Download Physics: Significant Digits Scientific Notation Worksheet

Physics: Significant Digits
Give the number of significant digits in each of the following measurements:
1. 1278.50
__________
7. 8.002
__________
13. 43.050
__________
2. 120000
__________
8. 823.012
__________
14. 0.147
__________
3. 90027.00 __________
9. 0.005789
__________
15. 6271.91 __________
4. 0.0053567 __________
10. 2.60
__________
16.
5. 670
__________
11. 542000.
__________
17. 3.47
6. 0.00730
__________
12. 2653008.0
6
__________
__________
__________18. 387465 __________
Round off the following numbers to three significant digits:
19. 120000 _______________
22. 4.53619 _______________
20. 5.457
_______________
23. 43.659 _______________
21. 0.0008769 _______________
24. 876493 _______________
Perform the following operations giving the proper number of significant figures in the answer:
25. 23.4 x 14_______________ 28. 0.005 - 0.0007 _______________
26. 7.895 + 3.4_______________ 29. 7.895 ÷ 34
_______________
27. 0.0945 x 1.47_____________ 30. 0.2 / 0.0005
_______________
Scientific Notation Worksheet
Convert into scientific notation:
Convert into standard notation:
1) 3,400 ___________________________
2) 0.000023 ________________________
3) 101,000 _________________________
4) 0.010 ___________________________
5) 45.01 ___________________________
6) 1,000,000 ________________________
7) 0.00671 _________________________
8) 4.50 ____________________________
Sc. 10 Physics
SACHS
9) 2.30 x 104 ________________________
10) 1.76 x 10-3 _______________________
11) 1.901 x 10-7 ______________________
12) 8.65 x 10-1 _______________________
13) 9.11 x 103 _______________________
14) 5.40 x 101 _______________________
15) 1.76 x 102 _______________________
16) 7.4 x 10-5 ________________________
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Solutions
1) 3.4 x 103
3) 1.01 x 105
5) 4.501 x 101
7) 6.71 x 10-3
2) 2.3 x 10-5
4) 1.0 x 10-2
6) 1 x 106
8) 4.50
9) 23,000
11) 0.0000001901
13) 9,110
15) 1.76
16) 0.000074
10) 0.00176
12) 0.865
14) 54.0
Solving Equations Worksheet
Part 1.
Solve for the variable. Show your work.
a. x + 4 = - 7
b. 2 – x = 13
d. y = 18
5
e. 3y – 20 = 7
g. 3x + 2 = 4x – 7
h. y = 1
10 20
c. 15y = 45
f. -4y + 20 = - 8
Part 2.
Rewrite the equation in terms of the specified variable.
a.
( t:
b.
c.
a = vf – vi
t
vi:
e.
Ek = 1 mv2
2
m:
f.
g:
h.
g.
d.
vf:
Ep = mgh
m:
Ek = 1 mv2
2
v:
v:
Part 1 solutions
A: (-11) B: (-11) C: (3) D: (90) E: (9) F: (7) G: (9) H: (0.5)
Sc. 10 Physics
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Converting Units Science 10
Convert the following and show the appropriate work.
1.
3.
5.
7.
9.
50 km/h à m/min (8.3 x 102 m/min)
11.0 m/s à km/h (39.6 km/h)
3.00 x 108 m/s à km/h(1.08 x 109 km/h)
4.49 m/s à km/h(16.2 km/h)
25.00 cm/min à m/s(4.167 x 10-3 m/s)
2. 12.1 m/min à km/h (7.26 x 10-1 km/h)
4. 2.3 x 102 m/s à km/h(8.3 x 102 km/h)
6. 9.81 m/s à cm/min(5.89 x 104 cm/min)
8. 1.20 x 105 km/h à m/min(2.00 x 106m/min)
10. 20 km/min à m/s(3.3 x 102 m/s)
Science 10 (v = d/t)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Janice walks 100 m in 50.0 s. What is her average velocity? ( 2.00 m/s)
Barry rides his bike from Lethbridge to Calgary a distance of 250 km without stopping.
The trip takes him 10.0 hours. What was his average speed? ( 25.0 km/h)
Little Mikey, the fish, swims in a straight line for a period of 50.0 minutes while covering
a distance of 700 m. What was Little Mikey's average speed in m/s? (0.233 m/s)
Ricky walks at a constant speed of 2.00 m/s for a period of 3.00 mins (180 s). If she
walked in a straight line how far from where she started would she end up? (360 m)
A rabbit is hopping away from a dog at a uniform speed of 1.25 m/s in a straight line for
245 s. How much distance did the rabbit cover? (306 m)
Archie can jog at a uniform speed of 0.50 m/s. If he jogs for 25 minutes how far did he
jog? (7.5 x 102 m)
Terri drove from Grande Prairie to Thorhild to visit the new Edmonton landfill. Suppose
that Thorhild is 320 km from Grande Prairie and that she was driving at a constant speed
of 80 km/h, how long would it take her? (4.0 h)
Rhoda ran a 2.00 km race at a constant speed of 1.10 m/s. How long did she take to
complete the race? (1818 s, 1.82 x 103 s)
A plane can fly from Trochu to Vancouver, a distance of 1300 km, at a constant speed of
652 km/h. How much time did this take? (1.99 h)
Veronica ran in a marathon (26.2 km) recently and completed the race in 8.23 hours.
