _________ nm
b) 520 nm = ___________________ m
c) 685 nm = _________________m
d) 4.55x10-7 m = ____________ nm
4. Each of the conversions you performed in the previous question correspond to a specific
color of visible light. Use Figure 1 to identify the color of light for each.
a) color: ________________________
b) color: _________________________
c) color: ________________________
d) color: _________________________
5. Arrange the following in order from smallest to largest wavelength: AM radio waves, x rays,
infrared waves, ultraviolet waves, and visible waves.
6. Why do you think the name “ultraviolet” is used instead of “ultragreen”? (Hint: look at the
spectrum above.)
Information: Speed of Light
Up until the 17th century it was not known whether light had a finite speed or if it traveled
instantaneously. We now know that light has a very fast speed and it does not travel
instantaneously. The speed of light has been determined to be 3.0x108 m/s.
Critical Thinking Questions
7. The diameter of the Earth is about 40,000,000 m. How many times can light travel around
the Earth in one second?
8. The distance between Earth and the sun is about 150,000,000 km. How long does it take for
the sun’s light to reach us on Earth? (Hint: first convert km to meters!)
9. A light-year is how far light can travel in one year. What is the distance of one light-year in
meters? (Hint: you know how many meters light can travel each second. All you need to do
is find out how many seconds are in a year.)
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Information: Calculating Speed and Frequency
You have learned the equation for waves involving speed, frequency (f) and wavelength ().
The speed of light is given the symbol, c. Remember, c is always 3.0x108 m/s. Therefore, using
the equation you have previously learned, we can write:
c = f  
Critical Thinking Questions
10. What units must wavelength have if the above equation is to work?
11. Calculate the wavelength of light if the frequency of the light is 4.8x1014 Hz. About what
color is this? (Refer to Figure 1)
12. Find the frequency of light that has a wavelength of 410 nm. (Be careful of units!)
13. Calculate the wavelength of light that has a frequency of 5.1x1014 Hz.
14. What is the frequency of light that has a wavelength of 535 nm?
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