Description
Physics Lab with 3 docs.
Unformatted Attachment Preview
This lab explores the behavior of objects in elastic collisions and how
differences in mass may affect those collisions.
Preparation (15 minutes)
• Activity 1: Elastic Collision with Equal Masses (25 minutes)
• Activity 2: Elastic Collision: Mass Added to Cart A (25 minutes)
• Activity 3: Elastic Collision: Mass Added to Cart B (25 minutes)
Note: Additional time (one to two hours) will be needed to complete the
lab report following the activities. Read through the Momentum
Investigation Manual, including the overview, objectives, and
background information.
•
Review what materials will be needed (p. 6), the Safety procedures (p. 7
), and acquire the needed materials that are not already supplied.
•
•
•
•
•
•
Prepare for the activity by reading through the entire set of instructions
prior to starting. The instructions are found on pages 8–18.
Set out all materials necessary for this activity that are listed in the
Materials section (p. 6) in preparation to perform the activity.
Ensure that you have set aside the necessary time to perform the
activity. This is listed in the Time Requirements section (p. 3).
Perform the activities (pp. 10–18), following the instructions carefully.
Allow additional time (one to two hours) to complete the lab report, and
upload the lab report document when finished.
Use the PHY 150 M7 Momentum Lab Report template to complete the
lab assignment.
Momentum
Student Name
Date
Activity 1: Elastic Collision with Equal Masses Data Table 1
Table 1A. Cart A before collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Average time, t
(s)
Velocity = d/t
(m/s) vA
Average time, t
(s)
Velocity = d/t
(m/s) vA’
Average time, t
(s)
Velocity = d/t
(m/s) vB’
Trial 1:
Trial 2:
Trial 3:
Table 1B. Cart A after collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Trial 1:
Trial 2:
Trial 3:
Table 1C. Cart B after collision.
Cart B mass, m Distance, d (m)
(kg)
Time, t (s)
Trial 1:
Trial 2:
Trial 3:
Calculations for Activity 1. Elastic Collision with Equal Masses
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
Helpful equations:
Momentum before the collision = +
Momentum after the collision = ′ + ′
+ = ′ + ′
= |
first value − second value
| 100%
first value + second value
2
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation).
2. Calculate the percent difference between the two values.
3. Explain any difference in the values before and after the collision.
1
© 2016 Carolina Biological Supply Company
Activity 2: Elastic Collision: Mass Added to Cart A Data Table 2
Table 2A. Cart A before collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Average time, t
(s)
Velocity = d/t
(m/s) vA
Trial 1:
Trial 2:
Trial 3:
Table 2B. Cart A after collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Average time, t Velocity = d/t
(s)
(m/s) vA’
Trial 1:
Trial 2:
Trial 3:
Table 2C. Cart B after collision.
Cart B mass, m Distance, d (m)
(kg)
Time, t (s)
Average time, t
(s)
Velocity = d/t
(m/s) vB’
Trial 1:
Trial 2:
Trial 3:
Calculations for Activity 2. Elastic Collision: Mass Added to Cart A.
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
Helpful equations:
Momentum before the collision = +
Momentum after the collision = ′ + ′
+ = ′ + ′
= |
first value − second value
| 100%
first value + second value
2
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation).
2. Calculate the percent difference between the two values.
2
© 2016 Carolina Biological Supply Company
3. Explain any difference in the values before and after the collision.
Activity 3: Elastic Collision: Mass Added to Cart B Data Table 3
Table 3A. Cart A before collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Average time, t
(s)
Velocity = d/t
(m/s) vA
Average time, t
(s)
Velocity = d/t
(m/s) vA’
Average time,
t (s)
Velocity = d/t
(m/s) vB’
Trial 1:
Trial 2:
Trial 3:
Table 3B. Cart A after collision.
Cart A mass, m Distance, d (m)
(kg)
Time, t (s)
Trial 1:
Trial 2:
Trial 3:
Table 3C. Cart B after collision.
Cart B mass, m Distance, d (m)
(kg)
Time, t (s)
Trial 1:
Trial 2:
Trial 3:
Calculations for Activity 3. Elastic Collision: Mass Added to Cart B.