What was her average speed in km/h? (3.18 km/h)
Natasha ran at a constant speed of 2.00 m/s for 65 s and then walked at 1.00 m/s for 85 s.
How far did she travel in all? (Hint: Do this in two steps.) (Ans. 215 m, 2.2 x 102 m)
Sc. 10 Physics
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Graphing Practice
A.
Graph the following data on a sheet of graph paper. Remember to include a title, name each axis
and give them units. Make the graph about one-half the size of the sheet. Plot both sets of data
(Bill and Mike) on the same graph. Draw lines of best fit for each person.
Bill’s Running Data
Distance (km)
0.0
0.3
0.6
0.8
1.1
1.4
1.6
1.8
2.1
2.5
2.8
2.8
3.3
3.4
3.7
4.0
4.2
4.4
Mike’s Running Data
Time (min)
0.0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
32.5
Distance (km)
Time (min)
0.0
0.3
0.5
0.6
0.9
1.0
1.2
1.5
1.6
1.9
2.1
2.3
2.4
2.6
2.9
3.0
3.3
3.4
3.6
3.9
4.0
4.3
4.4
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
43
B.
Calculate the slope of the line for each runner. You must choose two points on the line of best
fit. Draw a triangle and determine the rise and the run. Substitute into the formula and include
units in your calculations and the answer.
Sc. 10 Physics
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Graphing Analysis
1. Below is a graph of Sean’s speed as detailed in a speed-time graph.
Speed vs time
4.0
Speed
(m/s)
0
a)
5.0
time (s)
10
Using the method of finding the area from a speed-time graph to obtain the distance
travelled, fill in the table of values.
distance (m)
time (s)
0.0
1.0
2.0
3.0
4.0
5.0
b)
Show the sample calculation for the time of 3.0 s.
c)
On a sheet of graph paper, plot a distace-time graph.
2.
Determine Sean’s average speed using the distance-time graph. Show your work.
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4.
Each of the following graphs shows an attempt at calculating the slope of a line. Each
has an error. Explain what the error is and make the correct calculation.
A.
Distance vs Time for a small child
walking
Distance (m)
20
This calculation
has an error.
rise
run
slope =
10
18 m
10 s
= 1.8 m/s
=
B.
Distance vs Time for a cycling trip
Distance (km)
100
This calculation
has an error.
slope =
50
=
rise
3.6 h
= 0.36 h/km
4
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C.
Distance vs Time for a hiking trip
Distance (km)
This calculation
has an error.
rise
run
10
15
5
= 3
1
2
3
4
D.
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750
Distance vs Time for an ant
crossing the sidewalk
This calculation
has an error.
rise
run
=
= 5 mm/s
250
125
200
100
25
Time (s)
Sc. 10 Physics
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Science 10 Uniform Motion Lab
(22 Marks)
Title Page:
Include the title of the lab, your name underlined, lab partner's name, the class and due date.
Objective:
The objective is to illustrate constant motion by constructing graphs of distance versus time and
velocity versus time for the uniform motion (constant speed) from the data obtained using the air table.
Apparatus:
The air table.
Procedure:
Level off the table as much as possible. Place one puck in the top right hand corner on a folded
piece of paper (only one puck is used for this experiment). Shoot the other puck and simultaneously activate
the sparktimer. Both pucks must be on the paper to complete the circuit. Set the timer to 50 ms.
Observations:
- Staple data sheet onto back of lab write up.
Analysis:
A. You will determine when the spaces between dots seems to be constant. You will identify this dot as the zero
point. From this point measure the distance to all other points using units of millimeters. You will make
a table of values of this information. You will plot this information in the form of a distance - time graph.
Only the graph is to appear on the graph paper. It must be done only in pencil.
(1)- Table of values.
(1)- Scale on graph.
(1)- Labels/units on graph.
(2)- Line of best fit on the graph.
(2)- Calculation of slope including showing triangle used on graph. (include units)
(1)- What does the slope of a distance-time graph represent. Answer in a complete sentence.
B. Calculate the average velocity for the entire run using an equation learned in class.
(1)- Show a sample calculation for the above.
(1)- Compare this value with the slope obtained from the distance-time graph.
C. Determine the average velocity during each time interval and make a graph plotting it against the midpoint of
the time interval.
(1)- Sample calc of average velocity for time period t = 200ms - 250ms
(1)- Table of values.
(1)- Scale on graph.
(1)- Labels/units on graph.
(2)- Line of best fit on the graph.
(1)- What does the area of a velocity-time graph represent. Answer in a complete sentence.
(2)- Calculate the area under the curve between time t= 200ms and 300ms
(1)- What is the distance between t= 200ms and 300ms using the air table data sheet.
Conclusion:
Restate objective. "The objective of this lab was to"
(2)- Did this lab satisfy the objective? Why/ why not? Are the graphs representative of an object moving with a
uniform speed?
Note: One mark will be deducted if the contents are not in the above-mentioned order.
Sc. 10 Physics
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Constant Acceleration
1. A car is stopped at a red light and the light suddenly turns green. After 6.00 s the car is
travelling at a speed of 4.25 m/s. Determine the acceleration of the car.
