PHYS 1401 – General Physics I
Impulse and Momentum
Skeptic: ___________________ Encourager: _________________________
Materials
Cart
with force probe attached Labpro
Motion
Detector Force
Probe
Rubber Band
1 x
collision cart (w/o plunger) Laptop
and (w/o force
probe adapter)
1 x
dynamics cart (w/ plunger) 2
x Photogates
Masking
tape 2
x 2.5 cm flags for air track cart
Introduction
In this lab, we will investigate the
relationship between impulse and momentum and then investigate conservation of
momentum..
Preliminaries
Answer
the following questions in your group before proceeding with the lab activity.
In
this lab you will aim tug a dynamics cart with an attached force sensor
1. If the cart is initially at rest, sketch a
graph of what you think the velocity versus time graph will look like for this
experiment.
2. Sketch a graph of what you think the force
versus time will look like.
3. If the initial velocity of the cart is
increased, what do you think will be the affect on your answers to questions 1
and 2?
4. If instead you push briefly on the force
probe with the cart initially at rest towards the motion detector, sketch
graphs of what you think the Velocity vs. Time and the Force vs. Time will look
like.
Part I – Impulse and Momentum
Procedure
In this experiment we will use a force probe
attached to a dynamics cart and a motion detector. We will pull the cart, with a rubber band
attached to the force probe and record the force as we pull on it. We will simultaneously record the velocity of
the cart using the motion detector.
1.
Set up
Determine
the mass of the cart along with the force probe. Plug the force sensor into CH 1 on the LabPro and the Motion Detector into DIG/SONIC 1. Position the sensors so that the tip of the force
sensor faces away from the motion detector.
Make sure that the switch on the force probe is in the
+/- 10 N position. The motion
detector needs to be at least .5 m from the cart. Start LoggerPro and
double click on the folder titled “_Physics with Computers” and then open the
file “20 Impulse and
Momentum”. Click OK on the Confirm
Sensors box if it opens.
2. Data Collection and Analysis
Part 1 - Tugging a cart at rest away form the
motion detector
Click
on the 0 button (should be next to the collect button) and
then click OK on the box that opens to zero the force probe. Click on the
collect button and once you hear the motion detector steadily clicking, use the
rubber band to give the cart a brief horizontal tug away from the motion
detector. You should obtain a brief
impulsive force and a velocity graph with two plateaus. Check with your instructor to make sure you
have good data.
Before and after the tug, the cart should
have had a constant velocity. On the
velocity versus time graph, click and drag over the part of the graph which
indicates the constant velocity before the tug.
Click on the button which says STAT , and
record the mean value of the initial velocity.
Repeat this step for the velocity of the cart after the tug. To analyze our data we will calculate a
quantity called momentum.
Momentum
which is denoted by the letter p is defined as p = mass x velocity or p = mv.
Q1. Complete the following table.
|
Mass |
Velocity |
Momentum
= mass x velocity |
Initial |
|
|
|
Final |
|
|
|
Q2. Determine the change in momentum of the
cart. Be sure to include units.
Click
on the Force vs. Time graph, and then click and drag over the impulse. Click on the button which shows a graph with
a shaded area underneath it, . This will calculate the area of the region
that you indicated which is the impulse.
Q3. Record the impulse I =
Q4. What is the sign of the impulse? In terms of the motion of the cart, why does
the impulse have that sign?
Q5. What are the units of the impulse given by
the computer? Show that these are the
same as the units of momentum.
Q6. Calculate the percent difference between the
impulse and the change in momentum using the following formula
%
difference =
Part 2 - Pulling harder on a cart initially at
rest away from the motion detector
P7. If you give the force probe a sharper tug,
how do you think the impulse will change?
Q8. Test your answer to P7 by running the
experiment again with a sharper tug on the cart greater than the previous
run. Record your data in the space
below.
|
Mass |
Velocity |
Momentum |
Initial |
|
|
|
Final |
|
|
|
Q9. Determine the change in momentum of the
cart. Be sure to include units.
Q10. Record the impulse: I =
Q11. Determine the % difference
Part 3 - Pulling away from the motion detector on
a cart initially moving towards the motion detector
P12. Now, if the cart initially moves towards the
motion detector, and you pull away, sketch predictions of what the graphs of
Force vs. time and velocity vs. time will look like.
Q13. Test your answer to P12 by running the
experiment again with the cart initially moving towards the motion detector and
then giving a brief tug in the opposite direction.
|
Mass |
Velocity |
Momentum |
Initial |
|
|
|
Final |
|
|
|
Q14. Determine the change in momentum of the
cart. Be sure to include units.