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
Helpful equations:
Momentum before the collision = +
Momentum after the collision = ′ + ′
+ = ′ + ′
= |
first value − second value
| 100%
first value + second value
2
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation).
2. Calculate the percent difference between the two values.
3
© 2016 Carolina Biological Supply Company
3. Explain any difference in the values before and after the collision.
Questions for Momentum:
1. The law of conservation of momentum states that the total momentum before a
collision equals the total momentum after a collision provided there are no
outside forces acting on the objects in the system. What outside forces are
acting on the present system that could affect the results of the experiments?
2. What did you observe when Cart A containing added mass collided with Cart B
containing no mass? How does the law of conservation of momentum explain
this collision?
3. In one of the experiments, Cart A may reverse direction after the collision. How is
this accounted for in your calculations?
4
© 2016 Carolina Biological Supply Company
Momentum
Carolina Distance Learning
Investigation Manual
2
Table of Contents
Overview …………………………………………………………………………………………… 3
Objectives …………………………………………………………………………………………. 3
Time Requirements ……………………………………………………………………………. 3
Background ………………………………………………………………………………………. 4
Materials ……………………………………………………………………………………………. 6
Safety ………………………………………………………………………………………………… 7
Alternate Methods for Collecting Data using Digital Devices. …………. 8
Preparation ……………………………………………………………………………………….. 9
Activity 1. Elastic Collision with Equal Masses ………………………………….. 10
Activity 2. Elastic Collision: Mass Added to Cart A ………………………….. 13
Activity 3. Elastic Collision: Mass Added to Cart B ………………………….. 16
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Overview
In the following activities, students will investigate how the law of conservation of
momentum applies to collisions. Students will perform a series of experiments
and record data on mass, distance, and time, which are used to calculate the
velocity and momentum of moving components of a system before and after a
collision.
Objectives
Observe collisions between two dynamic carts
Determine how differences in cart mass affect the collisions
Apply the law of conservation of momentum to collisions
Time Requirements
Preparation ………………………………………………………………………… 15 minutes
Activity 1 ……………………………………………………………………………. 25 minutes
Activity 2 ……………………………………………………………………………. 25 minutes
Activity 3 ……………………………………………………………………………. 25 minutes
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Background
Momentum is a vector. The momentum p of an object is the product of its mass m (in
kg) times its velocity v (in m/s), as in the following equation:
=
The law of conservation of momentum holds that the amount of momentum in a system
must remain constant if that system is not affected by external forces.
The law of conservation of momentum is often applied to analyzing collisions, because
if there are no external forces on the system, the total momentum of all the
components of the system before the collision must equal the total momentum of those
components after the collision.
The game of pool offers a good example of the law of conservation of momentum.
Consider a cue ball that strikes a stationary pool ball (Figure 1). The cue ball starts with a
mass m1 and a velocity v1. The stationary ball starts with a mass m2 and a velocity v2,
After the collision, the two balls move at different velocities than those before the
collision, but the total momentum of the system (i.e., the sum of the momentums of
each ball) will be the same before and after the collision.
Figure 1
The application of the law of conservation to this example is demonstrated by the
following equation:
1 + 2 = 1 ′ + 2 ′
1 1 + 2 2 = 1 1 ′ + 2 2 ′
Note: By convention, momentum and velocity after the collision are indicated with a
“prime” symbol (‘). v’ is read “v prime”.
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Consider the collision of two billiard balls. The cue ball has a mass m1 of 0.17 kg and an
initial velocity v1 of 3 m/s. The cue ball strikes a stationary pool ball that has a mass m2 of
0.17 kg and a v2 of 0 m/s. After the collision, the cue ball has a velocity v1’ of 1.2 m/s.
What is the final velocity of the other ball?