(0.708 m/s2, 7.08 x 10-1 m/s2)
2. A golf ball is sitting on a tee. 0.53 s after the ball is hit it is travelling with a speed of 65.0
km/h (18.06 m/s). What is the acceleration of the ball during that period?
(34 m/s2, 3.4 x 101 m/s2)
3. A car is moving at a speed of 50.0 km/h (
m/s) and it accelerates to 60.0 km/h
(
m/s) in a period of 4.5 s in order to pass another vehicle. What is the acceleration of the
car in terms of m/s2? (0.62 m/s2, 6.2 x 10-1 m/s2)
4. A bike starts from rest and obtains a speed of 2.00 m/s while accelerating at a rate of 0.50
m/s2. How long did it take for the bike to gain the speed of 2.00 m/s? (4.0 s)
5. A person is running and slows down changing her speed by 1.50 m/s (-1.50 m/s) while
decelerating at a rate of 0.62 m/s2 (-0.62 m/s2). How long did it take her to accomplish this
task? (2.4 s)
6. A spider is moving and when it senses danger it changes its speed by 0.450 m/s. It was
accelerating at a rate of 0.952 m/s2. How many seconds did it take the spider to do this?
(0.473 s, 4.73 x 10-1 s)
7. Curious George accerates at a rate of 2.05 m/s2 for a 12.0 s time period. By how much did
his speed change? (24.6 m/s, 2.46 x 101m/s)
8. Francine was walking and decided to pick up the pace and run. She accelerated at a rate of
1.43 m/s2 for 4.60 s. By how much did her speed change? (6.58 m/s)
9. A plane is coming in for a landing. It is moving at a rate of 150 km/h when the tires first
touch the pavement. If it can decelerate at a rate of 25920 km/h2 (2.00 m/s2) by applying the
brakes, how many seconds does it take for the plane to stop? Hint: Convert everyting to
meters and seconds. (20.8 s, 2.08 x 101 s)
Sc. 10 Physics
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Science 10 Uniform Acceleration Lab
(24 Marks)
Title Page:
Include the title of the lab, your underlined name, lab partner's name, the class and due date.
Objective:
The objective of the lab is to construct graphs that are representative of an accelerating body.
Apparatus:
The air table utilized in the uniform motion lab.
Procedure:
Tilt the air table by placing a book under one of the legs. Make sure that one of the pucks is
placed on a folded corner of the paper on the air table. Set the timer to 50 ms. Place the other puck on the
elevated side of the table. Release the puck and simultaneously start the timer. Continue pressing the timerstarter until the puck reaches the other end of the table.
Observations:
- Staple data sheet onto back of lab write up.
Analysis:
A. You will identify the first dot as the zero point. From this point measure the distance to all other points using
units of millimeters. You will plot this information in the form of a distance - time graph.
(1)- Table of values.
(1)- Scale on graph.
(1)- Labels/units on graph.
(2)- Draw a curve of best fit by freehand.
B. Determine the average velocity during each time interval and make a graph plotting it against the midpoint of the
time interval.
(1)- Sample calc of average velocity for time period t = 200ms - 250ms
(1)- Table of values.
(1)- Scale on graph.
(1)- Labels/units on graph.
(2)- Line of best fit on the graph.
(1)- From the graph, determine the initial velocity.
(1)- What does the area of a velocity-time graph represent. Answer in a complete sentence.
(2)- Calculate the area under the curve between time t= 200ms and 350ms
(2)- Calculate the actual distance covered using the initial data for the time period t= 200ms and 350ms.
C. Determine the acceleration of the puck.
(3)- Using the velocity-time graph only.
(1)- Calculate the equation of the line for the velocity-time graph. (y = mx + b) (vf = at +vi)
Conclusion: Please answer these questions in complete sentences.
Restate objective.
(1)- What did you notice about the spacing between dots as the time increased?
(1)- What was the shape of the distance-time graph?
(2)- Are these graphs representative of an accelerating object? Comment on each graph.
Note: One mark will be deducted if the contents are not in the above-mentioned order. The graphs should be
large and done only in pencil. Nothing other than the graphs should be on the graph paper.
Sc. 10 Physics
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Forces
1. A 3.00 kg bowling ball is accelerating at a rate of 1.40 m/s2. What is the force exerted on
the ball? (4.20 N)
2. A 500 kg cow accelerates at a rate of 2.30 m/s2. What force is the cow applying?
(1150 N, 1.15 x 103 N)
3. A 1200 kg car starting from rest accelerates to a speed of 80 km/h in 8.00 s. What force is
required in order to achieve this? (3333 N, 3.3 x 103 N)
4. A 340 kg motorcycle accelerates from 60 km/h to 90 km/h in 6.00 s. What force was
requirred in order to do this? (472 N, 4.7 x 102 N)
5. A 500 N force is applied to a 80.0 kg wagon with a boy in it. What is the wagon's
acceleration? (6.25 m/s2)
6. A speeding car is headed for Superman. Superman pushes the 1500 kg car with a 30000 N
force and brings it to a stop. What was the acceleration of the car? (-20.00 m/s2)
7. Robin pulls a box with a force of 250 N and the box accelerates at a rate of 2.13 m/s2. What
was the mass of the box? (117 kg)
8. A phone is thrown with a force of 46.0 N and it accelerates at a rate of 8.90 m/s2. How
much mass did the phone have? (5.17 kg)
9. A 7.90 kg chicken starts from rest and 5.0 s later is running with a speed of 2.35 m/s.
Determine the acceleration and force of the chicken. (0.47 m/s2, 3.7 N)
10. Indiana Jones, having a mass of 86.0 kg, is pulled with a force of 1000 N. Determine his
acceleration as well as his speed after 13.0 s that the force was applied if he was originally at
rest? (11.6 m/s2, 151 m/s)
Good Luck on the MID-UNIT EXAM
Sc. 10 Physics
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Review for Mid Unit Exam - Physics
Rule to determine the amount of significant digits in a number.