Q15. Record the impulse: I =
Q16. Determine the % difference
Part 4 - Pushing a cart initially at rest
towards the motion detector
P17. If the cart is initially at rest and you push
the cart towards the motion detector, sketch predictions of what the graphs of
Force vs. time and velocity vs. time will look like.
Q18. Test your answer to P17 by running the
experiment again. This time place the
cart at rest at the end of the track opposite the motion detector and briefly
push the cart towards the motion detector by pushing on the tip of the force
probe. Don’t allow the cart to run into
the motion detector.
|
Mass |
Velocity |
Momentum |
Initial |
|
|
|
Final |
|
|
|
Q19. Determine the change in momentum of the
cart. Be sure to include units.
Q20. Record the impulse: I =
Q21. Determine the % difference
Summary
I. On the graphs below, sketch the general shape
of the impulse and the corresponding change in velocity that you observed in parts
1-3 of this experiment.
II. On the graphs
below, sketch the general shape of the impulse and the corresponding change in
velocity that you observed in part 4of this experiment.
III. For the impulse
shown, sketch a graph of a possible change in velocity.
IV. For the indicated
change in velocity, sketch a graph of the impulse.
Part II – Conservation of Momentum
Introduction
In this part of the lab we will explore
conservation of momentum in a system of objects. Remember that we define momentum as mass ×
velocity or in symbols p = mv.
Q1. Is momentum a vector or a scalar quantity
(i.e. does direction matter)?
Q2. If a 0.50 kg cart moves to the right at 3.0
m/s, what is its momentum? Include
units.
Q3. If the same cart moves to the left at 3.0
m/s, how is your answer different than in Q2?
Momentum
is an important quantity in Physics because under certain conditions the total
amount of momentum in a system doesn’t change.
Q4. Define a system.
In this experiment we will collide two carts on the Pasco Dynamics track. We will use a probe called a photogate to measure the speed of each of the carts before
and after the collision. We will then
compare the total momentum of the system before and after the collision.
Q5. Describe the system that we are studying in
this experiment. (Note there is more
than one correct answer to this question, but there is a best answer.)
Procedure
1. Setup
Make sure that the
On the side of the cart, place a piece
masking tape to label the carts. Label
the cart with the plunger as 1 and the cart without as 2. Use the electronic balance to measure the
mass of each of the carts and record below.
Mass
of cart 1: m1 =
______________ kg
Mass
of cart 2: m2 =
______________ kg
Make sure that the LabPro
and laptop have the AC adapters connected and plugged in. Connect the LabPro
to the laptop using the provided USB cable, and connect the photogates
to DIG/SONIC 1 and DIG/SONIC 2 on the LabPro.
2. Setup the Photogates.
Note which of the photogates is plugged into DIG/SONIC 1. For the photogates
to work correctly, you always want a cart to pass through that photogate first. If
you look at the photogates you will observe two small
holes opposite each other. In one hole
there is a light source and in the other there is a light detector. When objects pass between the holes, they
block the light getting to the detector.
The computer can time how long the light is blocked and if it knows how
long the object is can use v = d/t to calculate how fast the object is
moving. Place a flag into the hole on
the top of each of the carts so that the flag passes with its width facing the photogate. Position
the height of the photogates so that the as the cart
passes through them the flag will block the photogate.
Measure the width of the flags on each
cart.
Width
of flag 1: d1 = ____________
m
Width
of flag 2: d2 = ____________
m
Start
up LoggerPro.
Click OK to close the Tip box and then click on the open file and then
double click on the Probes and Sensors folder, then the Photogates
folder and then double click on the file titled Two Gate Timing.
Click on the Experiment menu then click on
Set up Sensors
and then choose LabPro from the list. A window (called the sensor
set-up window) like the following should appear.
Right
click on the Photogate icon under DIG/SONIC 1 and
choose Set Distance or Length … The following window will appear
Choose
User Defined from the drop down box and then enter the width of the flag in
meters and then click on OK.
Repeat for the photogate
icon under DIG/SONIC 2, then close the sensor set-up
window.
Data Acquisition
When
you hit the collect button, the computer will wait for a cart to pass through photogate 1. It will
measure the velocity of a cart each time it passes through a photogate.
Collision
1
Position
the cart without the plunger between the two photogates. Hit the collect button. Once the computer is ready,
start the cart with the plunger extended so that it passes through photogate 1 and collides with the other cart via the
plunger. The computer should record the
velocity of the first cart before the collision and the second cart after.
Q6. Next to each other, draw two pictures showing
both carts - one before the collision and the other just after. Label the carts with their velocities before
and after the collisions. (For
simplicity, hereafter I will refer to a sketch like this as before and after sketch.)
Q7. What was the velocity of cart 2 before the
collision?
