PHYS 1401 – General Physics I

Conservation of Momentum

Leader: _________________________ Recorder: __________________________

Skeptic: _________________________ Encourager: ________________________

Materials

Air Track and air source LabPro

2 carts (also referred to as gliders) 2 Photogates

2 Bumpers (1 for each glider) Air Track Accessory Kit

Laptop Needle and Wax receiver

Introduction

In this lab we will investigate conservation of momentum. We will use carts on the air track to examine a collision and determine the extent to which momentum is conserved.

Procedure

We will conduct our one-dimensional collisions on an air track.

1. Prepare the Carts

Place a bumper with rubber band on one end of each cart to conduct the elastic collision. On the other end of the carts place the cylinder with wax on one cart and the cylinder with the needle on the other. . Place a flag on the top of each cart. The flag should be oriented so that the wide side is parallel to the cart.

2. Level the air track

We want to make the air track as level as possible. Place a cart on the middle of the track and slowly turn up the air until the cart just coasts with no resistance. Using the lowest setting on the air supply for which the cart floats will give better results. The cart should stay in place or move only very, very slowly. If this is not the case, make a slight adjustment on the adjustable feet and try again. Repeat this procedure until the track is as level as you can get it. Be sure to stop the cart after each adjustment.

3. Preliminary measurements

Use the electronic balance to find the mass of your carts. Measure the width of the flag on top of each cart. This width will be used to determine the velocity of each cart. Record the data and arrange the carts so that you know the mass of each.

Mass cart 1: _________________ (kg)

Mass cart 2: _________________ (kg)

Width of Flag: _______________ (m)

4. Set up

Place the two carts on the track and the two photogates so that one is between the two carts and the other is after the second cart. Plug the photogates into the LabPro with the gate between the carts plugged into CH1 and the other gate plugged into CH2. Open LoggerPro and open the experiment file called “Collision Timer” by following the path "Probes and Sensors" => "Photogates"=> "Collision Timer".

5. Enter the length of the flag into the computer

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.

6. Data Acquisition

We will conduct two different trials.

Trial 1 Elastic collision between equal masses

Make sure that both carts are stationary. With the bumper on cart 1 facing the bumper on cart 2, push the first cart towards the second. The front photogate will record the initial speed of cart 1 and the second photogate will record the speed of cart 2. You will need to put in direction information by hand. Make sure that you have enough data to complete all columns in your data table. Qualitatively observe how the velocity of the two carts changes before and after the collision.

Q1. Complete the information for this trial in the table below. Include the units.

Before

m₁

v_1i

p_1i

m₂

v_2i

p_2i

p_tot,i

After

m₁

v_1f

p_1f

m₂

v_2f

p_2f

p_tot,f

Q2. Which cart(s) had momentum before the collision? Which cart(s) had momentum after the collision?

Q3. Describe the transfer of momentum during the collision?

Q4. Was all of the momentum transferred during the collision? Determine Dp for the collision from Δp = p_tot,f – p_tot,i .

Q5. If Dp = 0, then momentum was conserved. Within reasonable experimental uncertainties was momentum conserved in this collision? Explain.

Q6. Another way to examine how well momentum was conserved is to calculate the percent change of the momentum. We define the percent change as

% change = x 100 %.

If momentum were conserved what would you expect the percent change to equal?

Q7. Determine the percent change. Within reasonable experimental error, does the percent change seem to be consistent with momentum being conserved? Explain. Note if the percent change is positive, then momentum increased in the collision and if the percent change is negative, then momentum was lost during the collision.

Q8. If the percent change is significantly different from 0%, what factors might have affected the momentum. Describe them and determine if their effect is consistent with the sign of the percent change.

Q9. The heading for this trial referred to this collision as elastic. An elastic collision is one in which the total kinetic energy is conserved in addition to the momentum. Determine the total KE before the collision KE_tot,i = ½ m₁v_1i² + ½ m₂v_2i²

Q10. Determine the total KE after the collision KE_tot,f = ½ m₁v_1f² + ½ m₂v_2f²

Q11. A common measure of how elastic a collision is the coefficient of restitution. The coefficient of restitution, g, is defined as g = KE_tot,f/KE_tot,i. If g = 1, then the collision was perfectly elastic. If g ¹ 1, then the collision was inelastic. Determine g for the collision.

Q12. Based on your value for g, was the collision nearly elastic? Explain.

Trial 2 Perfectly Inelastic Collision.

In trial 2, we will investigate a perfectly inelastic collision. A perfectly inelastic collision is one in which the objects stick together after the collision. Reverse the carts so that the needle is facing the cylinder with wax. Launch cart 1 towards cart 2 so that they stick together. You may need to practice this for a while. Once you can get the carts to stick reliably, launch cart 1 towards cart 2 so that they stick. Record the masses and velocities in your table. Note the behavior of the carts very carefully during the collision. This part of the experiment often gives poor results, and if you carefully observe what goes on during the collision, you may be able to see why.

Q13. After the collision the gliders will stick together. How many objects are moving after the collision?

Q14. Complete the information for this trial in the data table below. Include the units.

Before
m₁	v_1i	p_1i	m₂	v_2i	p_2i	p_tot,i

After
m₁	m₂	v_f	p_tot,f

Q15. Which cart(s) had momentum before the collision? Which cart(s) had momentum after the collision?

Q16. Describe the transfer of momentum during the collision?

Q17. Was all of the momentum transferred during the collision? Determine Dp for the collision from Δp = p_tot,f – p_tot,i .

Q18. If Dp = 0, then momentum was conserved. Within reasonable experimental uncertainties was momentum conserved in this collision? Explain.

Q19. Determine the percent change of momentum for this collision. (See Q6 for a definition.) Within reasonable experimental error, does the percent change seem to be consistent with momentum being conserved?

Q20. If the percent change is significantly different from 0%, what factors might have affected the momentum. Describe them and determine if their effect is consistent with the sign of the percent change.

Q21. Determine the total KE before the collision KE_tot,i = ½ m₁v_1i² + ½ m₂v_2i²

Q22. Determine the total KE after the collision KE_tot,f = ½ (m₁+ m₂) v_f²

Q23. Determine g for the collision (see Q11 for definition).

Q24. Based on your value for g, is it appropriate to describe this collision as inelastic? Explain.

Q25. To what extent was momentum conserved in either collision?

Q26. If momentum is not conserved, then external forces acted on the system. What external forces are relevant in this experiment?

Q27. Describe the difference between an elastic and an inelastic collision. (Hint your answer should be given in terms of which quantities are conserved.) Is a given collision more likely to be elastic or inelastic? Explain.