Find the first nonzero number. All numbers to the right of that
number including that number, including zeros, are also significant.
Convert:
3200 s into 2 sig. digs.
3.2 x 103 s
4.67 x 10-4 m/s
0.000467 m/s
0.0062 m
6.2 x 10-3 m
BEDMAS = brackets, exponents, divide, multiply, add, subtract.
Conversions
50 km/h à m/s
50 km x
1h
1000 m x 1 h
1 km
3600 s
= 50000 m
3600 s
=
13.9m/s
27.8 m/s à km/h
27.8 m x
1h
Sc. 10 Physics
1 km x
1000 m
3600 s
1h
=
SACHS
100080 km =
1000 h
100.1 km/h
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Formulas:
v=
d
t
slope = rise
run
*remember to always pick two points on the best fit line!!!
Area of a velocity-time graph:
A
= lw
= distance
Area for a triangle =
bh = distance
2
Acceleration:
a = ∆v
t
a=
vf - vi
t
Force:
F = ma
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uniform motion:
d
i
s
t
a
n
c
e
v
e
l
o
c
i
t
y
Graphs:slope = rise
run
time (sec)
(m/s)
Area = lw
=
distance
time (sec)
slope = avg. velocity
acceleration:
Area = lw
= distance
v
e
l
o
c
i
t
y
Slope = rise
run
slope = avg.
acceleration
(m/s)
Sc. 10 Physics
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PHYSICS 1st Half REVIEW
The major concepts of this half have been kinematics (uniform motion and acceleration),
graphing, forces.
MOTION
Speed is result of changing distance over a period of time. This is stated mathematically
as:
v= d
t
Note: This is an average speed!!!
We solved the problems using this formula such as:
1.
A skater was travelling along a level road. He covered a distance of 2.0 km in a time of
8.0 minutes. What was his average speed in m/s? (4.2 m/s)
2.
A girl rows a boat at a speed of 1.25 m/s. How long does it take her to cover 300 m?
(240 s)
3.
A trip from St. Albert to Havre, Montana takes about 8.75 h. If one averages 110 km/h
while driving and the time includes a lunch break of 30.0 minutes, how far is it from St.
Albert to Havre? (908 km)
4.
Convert 1250 km/h to m/s. (347.2 m/s)
GRAPHING
We learned how to plot points on a graph and how to read these graphs. We learned that
you must set up a graph in certain ways.
A)
B)
C)
D)
E)
The graph must be titled.
The independent variable (one you choose to manipulate) is placed on the horizontal or xaxis.
The dependent variable (responds to the manipulated one) is placed on the vertical or yaxis.
The data from a table of values is plotted on the graph and a best fit line is drawn. This
line does not have to pass through the origin but must be placed such that there are about
an equal number of points above and below the line.
The slope of the best fit line can be calculated by selecting a pair of points on the line and
calculating the rise and the run. Slope = rise / run
The slope tells how one variable changes in relation to the other. (On the distance vs.
time graph this gives us the average speed.)
Sc. 10 Physics
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velocity vs. time
velocity
distance
(m/s)
(m)
15.0
15.0-F)
5.0
5.0-0.0
0.0-0.0
0.0
G)
The area under the line represents the product of the axis. Example: in a speed vs time
graph the area is equal to the distance covered. Distance is equal to the y-axis (speed)
times the x-axis (time).
The graph must be big enough to see and the units must be equally spaced along the axis.
1.
From the graph, calculate the average velocity from the following graph.
1.0
3.0
3.0
2.0
time
time(s)
(s)
4.0
(slope = 3.0 m/s)
2.
From the graph, calculate the distance travelled between the third and the fourth second.
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(area = 13.5 m)
ACCELERATION
1.
2.
3.
4.
1.
2.
3.
4.
5.
6.
7.
8.
A change in speed over time resulted in an acceleration. Mathematically this is stated as:
a = vf - vi
t
A runner goes form rest to 25 m/s in 13.0 s. What is her acceleration? ( 1.9 m/s2)
A car accelerates from 50.0 km/h to 100 km/h in 9.80 s. What is its acceleration?
