Download Physics Packet 2013-2014 - Haverford School District

2013 – 2014
Student Name ______________________________________
Teacher Name ______________________________________
Part One: Motion
2
SECTION
AN OBJECT IN MOTION CHANGES POSITION.
CHAPTER 1
Motion
1.1 Reading Study Guide A
BIG IDEA The motion of an object can be described and predicted.
KEY CONCEPT An object in motion changes position.
Vocabulary
position the location of a place or an object
reference point a location to which other locations are compared
motion a change of position over time
Review
1. Name three directions in which an object can move.
Take Notes
I.
Position describes the location of an object. (p. 9)
2. Describe your position right now in relation to the position of another person,
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
place, or object.
A. Describing a Position (p. 10)
3. Why do you need a reference point to describe a location?
4. Describing a position on Earth requires two pieces of information. In the two
cases below, one piece of information is given. Fill in the missing piece.
Distance
Longitude
____________
____________
MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A 13
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3
4
Activity 1: Running the Race
•
What do you think?
o How can you measure a runner’s speed?
o
•
•
Does running twice as far take twice as much time?
Below, record the time it takes each runner to reach the 5, 10, 15, 20 and
25-meter positions.
Calculate the overall average speed for each runner using the equation
speed =
Runner Name
•
distance
time
5m
10 m
15 m
20 m
25 m
Average
Speed
Calculate the amount of time taken to run each 5-m interval.
o To calculate the time taken to run from 5-m to 10-m mark, you will
need to subtract the time at the 5-m mark from the time at the 10m mark.
o Record your information on the chart below.
0-5 m
5-10 m
10-15 m
15-20 m
20-25 m
Speed
Speed
Speed
Speed
Speed
Speed
5
•
Calculate the average speed during each 5-m interval.
o Record in the shaded part of the chart on the previous page.
§ Remember: Your distance for each interval is 5 meters!
•
Use your data to answer the questions listed below. Answer in complete
sentences.
1. In which distance interval did each runner have the greatest average
speed? Circle the fastest speed on your chart for each runner.
2. Was the time interval of greatest speed the same or different for
different runners?
3. Which runner holds the record for the fastest 5-m interval?
4. Choose one runner and describe that runner’s total dash in terms of
speed during distance intervals.
5. Estimate the amount of time taken for each runner to reach maximum
speed.
6. Write suggestions for the runners to improve their performances.
6
Physics to Go
Penn Relays Record Times
Distance (m)
Time - Men
(Minutes:seconds)
Time-Women (Minutes:seconds)
100
0:10.47
0:11.44
200
0:21.07
0:23.66
400
0:45.49
0.52.33
800
1:48.8
2:05.4
1500
3:49.67
4:24.0
Mile
4:08.7
4:49.2
3000
8:05.8
9:15.3
5000
15:09.36
16:59.5
1.
a. Calculate the average speed of the male who holds the Penn Relays
record for the 1500-m run.
b. From the data you gathered, are there students in your class who can
reach the same speed as the male 1500-m record holder?
c. Do you think the fastest student in your class could run the 1500-m in
record time?
2. Calculate the average speeds of women who hold Penn Relays records in
the 100, 200, 400 and 1500-m runs. What is the pattern of speeds?
a. 100m
b. 200m
c. 400m
d. 1500m
7
Activity 1: Speed Problems
Use the circle shown at right to calculate the answers to problems #1-4.
Include the units for each problem as well.
D
1. Calculate the speed for a car that went a distance of 125
miles in 2 hours time.
S
2. A baseball is thrown a distance of 60 meters. What is its speed if it takes
0.5 seconds to cover the distance?
3. How much time does it take a bird flying at a speed of 45 miles per hour to
travel a distance of 1,800 miles?
4. A comet is cruising through the solar system at a speed of 50,000
kilometers per hour for 4 hours time. How far did the comet travel during
this time?
5. A coach wants to find out the speed of the runners on a track team.
What simple equipment does the coach need in order to do this? How
should it be done?
- Equipment Needed:
-
What should be done:
8
T
Activity 2: Analysis of Trends
•
What do you think?
o Current trends indicate that women will start outrunning men in 65
years.
• Is it useful to compare track records over many years of
time?
•
Can future track records be predicted based on past
performances?
Part One
• Look at the graph below, “Speed Versus Year: Men’s Olympic 400-m
Dash”
o The average speed of runners is shown on the vertical axis, and the
year in which the race was run is shown on the horizontal axis.
o Take a moment to be sure you understand that the plotted points
shows a 100-year history of the speeds of male athletes in the
Olympic 400-m dash.
•
Sketch either a straight line or a smooth, curved line through the data
points to show what you think is the shape of the graph.
•
What do you see as the trend of average speed in the 400-m dash over
the past 100 years?
9
•
Make the best guess you can to sketch how the graph would continue to
the year 2020. This process of going beyond the data is called
extrapolation. Try it.
•
According to your extrapolation, what will be the speed of the winning
runner in the men’s Olympic 400-m dash in the year 2020?
Part Two
• Look at the graph below, “Speed Versus Distance: Men and Women,
Penn Relays”
o The average speed of runners is shown on the vertical axis, and the
distance of the race was run is shown on the horizontal axis.
o Make sure you understand that there are two sets of plotted points,
one for men and one for women.
o The points show how average speed varies with distance of the
race for both men and women.
•
Sketch the shapes of the graphs for men and women by connecting the
plotted points with either a straight line or a smooth, curved line.
•
What do you see as the trend of average speed for both men and
women as the distance of the race gets longer and longer?
10
•
Extropolate from the graphs to predict what the record speed at the Penn
Relays would be for the 10,000-m races for both men and women.
•
Try to use extrapolation to find a race distance for which men and women
would run at the same average speed. Comment on your attempt.
Physics to Go
1. A runner had an average speed of 10.14 m/s for 9.86 s. Calculate the
distance the runner traveled.
2. The table below gives the years and the winning times for the women’s
400-m dash in the Olympics.
Women’s 400-m Olympic Dash
Year
Time (Seconds)
Speed (m/s)
1964
52.00
1968
52.00
1972
51.08
1976
49.29
1980
48.88
1984
48.83
1988
48.65
1992
48.83
1996
48.25
2000
49.11
2004
49.41
2008
49.62
a. Calculate the winning speeds in the right column.
b. Plot a speed vs. year graph for the data in the given area on the next
page.
11
c. What is the trend of the average speeds over the past years?
d. From your graph, extrapolate what will be the winning speed in 2020.
12
Activity 2: Speed Practice Problems
Use the formula for speed to help you answer the questions on this page.
Make sure to show your work!
1. What is the average speed of a car that travels 200 km in 4 hours?
2. What is the average speed of a bus that travels 300 m in 4 seconds?
3. What is the distance traveled if a car had an average speed of 50
km/h for 3 hours?
4. What is the distance traveled if an airplane had an average speed
of 160 m/min for 20 minutes?
5. Complete the following chart. Be sure to write out the units for each
speed.
Distance
Time
Speed
10 meters
1 second
40 meters
2 seconds
75 millimeters
3 seconds
5 kilometers
10 hours
25 centimeters
100 seconds
75 meters
100 hours
18 centimeters
36 seconds
10 centimeters
0.5 seconds
50 millimeters
0.5 seconds
13
6. Complete the following chart. Be sure to write out the units for each
time.
