PHYS 1401 – General Physics I

Impulse and Momentum

 

Leader: ____________________                    Reporter: ___________________________

Skeptic: ___________________                     Encourager: _________________________

 

Materials

Pasco Dynamics Track                                     Laptop

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 Pasco track is level.  Place a cart on it and see of it rolls.  If it does, then adjust the foot so that when you place a cart on the track it doesn’t roll.

 

      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 __________________.