The law of conservation of momentum can be applied using the following equations:
1 1 + 2 2 = 1 1 ′ + 2 2 ′
(0.17 ) (3 ) + (0.16 ) (0 ) = (0.17 ) (1.2 ) + (0.16 )( 2′ )
0.51 ∙ = 0.204 ∙ + (0.16 )( 2′ )
0.306 ∙ = (0.16 )( 2 ′)
′
2 = 1.9 /
The momentum before the collision, represented by the left side of the equation, should
equal the momentum after the collision, represented by the right side of the equation.
(0.17 ) (3
) + (0.16 ) (0 ) = (0.17 ) (1.2 ) + (0.16 )(1.9 )
0.51 ∙ = 0.51 ∙
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Materials
Included in the central materials kit:
Tape measure
String
Pocket scale
Washers/weights
Protractor
1
1
1
30
1
Included in the Mechanics Module materials kit:
Foam board
Dynamic carts
Needed but not supplied:
Book
Calculator or computer
Masking tape
Permanent marker
Optional: Smartphone/tablet or other
digital recording device
1
2
1
1
1
1
Reorder information: Replacement supplies for the DL Physics Momentum investigation
(kit 580404) can be ordered from Carolina Biological Supply Company. Call 1-800-3345551 to order.
©2015 Carolina Biological Supply Company
7
Safety
Safety goggles should be worn at all times during these activities.
Read all the instructions for this laboratory activity before beginning. Follow the
instructions closely and observe established laboratory safety practices, including
the use of appropriate personal protective equipment (PPE) described in the Safety
and Procedure section.
Safety goggles should be worn during these activities, which involve the movement
and acceleration of objects. Take care during the execution of these activities to avoid
injuring hands and fingers or feet and toes through contact with moving or falling
objects. Make sure the area is clear of pets, children, and breakable objects.
Do not eat, drink, or chew gum while performing this activity. Wash your hands with
soap and water before and after performing the activity. Clean up the work area
with soap and water after completing the investigation. Keep pets and children
away from lab materials and equipment.
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Alternate Methods for Collecting Data using Digital Devices.
Much of the uncertainty in these experiments arises from human error in measuring the
times of events. Some of the time intervals are very short, which increases the effect of
human error due to reaction time.
Observing the experiment from a good vantage point that removes parallax errors and
recording measurements for multiple trials helps to minimize error, but using a digital
device as an alternate method of data collection may further minimize error.
Many digital devices, smart phones, tablets, etc. have cameras and software that
allow the user to pause or slow down the video.
If you film the experiment against a scale, such as a tape measure, you can use your
video playback program to record position and time data for the carts. This can
provide more accurate data and may eliminate the need for multiple trials.
If the time on your device’s playback program is not sufficiently accurate, some
additional apps may be available for download.
Another option is to upload the video to your computer. Different video playback
programs may come with your operating system or software suite or may be available
for download.
Some apps for mobile devices and computer programs available for download are
listed below, with notes about their features.
Hudl Technique: http://get.hudl.com/products/technique/
iPhone/iPad and Android
FREE
Measures times to the hundredth-second with slow motion features
QuickTime http://www.apple.com/quicktime/download/
Free
Install on computer
30 frames per second
Has auto scrubbing capability
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Preparation
Watch the following video for an overview of how to assemble your momentum carts.
http://bcove.me/qcsf1m6i
1. Attach a rubber stopper to the front of one cart with the steel nut provided. This is
Cart A.
2. Secure a steel spring with a rubber stopper and attach it to the front bumper of the
other cart. This is Cart B.
3. On a level surface such as a table, set up a ramp at an angle of 10-15° using the
foam board and one or more books (Figure 2). Use a protractor to measure the
angle.
Note: The foam board may bend in the middle as the cart rolls down the ramp,
especially in later experiments when mass is added. It may be necessary to add
one or more books beneath the foam board for support. The angle of the board
should allow the cart to transition from the board to the table without its front end
or rubber stopper contacting the table.
4. Secure the tape measure along the level surface where the carts will move. The
starting point of the tape measure should begin at the lower end of the foam
board.
5. Using pieces of masking tape, mark 10-cm increments along length of the table.
6. Mark the piece of tape 20 cm from the foam board as the start point.
7. Mark the piece of tape 70 cm from the foam board as the end point.
8. Place Cart B behind the end point so that the steel spring is behind the piece of
tape.