Distance
33 meters
Time
Speed
11 m/sec
45 centimeters
15 cm/hour
100 kilometers
3 km/minute
25 meters
50 m/minute
75 centimeters
25 cm/sec
121 meters
11 m/hour
6 meters
0.5 m/sec
0.5 meters
1 m/sec
14
Activity 2.5: Just Strolling Along
•
What do you think?
o How can you measure distance using a stopwatch?
o
Can you walk at a constant speed?
1. Time yourself as you walk a measured distance three times to see if there
is any consistency in your walking.
2. Record the distance that you walked and all the times that you measured
while walking the given distance.
3. Next, calculate your average speed.
Distance (m)
Time (s)
Speed (m/s)
4. Calculate your average speed for all trials: _______________________
5. Now that you have calculated your average speed, use this value to
calculate the distance between two points given to you by your teacher.
• You may use a stopwatch to measure the time it takes to walk from
one point to the other.
Time (s)
Speed (m/s) **from
above**
Mystery Distance
Average Mystery Distance __________________________________
15
Activity 3: Who Wins the Race?
•
What do you think?
o Who wins the race?
• The runner with the highest finishing speed?
•
The runner with the highest average speed?
•
The runner with the greatest top speed?
PART ONE:
Flat Track - Constant Speed
•
In table groups:
o Thread a piece of tape about 1 m long in the timer, and attach
one end to the car.
o Turn on the timer, and pull the car at a nearly constant speed so
that the tape is dragged completely through the timer.
o Cut the tape so that it only shows the dots (no empty space)
•
Find average speed:
o Count the number of ticks (one tick is the distance between two
dots)
o Average speed is cm divided by the number of ticks.
Average Speed = _________ cm/tick
•
Find top speed:
o The one (1) tick where the car was traveling the fastest.
• Using the area where the car was traveling the fastest. Use
the one (1) tick where there is the most distance between
the dots.
Top Speed = _________ cm/tick
•
Find final speed:
o The speed at the end of the race.
• Using the area at the end of the tape – usually the last 3 or 4
ticks.
• Distance in centimeters / number of ticks
Final Speed = _________ cm/tick
16
PART TWO:
Flat Track - Acceleration
•
In table groups:
o Thread a piece of tape about 1 m long in the timer, and attach
one end to the car.
o Turn on the timer, and push the car down the track so it is
accelerating. Make sure the tape is dragged completely through
the timer.
o Cut the tape so that it only shows the dots (no empty space)
•
Find average speed:
Average Speed = _________ cm/tick
•
Find top speed:
Top Speed = _________ cm/tick
•
Find final speed:
Final Speed = _________ cm/tick
PART THREE:
Elevated Track
•
In table groups:
o Elevate the track by putting some books underneath one end.
o Thread a piece of tape about 1 m long in the timer, and attach
one end to the car.
o Turn on the timer, and let gravity pull the car until the tape is
dragged completely through the timer.
o Cut the tape so that it only shows the dots (no empty space)
•
Find average speed:
Average Speed = _________ cm/tick
•
Find top speed:
Top Speed = _________ cm/tick
•
Find final speed:
Final Speed = _________ cm/tick
17
Physics to Go
1. A. Is average speed the same as actual speed at every point?
B. Does gravity make the car go at a constant speed or an accelerated
speed?
2. What would the spacing of dots look like for a ticker tape timer record of
an object that is slowing down in its motion?
3. From what you observed and measured during this activity, describe how
the speed of a toy car behaves as it travels:
a. On a straight ramp that slopes downward:
b. On a level surface when the car already has some speed at the
beginning:
c. On a straight ramp that slopes upward:
4. Aisha and Bert are running at constant speeds, Aisha at 9.0 m/s and Bert
at 8.5 m/s. They both cross a “starting line” at the same time. The “finish
line” is 100 m away.
a. How long does it take Aisha to finish the race?
b. How long does it take Bert to finish the race?
c. Where is Bert when Aisha crosses the finish line?
d. By how many meters does Aisha finish ahead of Bert?
18
Ticker Tape Diagrams
http://www.physicsclassroom.com/class/1Dkin/U1L2b.cfm
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» The Physics Classroom » Physics Tutorial » One Dimensional Kinematics
1-D Kinematics - Lesson 2
Describing Motion with Diagrams
Physics Tutorial
Introduction | Ticker Tape Diagrams | Vector Diagrams
1-D Kinematics
Ticker Tape Diagrams
Newton's Laws
A common way of analyzing the motion of objects in physics
Teacher's Guide
labs is to perform a ticker tape analysis. A long tape is
attached to a moving object and threaded through a device
that places a tick upon the tape at regular intervals of time - say every 0.10 second. As the
object moves, it drags the tape through the "ticker," thus leaving a trail of dots. The trail of
dots provides a history of the object's motion and therefore a representation of the object's
motion.
Vectors - Motion and
Forces in Two
Dimensions
Momentum and Its
Conservation
Work, Energy, and Power
Student Extras
Circular Motion and
Satellite Motion
Thermal Physics
Static Electricity
Current Electricity
Waves
Sound Waves and Music
Light Waves and Color
Reflection and Ray Model
of Light
Refraction and Ray
Model of Light
The distance between dots on a ticker tape represents the object's position change during
that time interval. A large distance between dots indicates that the object was moving fast
during that time interval. A small distance between dots means the object was moving slow
during that time interval. Ticker tapes for a fast- and slow-moving object are depicted below.
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The analysis of a ticker tape diagram will also reveal if the object is moving with a constant
velocity or accelerating. A changing distance between dots indicates a changing velocity and
thus an acceleration. A constant distance between dots represents a constant velocity and
therefore no acceleration. Ticker tapes for objects moving with a constant velocity and with an
accelerated motion are shown below.
1 of 2
11/15/11 12:03 PM
19
20
Activity 3: Ticker Tape Practice
These ticker tapes are of carts rolling along a track. In each case describe
the motion of the cart with a complete sentence or two. Does the cart
speed up, slow down, or move at a constant speed?
21
11. Which one(s) show the cart moving at a constant speed? __________________
12. Which one(s) show the cart speeding up the whole time? __________________
13. Which one(s) could be of a cart going downhill the whole time? ____________
14. Which one(s) could be of a cart going downhill and then along a level
track? ___________________________
15. Which one(s) could be of a cart going uphill the whole time? ______________
16. Which one(s) shows the cart speeding up during part of its trip? _____________
17. Which one(s) shows the cart slowing down during part of its trip? ____________
18. Which one shows the fastest speed during any part of its trip? _______________
19. Which one shows the fastest initial speed? __________________________________
20. Which one shows the fastest final speed? __________________________________
21. Which one is going the slowest at the end of its trip? ________________________
22
Ticker Tape Patterns Analysis Activity
Use your knowledge about ticker timer tape patterns to help you analyze
the ticker tape examples below. Review Ticker Tape Examples.
1.
Describe the motion involved by the object that left the
following ticker tape patterns.
a.
•
•
•
•
•
•
•
•
•
•
•
•
•
b.
•
•
•
•
•
•
c. Find the average speed and final speed of:
a. Cart A:
b. Cart B:
2.