(1.42 m/s2)
The acceleration of an object due to gravity is 9.81 m/s2. If an object is dropped and it is
moving at 30 m/s just before it hits the ground, how long did it fall for? (3.1 s)
A vehicle is clocked for 2.45 s and it is found that it accelerates at -3.89 m/s2. It also is
found that the vehicle was moving at 15.0 m/s at the end of the timing. How fast was the
vehicle moving when the time began? ( 24.5 m/s)
FORCE
Force is an object mass times its acceleration and it is measured in Newtons (N). F=ma
A 22.0 kg cart is pushed along a frictionless surface. It is accelerated at 0.30 m/s2. What
is the force causing the acceleration? (6.6 N)
A 35 kg cart is on a frictionless surface. What will be the acceleration when pulled
forward by a force of 6.0 N? ( 0.17 m/s2)
A 23.0 kg cart on a level surface slows down at 2.66 m/s2. What is the force decelerating
the cart? (-61.2 N)
The combined mass of you and a skateboard is 50.0 kg. if someone pulls you with a net
force of 72 N , what acceleration will occur? (1.44 m/s2)
A 5192 kg rocket in space fires its engines for 60.0 s. The thrust of the engines is
15000 N.
a) What is the acceleration of the rocket? ( 2.89 m/s2)
b) What is the final speed of the rocket if the initial speed of the rocket was 830 m/s?
( 1.00X10 3 m/s)
A 850000 kg space platform must be brought from a speed of 2200 m/s to 2500 m/s. It
will do this by firing a booster rocket with a thrust of 100000 N. For how many seconds
must the rocket burn in order to achieve this speed increase? ( 2550 s)
A 3.20 kg cart travelling at 1.90 m/s comes to rest in 8.50 s. What is the frictional force
acting on the cart? (-0.715 N)
When a 3000 kg Buick travelling at 28 m/s has its brakes locked up it will skid to a a stop
in 3.2 s. What is the magnitude of the force causing this? ( -2.6 x10 4 N)
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Work Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
A 15.0 N force is used to push a chair for a distance of 3.00 m. How much work was
done to accomplish this task? (45.0 J)
A 23.0 N force is required to lift a cute and cuddly bunny 20.0 cm. Determine the
amount of work required to do this. (4.60 J)
Kelly does 456 J of work in order to push an object 4.00 m. With what force was Kelly
pushing? (114 N)
6.00 J worth of work are done when a lamp is lifted 51.0 cm. How much force was used?
(11.8 N)
A horse was pushed with a force of 45.0 N thereby doing 250 J worth of work. Calculate
the distance that the horse was pushed. (5.56 m)
A cat did 2.00 J of work while lifting a peice of cheese with a force of 6.20 N. How high
was the cheese lifted? (0.323 m)
A 20.0 N box is lifted 5.00 m into a house window. How much work was done to lift the
box? (100 J)
Hillary pulls a 5.00 N cat for a 12.0 m distance. How much work did she do? (60.0 J)
Tony, the tiger, did 700 J worth of work while pulling a 100 N package of Frosted Flakes.
How far did he pull the package? (7.00 m)
650 J of work were done while a boulder was pushed 18.0 mm. What force was applied?
(3.61 x 104 N)
A 15.0 N telephone is dropped out of a window. 89.0 J worth of work were done on the
phone. From what height was the phone dropped? (5.93 m)
Silly Suzie pulls a sleeping lion with a 65.2 N force for a 23.0 cm distance. Calculate the
amount of work that she did before the lion woke up. (15.0 J)
Potential Energy
1.
2.
3.
4.
5.
6.
7.
Show ALL your work in answering the following questions.
How much work is required to raise an object of weight 13 N through a vertical distance
of 3.0 m? What is its potential energy after being raised? (39 J, 39 J)
What is the potential energy gained by a weight of 7.1 N when it is raised through a
height of 12 m? (85 J)
A 1.4 kg ball has 55 J of potential energy. How high from the ground is the ball? (4.0 m)
A log is raised 5.0 m and now has a potential energy of 9.8 x 102 J. What is the mass of
the log? (20 kg)
7.4 x 102 J of Ep are required by a hammer to drive in a stake. If the hammer has a mass
of 5.0 kg, how high must it be lifted? (15 m)
A 350 g mass is held at such a height that it has 560 J of energy. How high is the mass
from the ground? How much energy will it have just before it hits the ground if it is
dropped? (163 m, 560 J)
An average force of 15 N is required to compress a spring by 2.5 cm. What is the
potential energy of the spring? ( Hint: N are kg m/s2, convert all distances to metres)
(0.38 J)
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8.
9.
When an average force of 3.0 x 102 N is needed to stretch a spring by 1.9 cm, what is the
potential energy of the spring? (5.7 J)
When a maximum force of 72 N is applied to a metal coil it is compressed by 2.4 cm.
What is the potential energy of the spring? (1.7 J)
KINETIC ENERGY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
An electron of mass 9.1 x 10-31 kg has a kinetic energy of 1.4 x 10-19 J. What is its
speed? (5.5 x 105 m/s)
A 4.9 x 102 kg cart has a kinetic energy of 3.3 x 106 J. What is its speed? (1.2 x 102 m/s)
If a particle of mass 2.3 x 10-6 kg has a kinetic energy of 5.7 x 10-2 J, what is its speed?
(2.2 x 102 m/s)
What is the mass of an object which has a kinetic energy of 475 J when its speed is
14 m/s? (4.8 kg)
Calculate the mass of a particle whose speed is 3.2 x 103 m/s and kinetic energy is
4.5 x 10-8 J. (8.8 x 10-15 kg)
What is the mass of a bus whose speed is 35 km/h and kinetic energy is 2.0 x 106 J?