Q8. What was the velocity of cart 1 after the
collision?
The
total momentum of the system we define as the sum (taking into account
direction) of the individual momentums.
Q9. Fill in the table below with the details
before the collision. Note a subscript
of b refers to before the collision and t refers to total. Include units.
m1 |
v1b |
p1b
= m1v1b |
m2 |
v2b |
P2b
= m2v2b |
ptb = p1b + p2b |
|
|
|
|
|
|
|
Q10. Fill in the table below with the details
after the collision. Note a subscript of
a refers to after the collision and t refers to
total. Include units.
m1 |
v1a |
p1a
= m1v1a |
m2 |
v2a |
p2a
= m2v2a |
pta = p1a + p2a |
|
|
|
|
|
|
|
Q11. Did the total momentum of the system change
appreciably after the collision compared to before? In other words, compare the last columns of
the two tables you have just completed.
Q12. It may have changed a little bit. What forces might have affected the momentum
of the carts.
Q13. If you define your system as the two carts,
then is friction an internal force (between the carts) or external force
(between the carts and something else)?
Explain.
Q14. If you could eliminate friction do you think
the total momentum of the system would change from before to after the
collision?
Collision
2
Push
the plunger in completely until it clicks.
Position the carts between the photogate with
the cart with the plunger nearer to photogate 1 than
the other cart is to photogate 2. The plunger should be between the two carts.
Hit the collect button. Once the computer is ready, push down on the
button on top of the cart with the plunger so that the plunger releases. The
computer should record the velocity of each cart after the collision.
Q15. Next to each other, draw two pictures showing
both carts - one before the collision and the other just after. Label the carts with their velocities before
and after the collisions. (For
simplicity, hereafter I will refer to a sketch like this as before and after
sketch.)
Q16. What was the velocity of cart 1 before the
collision?
Q17. What was the velocity of cart 2 before the
collision?
The
total momentum of the system we define as the sum (taking into account
direction) of the individual momentums.
Q18. Fill in the table below with the details
before the collision. Note a subscript of
b refers to before the collision and t refers to total. Include units.
m1 |
v1b |
p1b
= m1v1b |
m2 |
v2b |
P2b
= m2v2b |
ptb = p1b + p2b |
|
|
|
|
|
|
|
Q19. Fill in the table below with the details
after the collision. Note a subscript of
a refers to after the collision and t refers to
total. Include units. Take into account the direction of each cart
after the collision.
m1 |
v1a |
p1a
= m1v1a |
m2 |
v2a |
P2a
= m2v2a |
pta = p1a + p2a |
|
|
|
|
|
|
|
Q20. Did the total momentum of the system change
appreciably after the collision compared to before? In other words, compare the last columns of
the two tables you have just completed.
Q21. If you could eliminate friction do you think
the total momentum of the system would change from before to after the
collision?
Collision
3
Push
the plunger completely in until it clicks.
Experiment with the orientation of the two carts with respect to each
other. In one orientation, you will find
that the two carts repel each other and in the other, you will find that they
attract each other. Position the carts
so that they attract each other. Hit the
collect button and gently push cart 1 so that it passes through photogate 1 and then collides with cart 2.
Q22. Next to each other, draw two pictures showing
both carts - one before the collision and the other just after. Label the carts with their velocities before
and after the collisions. (For
simplicity, hereafter I will refer to a sketch like this as before and after
sketch.)
Q23. What was the velocity of cart 2 before the collision?
Q24. How is this collision different from the
previous two?
The
total momentum of the system we define as the sum (taking into account
direction) of the individual momentums.
Q25. Fill in the table below with the details
before the collision. Note a subscript
of b refers to before the collision and t refers to total. Include units.
m1 |
v1b |
p1b
= m1v1b |
m2 |
v2b |
p1b
= m1v1b |
ptb = p1b + p2b |
|
|
|
|
|
|
|
Q26. Fill in the table below with the details
after the collision. Note a subscript of
a refers to after the collision and t refers to
total. Include units.
m1 |
m2 |
va |
pta = (m1 + m2) va |
|
|
|
|
Q27. Did the total momentum of the system change
appreciably after the collision compared to before? In other words, compare the last columns of
the two tables you have just completed.
Q28. If you could eliminate friction do you think
the total momentum of the system would change from before to after the
collision?
Q29. At this point, we have examined three
different collisions. In each did the
momentum change appreciably before and after the collision?
Q30. Was friction force an internal or an external
force?
Q31. If you could eliminate the externals forces
like friction, would the momentum have changed before and after the collision?
When
a physical quantity remains constant we say that it is conserved.
Q32. Complete the following statement. If the ______________ forces on a system can
be ignored, then the total momentum of the system is __________________.