Ticker tape diagrams are sometimes referred to as oil drop
diagrams. Imagine a car with a leaky engine that drips oil at a
regular rate. As the car travels through town, it would leave a
trace of oil on the street. That oil trace would reveal information
about the motion of the car. Explain the action of the car at
each interval.
a.
•
•
•
•
b.
• • • • • • • •
•
•
• • • • • • •
•
•
•
• • • •
•
•
•
c.
•
•
•
•
•
• • • •
•
•
d. Which cart had the greatest top speed?
e. Calculate this greatest top speed in cm/tick.
23
•
3.
Draw a diagram of what the ticker tape might look like for the
following examples.
a. A driver on a two-lane highway is traveling the speed limit
when it comes up behind a tractor pulling a large load of hay
bales. It follows the tractor for a short distance until oncoming traffic has dissipated, then it pulls out and passes it.
After it has passed the tractor it resumes traveling at the
speed limit.
b. A driver is in a small town where there is a lot of pedestrian
traffic. He drives the speed limit and slows to a stop at the
stop sign. After stopping, he begins to drive for a half a block,
when a small child runs out from behind a parked car. The
driver brakes hard and stops, just in time. After the child is
safely on the sidewalk, the driver resumes his trip. A half a
block away, he sees that a group of young people are
crossing the street and slows down. The young people get
across the street before he gets too close. He turns at the next
corner and into his driveway.
c. A roller coaster starts at a high point. As the roller coaster
leaves the dock it drops rapidly for thirty seconds before
climbing to the very highest point of the ride. As it leaves the
top point it drops and rises over three smaller hills before
finishing the rest of the ride.
24
SECTION
SPEED MEASURES HOW FAST POSITION CHANGES.
CHAPTER 1
Motion
1.2 Reading Study Guide A
BIG IDEA The motion of an object can be described and predicted.
KEY CONCEPT Speed measures how fast position changes.
Vocabulary
speed a measure of how fast something moves
velocity a speed in a specific direction
vector a quantity that has both size and direction
Review
1. What type of information should be included when describing an object’s
location from a reference point?
You should note the object’s ____________ and ____________ from the reference point.
Take Notes
I.
Position can change at different rates. (p. 16)
2. To measure speed, you need to know distance and ____________.
same amount of time.
more speed
distance
less speed
distance
in the
same
time
A. Calculating Speed (p. 17)
d
Use the formula for calculating speed (S ! t ) to answer questions 4 and 5.
4. What do each of the variables (letters) stand for?
5. If you travel 80 m in 40 s, what is your speed?
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
3. Fill in the diagram to show how two objects with different speeds move in the
24 MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A
024-025-span-urb-c0102-rsga 24
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25
26
CHAPTER
1
MOTION
Math Practice
CHAPTER 1
Motion
Speed and Distance-Time Graphs
Solve the equations to find the value for each question. Include the
appropriate units in your answer.
1.
S ! 600 m / 15 s
2.
S ! 240 km / 4 hr
3.
S ! 75 mi / 2.5 hr
4.
S ! (35 m " 20 m) / (10 s " 5 s)
5.
S ! (46 m " 18 m) / (10 s " 3 s)
6.
S ! (49 m " 21 m) / (14 s " 7 s)
Use the graph or the formula for speed to answer questions 7–12.
8.
Distance-Time Record for Trip A
A trucker made a delivery to a town 180 km from
his start point. The graph shows the time and
distance for the trip. During which part of the trip
was the trucker driving 55 km/h?
The trucker stopped at a truck stop for a one-hour
lunch break. During which part of the trip did he
take his lunch break?
180
160
140
Distance (km)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
7.
120
100
80
60
40
20
9.
What was the trucker’s speed as he drove from the
truck stop where he had lunch to his final destination?
0
0
1
2
3
4
5
Time (hours)
10.
A jogger runs along a road for a distance of 2700 m. If it takes her 900 seconds
to run that distance, what is her speed?
11.
A car travels 40 miles in the first hour and 50 miles in the second hour. What is
the car’s average speed over the entire trip?
12.
A bicyclist travels 10 km in half an hour, then rests for half an hour, then travels
50 km in three hours. What was the bicyclist’s average speed over the entire trip?
MOTION AND FORCES, CHAPTER 1, MATH PRACTICE 51
050-055-span-urb-c01-ma+mp 51
2/26/04, 10:50:37 AM
27
CHAPTER
MOTION
Math Support
Speed and Distance-Time Graphs
A Cyclist's Speed
d
The formula for speed is S ! —
t
120
S is the speed of the object, d is the distance the
object has moved, and t is the time it took the
object to move that distance.
If information about distance and time is presented
in a graph form, you can find the speed using the
distance and time information given in the graph.
Sometimes this involves subtracting one distance
from another and subtracting one time from another.
distance
120 m–90 m
100
Distance (meters)
CHAPTER 1
Motion
1
80
60
40
20
0
0
10
SAMPLE PROBLEM
20
30
Time (seconds)
time
50s–40s
40
50
Using the graph above, find the bicyclist’s speed between 40 s and 50 s.
Use the graph to find the distance at 50 s:
120 m.
Use the graph to find the distance at 40 s:
90 m.
Find the time interval between 40 s and 50 s:
50 s " 40 s ! 10 s.
120 m " 90 m ! 30 m.
Substitute the distance and the time
into the formula for speed:
d ! —
3m
—
S !—
t
10 s ! 3 m/s
Answer:
Between 40 s and 50 s, the
bicyclist’s speed was 3 m/s.
EXERCISES
............................................................................................................................................................................................
1.
Using the graph above, find the bicyclist’s
speed between 10 s and 30 s.
2.
Using the graph above, find the
bicyclist’s speed between 30 s and 40 s.
Find distances from graph.
Find distances from graph.
Calculate time interval.
Calculate time interval.
Calculate distance traveled.
Calculate distance traveled.
Substitute and solve.
Substitute and solve.
Answer.
Answer.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
Find the distance traveled between 40 s and 50 s:
50 MOTION AND FORCES, CHAPTER 1, MATH SUPPORT
050-055-span-urb-c01-ma+mp 50
28
2/26/04, 10:51:01 AM
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30
31
Activity 3.5: PASCO Motion Sensors
•
What do you think?
o How would you use your body to re-create the following motion
graph? Use some scientific terminology in your response.
100
50
Motion
Motion
0
Motion Sensors
• For each of the following graphs:
o Predict the type of motion needed to re-create the graph.
o Re-create the graph and describe the motion used.
Prediction #1:
Description of Motion:
32
Prediction #2:
Description of Motion:
Prediction #3:
Description of Motion:
33
Prediction #4:
Description of Motion:
** Now for fun, try to create some numbers, names or appropriate words!!**
34
Distance/Time Graph Practice Problems
Examine this graph carefully to answer questions 1 and 2.
1.
How far is the truck from its starting point after:
(a)
10 s
(b)
15 s
(c)
30 s
(d)
40 s
(e)
50 s
2. Under each graph, describe briefly the kind of motion that is taking place in
each of the situations represented by the following distance vs. time graphs.
a)
b)
c)
3.
35
3. Under each graph, describe briefly the motions represented by each of these
graphs. If the speed is changing, state whether it is increasing or decreasing.
a)
b)
c)
Use the following graph for question 4.