(4.2 x 104 kg)
If a crate has speed of 4.0 m/s and kinetic energy of 56 J, what is its mass? (7.0 kg)
A bale of hay has a mass of 1.1 x 102 kg. It is accelerated by a winch from 1.0 m/s to
3.0 m/s. Calculate its gain in kinetic energy. (4.4 x 102 J)
A car of mass 2.3 x 10 3 kg has its speed of 14 m/s cut in half. Estimate its loss in kinetic
energy. (1.7 x 105 J)
A car of mass 2.7 x 103 kg reduces its speed from 14 m/s to 5.0 m/s. What is its loss in
kinetic energy? (2.3 x 105 J)
Work and Energy Worksheet
1.
2.
3.
A 1.50 kg ball is dropped from a roof top 12.0 m above the ground. Calculate:
a) The Ep at the top. (177 J)
b) Using the Ek formula, the ball’s speed just before it hits the ground. (15.3 m/s)
c) How long does take the ball to reach the ground? (note: acceleration is gravity) (1.56 s)
d) The ball’s average speed? (7.69 s)
A 2.20 kg brick is dropped from a window 15.0 m high. Calculate:
a) The brick’s energy at the window. (324 J)
b) Speed just before the brick hits the ground. ( 17.2 m/s)
c) If the brick hits the some clay and sinks 7.00 cm into it. With what force did it
hit the clay. ( 4.62 x 103 N)
A 1.00 kg hammer is dropped 2.45 m onto a nail. The nail is driven 0.500 cm into the
board. Calculate:
a) The force the hammer hits the nails with. (4.81 x 103 N)
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b) The speed of the hammer just before it hits the nail. (6.93 m/s)
c) The acceleration of the hammer after it hits the nail. ( -4.81 x 103 m/s2)
4.
5.
6.
The Drop of Doom’s cage has a mass of 300 kg. It takes 4.08 s to fall the total distance of
20.0 m. Calculate:
a) Ep at the top. (5.89 x 104J)
b) Speed at the bottom. (19.8 m/s)
c) If the cage stops in a distance of 19.0 m, what force did the brakes apply? (3.01 x 103
N)
d) How long will it take the cage to come to a stop? (1.92 s)
A bowling ball is dropped from a height of 2.10 m. It has a total energy of 124 J.
Calculate:
a) The mass of the ball. (6.02 kg)
b) Time to fall. ( 0.654 s)
c) If the floor dents in 0.750 cm, the force with which it hits the floor.
(1.65 x 104 N)
A rock with 4900 J of energy falls off of a cliff and hits the ground with a speed of
31.3 m/s. Calculate:
a) The mass of the rock. (10.0 kg)
b) The height of the cliff. (49.9 m)
c) The rock hits the ground with a force of 1200 N, how far will it sink into the
ground? (4.083 m)
Power
1.
2.
3.
4.
5.
6.
7.
What is the power output of a machine which applies a force of 2500 N for 12.0 s if it
pulls a block through 60.0 m? (1.25 x 104 W)
An electric motor raises a 150 N weight a distance of 5.0 m in 3.50 s. What is its power
output? (2.1 x 102 W)
A truck gained 4.2 x 104 J of kinetic energy in 14.0 s. What is its power output?
(3.0 x 103 W)
How fast can a machine of power rating 2.6 kW raise a block of mass 5.3 kg a height of
15.0 m? (hint: F=mg) (0.30 s)
What is the power output when a force of 2.5 x 104 N is required to move a mass a
distance of 56.0 m in 7.0 s? (2.0 x 102 kW or 2.0 x 105 W)
A machine uses 3.5 kW for 10.0 minutes. If power costs 7.0¢ per kWh, how much did it
cost to run the machine? (4.1¢)
A kitchen oven is used to vook the Christmas turkey. It is on for 4.0 h and uses 15.0 kW
each hour. If electricity costs 6.62¢ per kWh, how much does it cost to cook the turkey?
($3.97)
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WORK, POWER and ENERGY
1.
2.
3.
4.
5.
6.
7.
8.
.
A 50.0 N acts on a 2.00 kg mass over a distance of 25.0 m. How much work is done?
(1.25 x 103 J)
Compute the power output of a machine that lifts a 400 kg crate through a height of 20.0
m in a time of 60.0 s . (1.31 kW)
A force of 50.0 N is applied to a 6.00 kg stationary object for a distance of 20.0 m.
Compute the work done (1.00 x 103 J)
How much work is done by a 25 N force that moves a 10 kg stationary object through 3.0
m in 1.6 s? (75 J)
A force of 3.00 N acts through a distance of 12.0 m in the direction of the force. Find the
work done. (36.0 J)
A 4.00 kg object is lifted 1.50 m.
(a) How much work is done against gravity? (58.9 J)
(b) Repeat if the object is lowered instead of lifted. (58.9 J)
A 60 kg woman walks up a flight of stairs that connect two floors 3.0 m apart
(a) How much lifting work is done by the woman? (1.8 kJ)
(b) By how much does the woman’s Ep change? (1.8 kJ)
Given the system below, calculate the speed of the ball at point A. (14.0 m/s)
What speed would it require at point A to reach point B? (22.1 m/s)
B
start 10.0 kg
25.0 m
10.0 m
A
9.