9. Place a book at the other end of Cart B so that the steel spring is behind the end
point when Cart B makes contact with the book. (See Figure 2)
10. Place Cart A at the top of the foam board so that the back end of the cart is even
with the end of the board. Use a permanent marker or piece of tape to make a line
on the board indicating the release point. The front of the cart should be behind this
line at the start of every trial.
Note: See Figure 2 for a visual depiction of the experimental set-up.
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Figure 2
Activity 1. Elastic Collision with Equal Masses
1. Measure the mass of Cart A and Cart B and record the data in the appropriate
section of Tables 1A, 1B, and 1C.
2. You will now measure the initial velocity vA of Cart A. Remove Cart B, and place
Cart A behind the release point at the raised end of the foam board.
3. Release Cart A, and allow Cart A to travel down the ramp onto the level surface.
4. Measure the time it takes for Cart A to travel from the start point to the end point.
Start the timer when the back end of Cart A crosses the start point, and stop the
timer when the front end of Cart A strikes the book. The distance for this trial will be
50 cm.
5. Repeat this process for three trials, and record the data in Data Table 1A.
6. You will now determine the final velocity vA’ of Cart A. Place Cart B on the level
surface. The spring should be at the start point.
7. Place Cart A at the raised end of the foam board behind the release point.
8. Release Cart A, and allow Cart A to impact Cart B. It is important that the impact is
straight and that both carts travel in a straight line along Cart A’s original direction
after the collision.
9. Start timing when Cart A collides with Cart B and until Cart A stops moving.
10. Observe the distance Cart A travels after the collision. If the cart does not move the
distance is zero, and if the cart moves backward the distance is negative.
11. Record the distance Cart A moves after the collision and record this distance in
Data Table 1B.
12. Repeat this process for three trials. Record the time for each trial in Data Table 1B.
13. You will now measure the final velocity vB’ of Cart B. Place Cart A at the raised end
of the foam board behind the release point.
14. Release Cart A, and allow Cart A to impact Cart B. It is important that the impact is
straight and that both carts travel in a straight line along Cart A’s original direction
after the collision.
15.Record the time for Cart B to travel from the start point to the end point. This
distance is 50 cm. Record this value in Data Table 1C.
16. Repeat this process for three trials, and record the data in Table 1C.
17. Complete Data Tables 1A, 1B, and 1C by calculating the average velocity of the
carts before and after the collision.
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Data Table 1A.
Cart A mass,
m1 (kg)
Cart A before collision.
Distance, d (m) Time, t (s)
Data Table 1B.
Cart A mass,
m1 (kg)
Cart A after collision.
Distance, d (m) Time, t (s)
Data Table 1C. Cart B after collision.
Cart B mass, m2 Distance, d (m) Time, t (s)
(kg)
Average time,
t (s)
Velocity = d/t
(m/s) vA
Average time,
t (s)
Velocity = d/t
(m/s) vA’
Average time,
t (s)
Velocity = d/t
(m/s) vB’
Calculations for Activity 1. Elastic Collision with Equal Masses.
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation).
2. Calculate the percent difference between the two values.
3. Explain any difference in the values before and after the collision.
+ = ′ + ′
©2015 Carolina Biological Supply Company
12
Momentum before the collision = +
Momentum after the collision = ′ + ′
−
= | + | 100%
(
)
2
©2015 Carolina Biological Supply Company
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Activity 2. Elastic Collision: Mass Added to Cart A
Repeat the procedure with mass added to Cart A.
1. Add five large washers to Cart A.
2. Using the electronic pocket balance, measure the mass of Cart A with the
additional washers. Record this value in Data Table 2A and 2B.
3. Using the electronic pocket balance, measure the mass of empty Cart B. Record
this value in Data Table 2C.
4. You will now determine the initial velocity vA of Cart A. Remove Cart B from the
surface, and place Cart A behind the release point at the raised end of the foam
board.