4.
a) From the graph above, calculate the average speed for the entire 45 m.
b) Find the average speed for each of the following time intervals:
•
0 m to 15 m
•
15 m to 35 m
•
35 m to 45 m
36
Activity 4: Understanding the Sprint
What do you think?
o It was not believed to be humanly possible to run a mile in less than
four minutes until Roger Bannister of England did it in 1954.
• How much time does it take to get “up to speed?”
For You To Do:
• PART ONE
o Carl Lewis established a world record for the 100-m dash at the
World Track and Field Championship held in Tokyo, Japan in 1991.
The times at which he reached various distances in the race (his
“split times”) are shown in the table below:
Distance
(m)
Time (s)
•
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0.00
1.88
2.96
3.88
4.77
5.61
6.45
7.29
8.13
9.00
9.86
Complete the table below using Lewis’ split times.
o Use subtraction to calculate the time taken by Carl Lewis to run
each 10 m of distance during the race.
o Then, calculate Lewis’ average speed during each 10 m of the
race.
Distance (m)
0.0 - 10.0
Time (s)
Average Speed (m/s)
1.88
5.32
10.0 - 20.0
20.0 - 30.0
30.0 - 40.0
40.0 - 50.0
50.0 - 60.0
60.0 - 70.0
70.0 - 80.0
80.0 - 90.0
90.0 - 100.0
37
•
PART TWO
• Use the data you created for the above table to make a bar graph to
give you a visual display of Carl Lewis’ average speed during each 10
m of his world record 100-m dash.
Carl Lewis' World Record 100-m Dash Average
Speed, 10-m Interval
Average Speed
(m/s)
12
11
10
9
8
7
6
5
4
3
2
1
0
0-10
10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90m
m
m
m
m
m
m
m 100 m
Distance (m)
•
Analyze the bar graph to answer these questions:
1. At what position in the dash did Lewis reach top speed?
2. How well did Carl Lewis keep his top speed once he reached it?
3. Did he seem to be getting tired at the end of the race? Give
evidence.
4. Can you tell how fast Lewis was going at an exact position in
the race, such as 15.0 m or 20.0 m? Why or why not?
38
•
PART THREE
•
Use the “splits” given at the start of this activity to plot a graph of Carl
Lewis’ position versus time.
Plot each position at the appropriate time and connect points to show
what you think is the shape of the graph.
•
Distance (m)
Carl Lewis' World Record for the 100m Distance vs. Time
110
100
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
11
Time (sec)
•
PART FOUR
•
Compare the two graphs and answer the following questions:
1. When the line graph is curving early in the run, do the bars on the
bar graph change in height or are they fairly steady in height?
2. What does this comparison mean?
3. When the line graph is climbing in a straight line, what is happening
to the heights of the bars on the bar graph?
4. What does this comparison mean?
39
40
Activity 4.5: Interpreting Motion Graphs
What do you think?
o If you were to measure the speed of a car rolling down a track, do
you think the car was going the same speed the whole time?
For You To Do:
1. Cut apart the 8 trip strips along the dotted lines.
2. Read the trip strips. Each strip represents a story or one or more
pieces of a story. Some of the strips describe Teasha’s trip to
school. The others describe Josh’s trip.
3. With your partner, identify the strip that matches each segment of
the two motion graphs below.
4. Place each strip onto the segment of the graph that describes it.
41
Analysis
1. Identify a place on each graph where the slope of the line changes. What does a
change in the slope of a motion graph indicate?
2. Which student –Teasha or Josh– started out faster? Explain how you know this.
3. How far into the trip did Josh turn around? Describe what the graph looks like at this
point in the trip.
4. Look at the motion graphs shown below. Match the descriptions here to the correct
graphs:
a. A car moving at a constant speed stops and then moves in the opposite direction
at the same speed.
b. A car moving at a constant speed stops and then moves faster in the same
direction.
c. A car moving at a constant speed changes to a higher constant speed.
d. A car moving at a constant speed changes to a lower constant speed.
42
5. A car that accelerates is one that speeds up, slows down, or changes direction.
Which graph below shows a car continually accelerating? Explain how the shape of
the graph shape shows this.
43
Activity 5: Acceleration
What do you think?
• Your mom is driving you to school with a cup of her favorite Wawa coffee
resting level in the cup holder.
• Describe the action of the coffee (if any) as she:
o Suddenly brakes at a red light
o
•
Presses the accelerator as the light again turns green.
What does it mean to accelerate?
For You To Do:
• In this activity, you will use an “accelerometer,” a device for measuring
acceleration.
• Look at the accelerometer and then answer the following questions in
complete sentences:
o Can you get the liquid in the accelerometer to slant one way or
the other while keeping the accelerometer level?
o
What do you need to do to get the liquid to slant?
PART ONE
Trial 1: Normal Speed (Low Acceleration)
Record the observations of the accelerometer as you are completing each
movement listed below.
• For each one, you should:
o Describe the height and direction the water moves in each of the
each situation.
§ Example: While walking forward from a resting position there
is a slow lean in the water in a forward direction,
o Draw a picture of what happened.
•
Standing still
•
Walking forward from a resting position and speed up a little.
44
•
Walk at a fairly constant speed
•
Walking at a constant speed and then slow down to a stop.
Trial 2: Faster Speed
Record the observations of the accelerometer as you did above for each of
the following movements:
•
Start from a resting position faster and speed up faster (fast acceleration)
•
Walk faster at a fairly constant speed and then slow down to a stop faster.
(fast stop)
Trial 3: Backwards
Record the observations of the accelerometer as you did above for each of
the following movements:
•
Accelerating while going backward.
•
Stopping while going backward.
45
Analysis
•
Someone said, “Deceleration while walking forward is the same as
acceleration while walking backward.”
o Do you agree or disagree?
o Use your observations of the accelerometer for your answer.
PART TWO:
1. Your teacher will set up an accelerometer that will be pulled by a falling
weight. Observe the system and answer the following questions:
a. Does the cart appear to accelerate?
b. How does the accelerometer show you that it’s accelerating?
c. Does the accelerometer show that the acceleration is constant or
changing?
d. How can you tell?
2. Which produced a steadier, constant acceleration: using the falling
weights or walking with the accelerometer?
3. What evidence do you have for your answer?
46
Physics to Go
1. Is there anything in nature that has constant acceleration?
2. If Carl Lewis were to carry an accelerometer during the start of a sprint,
describe what the accelerometer would do?
3. Did Carl Lewis accelerate for the entire 100 m of his world-record dash?
Explain his pattern of acceleration.
4. If you are running, getting tired, and slowing down, are you accelerating?
Explain your answer.
47
48
SECTION
ACCELERATION MEASURES HOW FAST VELOCITY CHANGES.
CHAPTER 1
Motion
1.3 Reading Study Guide A
BIG IDEA The motion of an object can be described and predicted.
KEY CONCEPT Acceleration measures how fast velocity changes.
Vocabulary
acceleration the rate at which velocity changes over time
Review
1.
Sam said he is walking north at a rate of 5 meters per second. Did he describe
his speed or his velocity?
Take Notes
I.
Speed and direction can change with time. (p. 25)
2.