10.
11.
A 2.00 kg ball was fired straight upward with an initial speed of 200 m/s.
a) Compute the maximum height reached (2.04 x 103 m)
b) Compute the ball’s speed at a height of 400 m (179 m/s)
A cannonball was dropped from the top of a cliff. The cliff is 150 m high, compute the
vertical speed of the ball just before impact (54.2 m/s)
A 2.00 kg object is dropped from a cliff 4.00 x 102 m high. Determine the:
a) vertical speed of the object just prior to impact (88.6 m/s)
b) vertical speed when it falls 150 m (54.2 m/s)
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PHYSICS REVIEW
The overriding theme to this unit has been ENERGY AND CHANGE. We have looked
at various kinds of energy and measured changes that take place because of energy.
MOTION
Speed is a result of changing distance over a period of time. This is stated mathematically
as:
v=d
t
Note: This is an average speed!
We solved problems using this formula such as:
1.
A cyclist was travelling along a flat road. He covered a distance of 5.0 km in a time of 15
minutes. What was his average speed in m/s? (5.6 m/s)
2.
A girl rows a canoe at a speed of 1.50 m/s. How long does it take her to cover 500 m?
(333 s)
3.
Most people travel to Calgary in about 2h 30 min. If they are travelling the speed limit of
110 km/h, how far is Calgary from Edmonton’s southern limit? (275 km)
4.
Convert 150 km/h to m/s. (41.7 m/s)
We learned how to plot points on a graph and how to read these graphs. We learned that
you must set up a graph in certain ways.
1) The graph must be titled.
2) The independent variable (one you choose to manipulate) is placed on the horizontal or
x-axis.
3) The dependent variable (responds to the manipulated one) is placed on the vertical or
y-axis.
4) The data from a table of values is plotted on the graph and a best fit line is drawn.
This line does not have to pass through the origin but must be placed such that there are
about an equal number of points above and below the line.
5) The slope of the best fit line can be calculated by selecting a pair of points on the line
and calculating the rise and the run. Slope = rise / run
The slope tells how one variable changes in relation to the other.(On a distance vs. time
graph this gives us the average speed.)
6) The area under the line represents the product of the axis. Example: in a speed vs time
graph the area is equal to the distance covered. Distance is equal to the y-axis (speed)
times the x-axis (time).
7) The graph must be big enough to see and the units must be equally spaced along the
axis.
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ACCELERATION
1.
2.
3.
A change in speed over time resulted in an acceleration. Mathematically this is stated as:
a= Vf - Vi
t
A runner goes from rest to 15.0 m/s in 3.0 s. What is her acceleration? (5.0 m/s2)
A car accelerates from rest to 100 km/h in 9.80 s. What is its acceleration? (2.84 m/s2)
The acceleration of an object due to gravity is 9.81 m/s2. If an object is dropped and it is
moving at 50 m/s just before it hits the ground, how long did it fall for? (5.1 s)
FORCE
1.
2.
3.
4.
5.
6.
7.
8.
Force is an objects mass times its acceleration and it is measured in Newtons (N). F=ma
A 2.0 kg cart is a free-body along a frictionless surface. It is accelerated at 0.80 m/s2.
What is the force causing the acceleration? (1.6 N)
A 3.5 kg cart has is on a frictionless surface. What will be the acceleration when pulled
forward by a force of 0.60 N? (0.17 m/s2)
A 3.0 kg cart on a level surface slows down down at 0.15 m/s2. What is the force
decelerating the cart? (0.45 N)
The combined mass of you and a skateboard is 50.0 kg. If someone pulls you with a net
force of 12 N what acceleration will occur? (0.24 m/s2)
A 45 000 kg rocket in space fires its engines for 60.0 s. The thrust of the engines is
200000 N.
A) What is the acceleration of the rocket? (4.44 m/s2)
B) What is the final speed of the rocket if the initial speed of the rocket was 830 m/s?
(1.10 x 103 m/s)
A 450 000 kg space platform must be brought from a speed of 7200 m/s to 7500 m/s. It
will do this by firing a booster rocket with a thrust of 100000 N. For how many seconds
must the rocket burn in order to achieve this speed increase? (1350 s)
A 2.0 kg cart traveling at 1.2 m/s comes to rest in 8.0 s. What is the frictional force
acting on the cart? (-0.30 N)
When a 2000 kg Buick traveling at 28 m/s has its brakes locked up it will skid to a stop in
4.2 s. What is the magnitude of the force causing this? (-1.3 x 104 N)
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WORK
Work is the product of a force acting over a distance where the force and the distance are
in the same direction. W=fd
Since f=ma, W=mad and if the work is against gravity the acceleration is g=9.81 m/s2.
Work is measured in Joules (J).
1.
2.
3.
4.
5.
How much work is done by a 230N force acting over a distance of 20.0 m? (4.60 x 103 J)
A 2300 kg car accelerates at 20.0 m/s2. If the car does this for 400 m, how much work
does the engine do? (1.84x107 J)
A horse does 3000 J of work in pulling a sled for 50 m. What force does he exert? (60 N)
A dog exerts a force of 95 N in pulling a wagon. If the dog does 780 J of work, how far
did it pull the wagon? (8.2 m)
An engine lifts a 2000 kg elevator a distance of 100 m. How much work does it do?