5. Release Cart A, and allow Cart A to travel down the ramp onto the level surface.
6. Measure the time it takes for Cart A to travel from the start point to the end point.
Start the timer when the back end of Cart A crosses the start point, and stop the
timer when the front end of Cart A strikes the book. (The distance for this trial will be
50 cm.)
7. Repeat this process for three trials, and record the data in Data Table 2A.
8. You will now determine the final velocity vA’ of Cart A. Place Cart B on the level
surface. The spring should be at the start point.
9. Place Cart A at the raised end of the foam board behind the release point.
10. Release Cart A, and allow Cart A to impact Cart B. It is important that the impact is
straight and that both carts travel in a straight line along Cart A’s original direction
after the collision.
11. Start timing when Cart A collides with Cart B and until Cart A stops moving.
12. Observe the distance Cart A travels after the collision. If the cart does not move the
distance is zero, and if the cart moves backward the distance is negative.
13. Use a piece of tape to mark a position on the table 40 cm from the end of the foam
board. Record a distance of 20 cm (40 cm-20 cm) in Data Table 2B as the distance
Cart A travels after the collision.
Note: 40 cm is a suggested end point. Variables such as the angle of the ramp
and the type of surface you use may require you to select a different distance in
order to calculate the final velocity, vA’, for Cart A. The distance should be about
½ to 2/3 the total distance Cart A travels after the collision so that the velocity of
Cart A over this distance can be considered constant. Measure the distance to
the end point you select from the start point at 20 cm. Record this distance in
Table 2B. Remember if Cart A reverses direction, vA’ will be negative.
14. Measure the time for Cart A’s movement after the collision for three trials. Record
the time for each trial, and record the data in Data Table 2B.
15. You will now find the final velocity vB’ of Cart B. Place Cart A at the raised end of the
foam board behind the release point.
©2015 Carolina Biological Supply Company
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16.
Release Cart A, and allow Cart A to impact Cart B. It is important that the impact
is straight and that both carts travel in a straight line along Cart A’s original direction.
17.
Record the time it takes for Cart B to travel from the start point to the end point.
18.
Repeat this process for three trials, and record the data in Data Table 2C.
19. Measure the distance from the start point to the end point. (This distance should be
50 cm) Record this value in Data Table 2C.
20. Complete Data Tables 2A, 2B, and 2C by calculating the average velocity of the
carts before and after the collision.
Data Table 2A. Cart A before collision.
Cart A mass,
Distance, d (m) Time, t (s)
m1 (kg)
Average time,
t (s)
Velocity = d/t
(m/s) vA
Data Table 2B.
Cart A mass,
m1 (kg)
Average time,
t (s)
Velocity = d/t
(m/s) vA’
Average time,
t (s)
Velocity = d/t
(m/s) vB’
Cart A after collision.
Distance, d (m) Time, t (s)
Data Table 2C. Cart B after collision.
Cart B mass, m2 Distance, d (m) Time, t (s)
(kg)
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Calculations for Activity 2. Elastic Collision: Mass Added to Cart A.
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation).
2. Calculate the percent difference between the two values.
3. Explain any difference in the values before and after the collision.
+ = ′ + ′
Momentum before the collision = +
Momentum after the collision = ′ + ′
−
= | + | 100%
(
)
2
©2015 Carolina Biological Supply Company
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Activity 3. Elastic Collision: Mass Added to Cart B
Repeat the procedure with mass added to Cart B.
Note: In this activity, Cart A may have a negative velocity after the collision. To allow
enough space to measure the velocity of Cart A, change the start point to 35 cm from
the end of the foam board.
1. Place 11 large washers in Cart B and five small washers in Cart A.
2. Using the electronic pocket balance, measure the mass of Cart B with the 11
washers. Record this value in Data Table 3C.
Note: For this activity, the mass of the target cart, Cart B, should have more Mass
than Cart A. In this scenario, Cart A will likely reverse direction after the collision. If
the mass of Cart A is too small, it will move to fast to record an accurate time. The
numbers of washers in step 1 are suggestions. You may need to adjust the number
of washers in each Cart to get an accurate measurement for time for each cart.
3. Using the electronic balance, measure the mass of Cart A with the five small
washers. Record this value in Data Table 3A and 3B.