Complete the supporting main-idea chart for acceleration.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
Acceleration
measures how quickly
and
are changing
speed of an object increases when acceleration
speed of an object decreases when acceleration
II. Acceleration can be calculated from velocity and time. (p. 27)
3.
In order to measure acceleration, what two things must you know?
A. Calculating Acceleration (p. 28)
4.
Fill in the words in the formula for acceleration. The first letter is given for
each word.
a____________ ! f____________ v____________ " i____________ v____________
(divided by)
t ____________
MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A 35
035-036-span-urb-c0103-rsga 35
49
2/18/04, 5:14:20 PM
50
Velocity and Acceleration Calculation Practice
Acceleration = final velocity - starting velocity = m or km
time
s2
h2
velocity = distance = m or km
time
s
h
SHOW YOUR WORK by writing the substitution of the numbers for the letters in the
formula. Always include the units in the formula.
1. Starting Velocity = 0 m/s
Final Velocity = 30 m/s
Time = 10 s
Acceleration = ___________
Is this acceleration or deceleration?
(circle one)
2. Starting Velocity = 100 m/s
Final Velocity = 60 m/s
Time = 15 s
Acceleration = ___________
Is this acceleration or deceleration?
(circle one)
3. Starting Velocity = 15 km/h
Final Velocity = 0 km/h
Time = .3 h
Acceleration = ___________
4. Starting Velocity = 6 km/h
Final Velocity = 75 km/h
Time = .25 h
Acceleration = ___________
Is this acceleration or deceleration?
(circle one)
Is this acceleration or deceleration?
(circle one)
51
5. In steamy South America in the cliffs of the Andes mountains, you are 007 in
hot pursuit of the bad guy traveling 1.5 km in 30 seconds (0.0083 hours). What’s
your speed in km/h?
Is this a velocity or acceleration problem? (circle one)
Circle the parts of the question that you’ll use to solve the problem. What are
your final units going to be? _______________
Solve:
Answer:_____________
6. You see the “curve ahead” sign and wonder, “Am I going too
fast?” Suddenly, you see the bad guy’s car skid out of control
going from 160 km/h to 100 km/h in 2 seconds (0.0005 hours)!!
What’s the bad guy’s deceleration?
Is this a velocity or acceleration problem? (circle one)
Circle the parts of the question that you’ll use to solve the problem. What are
your final units going to be? _______________
Solve:
Acceleration Practice Problems
Complete the following acceleration problems using the following formula:
Final Velocity – Initial Velocity
Time
SHOW YOUR WORK!
1. At a drag race, the light turns green and 0.00125 hours later, a dragster is
traveling 300 miles per hour. Calculate the acceleration of the dragster.
2. An object traveling 200 feet per second slows to 50 feet per second in 5
seconds. Calculate the acceleration of the object.
3. A car going 22 m/s accelerates to pass a truck. Five seconds later the car is
going 35 m/s. Calculate the acceleration of the car.
4. Quinn accelerates her skateboard along a straight path from 0 m/s to 4.0 m/s
in 2.5 seconds. Calculate the acceleration of the skateboard.
5. Find the average acceleration of a northbound subway train that slows down
from 12 m/s to 9.6 m/s in 0.8 seconds.
6. Elyse is traveling east on a dirt road when she spots a pothole ahead. She
slows her car from 14.0 m/s to 5.0 m/s in 6.0 seconds. What is the car’s
acceleration?
7. Lillie is running. She increases her initial speed of 30 km/h to 40 km/h so she
can win the race. If she takes 0.05 hours to complete this increase, what is
her acceleration?
53
CHAPTER
CHAPTER 1
Motion
1
MOTION
Math Support
Calculating Acceleration
Use the formula below when you calculate acceleration.
a ! vfinal "t vinitial
Recall that a is the acceleration, t is the time interval during which the velocity
changes, vfinal is the velocity the object has at the end of the time interval, and vinitial
is the velocity the object had at the beginning of the time interval.
SAMPLE PROBLEM
A soccer ball has a speed of 4 m/s. After 10 seconds, it rolls to a stop. What is the
acceleration of the ball?
What do you know?
vinitial ! 4 m/s
vfinal ! 0 m/s
t ! 10 s
Sometimes you may need to interpret a question to determine some of the
information. For example, the phrase “rolls to a stop” means that the object has a
final velocity of 0 m/s.
Solve.
a ! 0 m/s10"s4m/s
4 m/s
a ! "10
! 0 .4 m/s 2
s
When you have an answer, consider if it makes sense. The ball is slowing down, so
the acceleration should be negative.
Answer.
The soccer ball has an acceleration of "0.4 m/s2.
EXERCISES
............................................................................................................................................................................................
1.
A bicyclist initially at rest increases her
speed to 6 m/s in 30 seconds. What is her
acceleration?
2.
A car has an initial velocity of 25 m/s
and 3 s later has a velocity of 49 m/s.
What is the car’s acceleration?
Formula
Formula
Substitute.
Substitute.
Solve.
Solve.
Answer.
Answer.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
Substitute.
52 MOTION AND FORCES, CHAPTER 1, MATH SUPPORT
050-055-span-urb-c01-ma+mp 52
54
2/18/04, 5:28:58 PM
Activity 6: Running a Smart Race
What do you think?
• Good sprinters are usually not good distance runners.
o How do strategies for winning sprints and distance runs differ?
For You To Do:
§ Assume you are running a 1500-m race that requires four laps around an oval
track. You usually run this race at a constant speed in a time of 4 minutes
(240 seconds).
o Calculate and record the distance of each lap of the race.
o
Calculate and record the time it takes you to run one lap.
o
Record how you think you can develop a strategy to win the race.
§
Assume you are running against two opponents, one who starts fast (a
“rabbit”) and another who finishes fast (a “kicker”). You have studied their
split times from earlier track meets. From their splits, you have discovered that
both runners, like you, usually run the 1500-m in 4 minutes. But there are
differences:
o The “kicker” runs the final lap in 58 seconds.
o The “rabbit” runs the final lap in 63 seconds.
§
Calculate the speed of each runner during the final lap of the race in m/s.
(Remember speed = distance/time)
o Kicker
o
Rabbit
o
You
55
•
Make a graph of distance versus time for the three runners for the final lap
of the race.
o Scale distance vertically from 0 to 375 m and scale time horizontally
from 0 to 63.
o Assume that all runners are at d=0 when t=0 and that all runners
keep a constant speed during the final lap.
o Use the individual times to plot a line on the graph for each runner.
o Label the lines.
Attach Graph Here
56
Analysis Questions
1. Look at the distance versus time graph. The graph shows that all three
runners are “even” (375 m remaining to run) at the beginning of the final
lap.
a. In what order will the runners finish the race?
b. By how much time will the winner finish ahead of the second-place
runner? The third-place runner?
c. By how much distance will the winner finish ahead of the secondplace runner? The third-place runner?
*Hint: Speed x time = distance
2. You run the final lap in 60 seconds. During those 60 seconds, how far will
the rabbit and the kicker travel at the speeds calculated above?
**Remember that distance = speed * time
3. How far behind the rabbit can you be at the beginning of the final lap to
win the race?
4. How far ahead of the kicker must you be at the beginning of the final lap
to win the race?
57
Activity 7: Increasing Top Speed
What do you think?