(1.96 x 106 J)
ENERGY
Energy can be defined as the ability to do work. It does not have to be doing work, but it
must have the potential to do so. We discussed two kinds of energy, potential and
kinetic.
Potential Energy is the energy an object has because of its position or state. A brick held
above one’s head has the potential to do work (damage to the head). Its ability to do
work can be described mathematically as: Ep= mgh
Other forms of potential energy include chemical and electrical.
1.
2.
3.
4.
A piano is being moved to a second floor apartment by lifting up on a rope. If the piano
has a mass of 280 kg and it is lifted 6.00 m, how much potential energy does it have?
(1.65 x 104 J)
A penny of mass 3.0 g is held on top of a 50 story (150 m) highrise. How much Ep does
it have? (4.4 J)
A hammer has 560 J of energy stored in it when it is held 2.00 m above the ground. How
much mass does the hammer have? (28.5 kg)
A 240 g baseball is thrown into the air. It has 71 J of energy at its peak. How high is the
ball thrown? (30 m)
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KINETIC ENERGY
This is the energy an object has due to its being in motion. It is affected by the objects
mass and the velocity it is travelling at. Mathematically Ek = 0.5 mv2
1.
2.
3.
4.
5.
How much kinetic energy does a car of mass 2200 kg moving at 25.0 m/s have?
(6.88 x 105 J)
A cat with mass of 3.0 kg can run at 15 m/s. What is its kinetic energy? (3.4x 102 J)
A sled has 750 J of energy when it travels at 10.0 m/s. What is the mass of the sled?
(15.0 kg)
A bicycle and rider have a combined mass of 78 kg. If they can acquire 15600 J of
energy, how fast are they going? (20 m/s)
A train with a mass of 5.00 x 104 kg is travelling at 22.0 m/s. How much work can it do if
it crashes into another train? (1.21 x 107 J)
POWER
Power is defined as the rate of doing work. It is measured in Joules per second or Watts.
P = W/t
Electrical energy is a unit of work measured in kilowatt hours. That is power times time.
Ee = P*t
1.
2.
3.
4.
5.
6.
7.
A horse does 3000 J of work in 4.0 s. How much power does it put out?
(750 W or 1 horse power)
An elevator lifts 500.0 kg a height of 12.00 m in 9.000 s. What is its power rating?
(6540 W)
A car engine creates 1.5 x 105 W of power. If it goes for 10 s how much work does the
engine do? (1.5 x 106 J)
A machine does 2.00 million Joules of work. If its power rating is 3750 W, how long
does it work for? (533 s or 8.88 min)
A Christmas tree light is rated at 7.0 W. If it is left on for 8.0 hours, how much energy is
used? (0.056 kWh)
A flood light is rated at 500 W. It is used for 30 minutes. How much energy does it use?
(0.25 kWh)
¢
Tran-Alta Utilities charges 6.62 per kWh for electrical energy. A standard range is rated
at 12 000 W and it takes 4.00 h to cook a turkey. How much does it cost to cook your
Christmas dinner? ($3.18)
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CONSERVATION OF ENERGY
Energy in a closed system is always conserved. This means that energy is never created
nor destroyed, it just changes form. Much of the energy in earth bound systems is
changed to heat, light, or sound and therefore is not useful to us.
1.
2.
3.
4.
5.
6.
7.
8.
A toy rocket has a mass of 200 g and is fired straight up with a velocity of 50.0 m/s.
How high does it go? (127 m)
A 20.0 kg box falls from a shelf that is 2.00 m high. How fast is it moving just before it
hits the ground? (6.26 m/s)
A 75.0 kg diver falls from the 3.00 m board into the water. She goes 2.40 m into the
water before stopping. Calculate the average force the water exerted on the diver.(920 N)
A 3.00 kg sledge hammer is dropped onto a nail from a height of 0.981 m. If the average
force on the head of the nail is 1444 N, how far into the board did the nail go? (2.00 cm)
A 15.0 kg box of bricks is stored on a shelf 2.3 m above the floor.
a) If the shelf tips over, what is the velocity of the box as it hits the floor? (6.7 m/s)
b) A 30 kg box is next to the box mentioned above. What is its velocity? (6.7 m/s)
c) What can we conclude from this? (all falling masses accelerate at the same rate)
A 3.00 kg cannon ball hits the ground with a speed of 5.0 m/s. If it started from rest,
from what height was it dropped? (1.3 m)
A high calibre bullet has a mass of 1.00 x 10-3 kg and travels at 825 m/s.
a) Calculate the kinetic energy of the bullet. (340 J)
b) How fast must a 7.50 kg chicken travel to have the same kinetic energy? (9.53 m/s)
c) From what height must this chicken jump in order to have the same amount of
energy?
(4.62 m)
d) What mass must a bullet travelling at 1400 m/s have in order to have the same kinetic
energy? (3.47 x 10-4 kg)
A 10.0 kg rocket is fired straight up at a speed of 100 m/s.
a) How high will it go? (510 m)
b) What initial velocity is required to reach a height of 75.0 m? (38.4 m/s)
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