4. Using a piece of tape, mark a point on the level surface 35 cm from the lower end
of the foam board. This will be the new start point.
Note: In this scenario, Cart A will likely reverse direction after the collision. Moving
the start point, where the collision will occur, farther from the foam board should
provide adequate space for Cart A to move after the collision so that a time can
be recorded and a velocity can be calculated. Remember if Cart A reverses
direction after the collision then vA’ will be negative.
5. You will now determine the initial velocity vA of Cart A. Remove Cart B, and place
Cart A behind the release point at the raised end of the foam board.
6. Release Cart A, and allow Cart A to travel down the ramp onto the level surface.
7. Measure the time it takes for Cart A to travel from the start point to the end point.
Start the timer when the back end of cart a crosses the start point, and stop the
timer when the front end of Cart A strikes the book. The distance for this trial will be
35 cm (70 cm – 35 cm).
8. Repeat this process for three trials, and record the data in Data Table 3A.
9. You will now find the final velocity vA’ of Cart A. Place Cart B on the level surface at
the start point.
10. Place Cart A at the raised end of the foam board behind the release point.
11. Release Cart A, and allow Cart A to impact Cart B. It is important that the impact is
straight and that both carts travel in a straight line after the collision.
12. Observe the distance and direction Cart A travels after the collision. If Cart A does
not move after the collision, remove a washer from Cart A and repeat the previous
step.
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13. Once Cart A and B move consistently after the collision, measure a point 10 cm
from the start point. This will be the end position for Cart A. Record this distance in
Data Table 3B.
Note: 10 cm is a suggested end point. Variables such as the angle of the ramp
and the type of surface you use may require you to select a different distance in
order to calculate the final velocity, vA’, for Cart A. The distance should be about
½ to 2/3 the total distance Cart A travels after the collision so that the velocity of
Cart A over this distance can be considered constant. Measure the distance to
the end point you select from the start point at 35 cm. Record this distance in
Table 3B. Remember if Cart A reverses direction, vA’ will be negative.
14. Record the time for Cart A to travel from the start point (where the collision occurs)
to the end point for Cart A, 10 cm from the start point.
15. Repeat this process for three trials, and record the data in Data Table 3B.
16. You will now find the final velocity vB’ of Cart B. Measure the distance from the start
point to the end point. This distance should be 35 cm (70 cm -35 cm). Record this
distance in Table 3C.
17. Place Cart A at the raised end of the foam board behind the release point.
18. Release Cart A, and allow Cart A to impact Cart B. It is important that the impact is
straight and that both carts travel in a straight line along Cart A’s original direction
after the collision.
19. Record the time it takes for Cart B to travel from the start point to the end point.
20. Repeat this process for three trials, and record the data in Data Table 3C.
21. Complete Data Tables 3A, 3B, and 3C by calculating the average velocity of the
carts before and after the collision.
Data Table 3A.
Cart A mass,
m1 (kg)
Cart A before collision.
Distance, d (m) Time, t (s)
Data Table 3B.
Cart A mass,
m1 (kg)
Cart A after collision.
Distance, d (m) Time, t (s)
©2015 Carolina Biological Supply Company
Average time,
t (s)
Velocity = d/t
(m/s) vA
Average time,
t (s)
Velocity = d/t
(m/s) vA’
18
Data Table 3C. Cart B after collision.
Cart B mass, m2 Distance, d (m) Time, t (s)
(kg)
Average time,
t (s)
Velocity = d/t
(m/s) vB’
Calculations for Activity 3. Elastic Collision: Mass Added to Cart B.
Apply the law of conservation of momentum to the two-cart system by calculating the
momentum before and after the collision.
1. Calculate the momentum of the system before the collision (the left side of the
equation) and after the collision (the right side of the equation.)
2. Calculate the percent difference between the two values.
3. Explain any difference in the values before and after the collision.
+ = ′ + ′
Momentum before the collision = +
Momentum after the collision = ′ + ′
−
= | + | 100%
(
)
2
©2015 Carolina Biological Supply Company
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