• A cheetah can reach a top speed of 60 miles per hour (about 30 m/s).
o What can a runner do to increase top speed?
For You To Do:
1. Watch the video of the runner.
• Use the total distance traveled and the total time to calculate the
runner’s speed in yards per second.
Speed(m/second) = distance (meters)
time (seconds)
2.
Find Stride Frequency
a. Count the number of strides taken by the runner during the entire run.
b. Use the number of strides and the total time to calculate the runner’s
stride frequency in strides per second.
Stride frequency (strides/second) =
Number of strides
Time (s)
3. Find Stride Length
a. Calculate the average length of one stride for the runner.
b. To do so, measure the length of several single strides and calculate the
average length per stride.
c. The unit for your answer will be m/stride.
Stride Length = distance / # strides
4. Calculate the speed of each runner using stride length & stride frequency.
a. Your answer will be in m/second.
Speed = Stride Frequency x Stride Length
58
5. Compare the results of using the two equations calculating speed.
a. You calculated speed using two different equations. Did your two
answers agree?
b. How good is the agreement?
c. How would you explain any difference in results?
Your Turn:
1. You will test the “new” equation on a 12-meter track.
2. Marks have been placed at .75-meter intervals.
a. Starting from the “zero” mark, walk so that you step on each mark.
b. Count the number of strides to complete the walk, and use a
stopwatch to measure the total time.
Intervals of .75 m on a 12 - m track
Your time _____________ seconds
# of Strides _______
•
Calculate speed using distance/time.
•
Calculate your stride frequency:
o Stride frequency (strides/second) =
•
Calculate your speed using the stride frequency and stride length (.75 m).
o Speed = Stride Frequency x Stride Length
59
Number of Strides
Time (seconds)
•
What do you think happens to your speed if you change your stride
length?
o Increase stride length:
o
Decrease stride length:
Test Your Hypothesis:
Intervals of .50 m on a 12 - m track
Your time _____________ seconds
# of Strides _________
•
Calculate speed using distance/time.
•
Calculate your stride frequency:
o Stride frequency (strides/second) =
•
Calculate your speed using the stride frequency and stride length (.50 m).
o Speed = Stride Frequency x Stride Length
Number of Strides
Time (seconds)
Comparison:
•
On the .50 meter interval track, you calculated speed two different ways.
How well do your speeds calculated by both methods on this track
compare?
60
•
Compare your performances on the two different tracks.
o Was your speed on the track that had 0.75 m stride lengths about
the same as, different from, your speed on the track, which had
0.50 m intervals? Why?
o
If you must step on each mark, what would you need to do to
make your speed on the second track equal to your speed on the
first track?
Physics To Go:
1. A runner’s stride length is 2.0 m and her frequency is 1.8 strides/s.
o Calculate her average speed.
o
What would be her time for a 200-m race?
2. A runner maintains a constant speed of 6.0 m/s. If his stride length is 1.5 m,
what is his stride frequency?
3. If the runner in Question 2 increases his stride length to 1.6 m without
changing his stride frequency, what will be his new speed?
4. If a marching band has a frequency of 2.0 strides/s and if each stride
length is 0.65 m, what is the band’s marching speed?
61
Activity 8: Projectile Motion
What do you think?
• What is the path of a ball that rolls off the table and falls to the floor?
•
Do you think the speed a ball is going has any bearing on the time it takes
to drop from the table to the floor?
For You To Do:
•
•
•
Set up a ramp by placing books or blocks at the end of the aluminum
track so that the other end of the ramp is a few inches before the edge of
the table.
From the desired position on the track, roll a tennis ball down the ramp so
that it rolls off the table and strikes the floor.
On the chart below:
o Sketch the path taken by the ball from the end of the table until it
reaches the floor.
o Use a stopwatch to time the ball from when it leaves the edge of
the table until it strikes the floor. Record the times and calculate
the average time.
o Mark where the ball strikes the floor, then measure the distance.
1/3 of way up track
2/3 of way up track
All the way up track
Sketch of Path:
Sketch of Path:
Sketch of Path:
Average Time (s):
Average Time (s):
Average Time (s):
Distance from Table (cm):
Distance from Table (cm):
Distance from Table (cm):
Speed of the Ball (cm/s)
Speed of the Ball (cm/s)
Speed of the Ball (cm/s)
62
Analysis:
•
How does the release point of the ball affect the speed of the ball?
•
How does the speed affect the amount of time it takes for the ball to fall
from the edge of the table to the floor? (Compare all three runs)
•
How does the release point of the ball affect how far from the table the
ball strikes the floor?
63
Activity 8.5: Gravity – Measuring
“g”
Objective: To find the acceleration of an object in freefall.
Materials: Ball, stopwatch, calculator
Background: This experiment will use very basic equipment to measure an
important quantity, the acceleration of an object in freefall. This is also known as
the acceleration due to gravity, or g. The acceleration due to gravity is nearly
the same at all points on the earth’s surface, or about 10 m/s. You will compare
your result to this accepted value.
Procedure:
1. Choose one person to be a ball dropper.
a. This person will drop a ball from the top of the bleachers.
They will have their arm straight out on the top railing of the
bleachers and drop the ball straight down.
2. Choose another person to be the timer.
3. Choose a third person to be the recorder.
4. Drop the ball from the designated height ten (10) times and record
the time in the chart below.
a. Be sure to time exactly from when the ball is released to
when it strikes the ground.
Tr ial
1
Drop Distance (m )
2
3
4
5
6
7
8
9
10
5. Find the average time. _________________ seconds
64
Tim e (s)
6. When an object moves with constant acceleration from rest, it’s
distance can be found by using the following equation:
d=
1
g t2
2
Manipulate this equation and solve for g
g=
2d
t2
65
66
67
68
69
Acceleration Due to Gravity Calculations
1. Solve for Velocity using V = G x T
a. A penny dropped into a wishing well reaches the bottom in 1.50
seconds. What was the velocity at impact?
b. In a bizarre but harmless accident, Superman fell from the top of
the Eiffel Tower. How fast was Superman traveling when he hit the
ground 7.8 seconds after falling?
c. A water balloon was dropped from a high window and struck its
target 1.1 seconds later. What was its velocity on impact?
2. Solve for Distance using
D=
1
g t2
2
a. A stone tumbles into a mineshaft and strikes bottom after falling for
4.2 seconds. How deep is the mineshaft?
b. A volleyball serve was in the air for 2.2 seconds before it landed
untouched in the far corner of the opponent’s court. What was the
maximum height of the serve?
c. A boy threw a small bundle toward his girlfriend on a balcony 10.0
meters above him. The bundle stopped rising in 1.5 seconds. How
high did the bundle travel? Was that high enough for her to catch
it?
70
Activity 9: Projectile Motion Online Lab
http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html
What is the effect of Launch Angle on the motion of a projectile?
•
•
Refresh the web page and set these variables: Mass = 10 kg Initial Velocity = 50 m/s
Make sure the “show trails” is checked and that “air resistance” is NOT checked
Angle of
Launch
Maximum
Range
(distance)
(degrees)
(meters)
Maximum Elevation
(height)
(meters)
End Velocity
Total Time
(m/s)
(s)
10
20
30
40
45
50
60
70
80
90
1. At what angle was the maximum range (horizontal distance) reached?
___________
2. At what angle was the maximum elevation achieved? ________________
3. At what angle was the greatest "hang" time achieved? _______________
71
4. Compare the maximum range (horizontal distance) reached for these pairs
of launch angles.
a.
10o = __________ meters and 80o = __________ meters
b.
20o = __________ meters and 70o = __________ meters
c.
What pattern is observed for these angles and their maximum
ranges?
________________________________________________________________
_________________________________________________________________
c.
Do you notice any other paired combinations in the data table
that share the same maximum range? _______ List them:
____________ ___________
5. A projectile is launched at an initial speed of 50 m/s with a horizontal angle of
76o . Use the simulation to answer these questions: What is its range? ________
State another angle that will produce the same range. _________
a. Does the simulation verify your prediction? _____________
b. What is the sum of the two angles that produce this range? __________.
72
Part Two: Forces
73
Activity 10: Inertia Around A Curve
What Do You Think?
o
Which type of car, a heavier or lighter one, needs more force to
slow down with the same deceleration?
Procedure:
o
o
Set up the circular track as shown to the left, and make sure it is
placed where everyone in your group can easily see it.
o Practice sending the metal marble counterclockwise
around the inside of the circular track with enough speed
to make it go around two or three times before stopping.
o Set the opening to “A”
o Predict where you think the metal marble will roll once it
has gone around the circular track and travels out
through the opening.
o Place the miniature road cone on the table to mark the
position of your prediction.
Write your observations below:
74
o
o
o
o
o
o
o
o
Set the opening to “B”
Predict where you think the metal marble will roll once it has gone
around the circular track and travels out through the opening.
Place the miniature road cone on the table to mark the position of
your prediction.
Write your observations below:
Set the opening to “C”
Predict where you think the metal marble will roll once it has gone
around the circular track and travels out through the opening.
Place the miniature road cone on the table to mark the position of
your prediction.
Write your observations below:
75
Analysis:
Change in Motion
Force Responsible
Marble Accelerated from Rest
Marble goes in a circle
Marble slows down
Analysis Questions:
1) Describe the changes in direction and speed of the marbles when they
traveled:
a. Inside the circular track
b. Outside the circular track
2) Describe the changes in the path of the marble that occurred when you
changed:
a. The opening position of the circular track
b. The mass of the marble
76
3) Imagine that a car is approaching a curve in the road when it suddenly loses
its steering and brakes. The area is flat and there is no guardrail on the road.
a. On the diagram below, draw a line showing the car’s path
when it loses its steering and brakes.
b. Explain why the car will take that path.
c. How would your answer change if the car has more mass?
Explain.
77
78
79
Activity 11: The Net Force Challenge
What Do You Think?:
o Can you describe the motion of these blocks?
Procedure:
Part A: Balanced Forces
1. Place the block on the table, and hook both force meters to it as shown
below.
Note: Each mark on the force meter is 0.1 N
2. While NOT moving the block, have one group member pull gently with 1.0
N on one force meter, while another pulls gently with 1.0 N on the other
force meter.
3. Draw a force diagram of the block below.
Part B: Unbalanced Forces
4. Pull gently with 1.5 N on one force meter, while another group member
pulls gently with 1.0 N on the other force meter. The other group members
should watch the block and observe its motion.
5. Switch roles, and repeat step 4 until each group member gets to pull the
block and observe its motion.
6. Discuss with your group members the motion of the block.
7. Was the block accelerating? How do you know?
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8. Draw another force diagram below and record the forces from step 4.
Nonzero Net Force
Part C: The Challenge
In this part of the activity, your challenge is to decide if the forces on the block
are balanced or unbalanced.
9. Unhook one of the force meters. Place two metal cylinders on the block
and secure them with the rubber band as shown below.
10. Practice pulling gently on the force meter so that the block slides steadily
and as slowly as possible.
11. When you can do this well, read the force needed to pull the block slowly
and steadily.
12. Switch roles, and repeat steps 10 and 11 until each group member gets to
pull the block and observe its motion.
13. With your group members, discuss the motion of the block.
14. Identify all the forces on the block.
15. Is the block accelerating or not? How do you know?
16. Draw a force diagram of the block at Step 11. Title your diagram “Zero
Net Force” or “Nonzero Net Force” depending on the conclusion of your
group.
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Analysis Questions
1. Describe an example and draw a force diagram of a situation with:
Example
Force Diagram
Balanced Forces
Unbalanced Forces
2. Imagine that a parked car is hit from the left with 30,000 N of force at
the exact same time it is hit from the right with 40,000 N of force.
a. Draw a force diagram showing the two forces acting on the
parked car.
b. Draw another force diagram showing only the net force on the
parked car.
3. The force diagram below shows an object with zero net force, but
there is one force missing. What is the missing force? Label is on the
diagram.
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4. Looking back at your work from Part A. Could the block in Part A have
been moving? Explain.
5. For each situation a-e below, explain why there is or is not a zero net
force acting on the car.
a. A car is parked on a level parking space.
b. A traffic light turns green, and a car starts to move.
c. A car drives steadily at 25 mph.
d. A car is slowing down from 30 mph to 10 mph.
e. A car goes around a corner at 10 mph.
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Name
Date
Anticipation Guide: Newton’s Laws of Motion
Before starting the activity, mark whether you agree (+) or disagree (—) with each
statement below.
After completing the activity, mark whether you agree (+) or disagree (—) with each
statement below. Under each statement, explain how the activity gave evidence to
support or change your ideas.
Before
After
1. The heavier the car, the more force is needed to make it
speed up.
2. A force is always needed to keep an object moving.
3. A force is always needed to slow down an object.
4. It takes more force to slow down a small car than a large
©2006 The Regents of the University of California
truck, because the truck is heavier.
5. When a falling object hits the ground, the ground applies
an upward force on the object.
6. Friction exists only when two solid objects rub against
each other.
Issues and Physical Science • Student Sheet 80.1
E-73
84
Activity 12 - Newton’s Laws of Motion
Stopping to Think Questions
1. Which has more inertia: a heavy ball or a light ball rolling at the same
speed in the same direction? Think about which one is more resistant to a
change in motion.
2. What would happen to a baseball if you could throw it in outer space?
Explain in term of inertia and friction.
3. A car travels along a straight road at a steady 40 mph. Are the forces on
the car balanced or unbalanced? Explain.
4. Can a light object that was hit with a small force accelerate as rapidly as
a heavier object hit with a big force? Why or why not?
5. If you hold a backpack in your hand, the force of gravity pulls it
downward. What force keeps it from falling to the ground?
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Activity 12: Newton’s Laws of Motion
Analysis Questions
6. Spaceships that travel millions of miles into outer space use very little fuel.
How can they go so far on so little fuel?
7. Use Newton’s laws to explain why it is easier to turn a truck when it is
empty than when it is carrying a heavy load.
8. An engine can exert a force of 1,000 Newtons. How fast can this engine
accelerate:
a. A 1,000 kg car?
b. A 2.000 kg car?
9. Use Newton’s third law to explain why a blown up but untied balloon will
fly around the room when you let it go.
10. Motor oil, axle grease, and other lubricants are slippery. Why do you think
people spend the money to put these lubricants in their cars?
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88
CHAPTER
FORCES
2 Math Support
Using F = ma
In the formula F ! ma, F ! force, measured in newtons (N); m ! mass, measured in
kilograms (kg); and a = acceleration, measured in meters per second squared (m/s2).
One newton ! 1 kilogram meter per second squared; 1 N ! 1 kgpm/s2
SAMPLE PROBLEM
How much force is needed if the mass is 10 kg and the acceleration is 100m/50s2?
What do you know?
F ! ma
m ! 10 kg, a ! 2 m/s2
Substitute.
F ! 10 kg • 2 m/s2
Calculate.
F ! 20 kg • m/s2 or 20 N
Check units.
CHAPTER 2
Forces
Formula
Force is measured in newtons (N).
EXERCISES
............................................................................................................................................................................................
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
Solve for force.
1. m ! 75 kg, a ! 3 m/s2
2. m ! 4 kg, a ! 6 m/s2
Formula
Formula
Substitute.
Substitute.
Calculate.
Calculate.
Check units.
Check units.
Solve for mass.
Solve for acceleration.
3. F ! 45 N, a ! 39 m/s2
4. F ! 45 N, m ! 6 kg
Rearrange formula.
Rearrange formula.
Substitute.
Substitute.
Calculate.
Calculate.
Check units.
Check units.
MOTION AND FORCES, CHAPTER 2, MATH SUPPORT 125
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2/19/04, 2:09:23 PM
89
CHAPTER
2
FORCES
Math Practice
Finding Force, Acceleration, and Mass
Solve each equation. Use correct units. Remember to show all work.
1. m ! 5 kg, a ! 8 m/s2
2. F ! 75 N, a ! 5 m/s2
Solve for force.
Solve for mass.
4. F ! 12 N, a ! 6 m/s2
3. m ! 15kg, F ! 60 N
Solve for acceleration.
Solve for mass.
CHAPTER 2
Forces
5. F ! 220 N, a ! 11 m/s2
6. m ! 7 kg, a ! 5 m/s2
Solve for mass.
Solve for force.
7. m ! 42 kg, a ! 25 m2
8. m ! 75 kg, F ! 425 N
Solve for force.
Solve for acceleration.
9. m ! 27 kg, F ! 108 N
Write and solve an equation to find the missing quantity.
10. A bowling ball with a mass of 7 kg leaves your hand with an acceleration of
63 m/s2. What size force did you apply?
11. How much does a 5 kg cart accelerate when you lift it with exactly 45 N of force?
12. Suppose you and a classmate push a cart loaded with bricks to demonstrate
force. You apply a force of 500 N, and the cart accelerates at a rate of 0.5 m/s2.
What mass does the cart have?
13. You push a merry-go-round on which your friend is riding. Your friend weighs
45 kg, and the merry-go-round weighs 163 kg. The merry-go-round leaves
your hand with an acceleration of 52 m/s2. What size force was applied?
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
Solve for acceleration.
14. It takes a force of about 45 N to lift your backpack. You lift it with an
acceleration of 3 m/s2. What is the mass of the backpack?
126 MOTION AND FORCES, CHAPTER 2, MATH PRACTICE
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90
SECTION
FORCES ACT IN PAIRS.
2.3 Reading Study Guide A
BIG IDEA
Forces change the motion of objects in predictable ways.
KEY CONCEPT
Forces act in pairs.
Vocabulary
Newton’s third law every time one object exerts a force on a second object, the
second object exerts a force that is equal and opposite in direction
Review
What two factors determine the acceleration of an object?
Take Notes
I.
Newton’s third law relates action and reaction forces. (p. 57)
2.
Describe the forces at work between the bat and baseball.
A. Action and Reaction Pairs (p. 58)
3.
Describe the action and reaction forces that occur between the diver and the
diving board.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company
CHAPTER 2
Forces
1.
100 MOTION AND FORCES, CHAPTER 2, READING STUDY GUIDE A
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Adventures in Energy Skate Park
Skateboarding has seen an immense growth in popularity over the last
several years. What started as a way for surfers to kill time when the waves
were not high enough for surfing has turned into an organized,
competitive sport that boasts internationally known athletes and a million
dollar industry. One way physics comes into play in the half-pipe is with
the principle of conservation of energy. This principle states that energy
cannot be added or subtracted from the original energy of a system.
Energy can, however, be transformed, between forms. The primary forms
of energy that skaters experience in the half pipe are potential energy
and kinetic energy. Potential energy is stored energy that is related to
height. When skaters are at the tops of the ramps, they have the highest
amount of potential energy. Kinetic energy is energy of motion. The faster
skaters move, the more kinetic energy they have. In a half pipe, energy is
constantly transformed between potential (at the top) and kinetic (as
they travel down the sides) as the skater goes back and forth between
the ramps. However, they cannot continue this movement forever, due to
the force of friction which acts against skaters, causing them to slow down
unless they apply more force to their movements.
Read the text above to answer questions 1-4:
1. Define potential and kinetic energy.
• Potential
•
Kinetic
2. Describe when potential and kinetic energy are at their highest in
the half pipe.
3. Why did skateboarding begin?
4. What force acts against the skateboard and slows skaters down?
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THE LAB ACTIVITY
Purpose – The purpose of the energy skate park simulation is to see how
energy gets transferred in a real world application. In this simulation you
will manipulate the skater and track to determine how it affects the
energy of the system. In our skate park, there is no friction, so you will not
be dealing with that factor.
START THE SIMULATION:
http://phet.colorado.edu/new/simulations/sims.php?sim=Energy_Skate_P
ark
Click on Run Now (Green button)
As the skate park opens on your screen, observe the movements of the
skater in the half pipe.
1. Does the skater hit the same height on the opposite sides of the
track? (Use the “pause” button and the measuring tape to help
you determine this!)
Now, turn on the energy Pie Chart, Energy vs. Position Graph, and Bar
Graph. (You may need to move things around a little to see everything.)
2. On all three visual aids, what color represents potential energy and
which is kinetic energy?
• Potential energy
•
Kinetic energy
3. When does the skater have the highest amount of kinetic energy?
4. When does the skater have the highest amount of potential
energy?
5. When does the skater have the lowest amount of kinetic energy?
6. When does the skater have the lowest amount of potential energy?
7. Describe how the bar graph changes as the skater moves along
the track.
• What happens when the skater is high on the track?
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•
What happens when the skater is low on the track?
8. Explain which visual aid (the pie, energy vs. position, or bar graph)
helps you understand conservation of energy better, and why.
PART B: CREATING A SKATE PARK
9. Thanks to your great skateboarding skills, city officials have asked
you to add your expertise with designing a new skate park.
• Experiment with the different tracks that are available under
the tracks icon at the top of the page and build your idea of
the perfect track.
• Draw your track below.
o If your first track did not work (skater got stuck or fell
off), design another track and explain why your first
idea didn’t work.
o How can you use what you know about kinetic and
potential energy to help you with your designs?
CONCLUSION
10. What affects the relationship between potential and kinetic
energy?
JFF – Just for fun (IF YOU FINISH EARLY!!)
1. See if you can have the skater do two loops. Draw your track.
2. See if you can have the skater go airborne, but land on another
track.
3. See if you can have the skater say cow-a-bunga.
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Active Physics: Sports
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