N otes on Chapter 7 A
pp 61 - 67 of your lab book

Conservation of momentum tells us what the outcome of a collision will be.

Conservation of momentum: the total momentum of a system before = the total momentum of a system after

In our lab today, we collide two carts of different masses. We will have one mass at rest, and the other moving at a constant velocity. We will again use the air track to reduce friction. In the absence of friction, our conservation law can be applied simply.

Mass 1, m₁ = the moving mass
Mass 2, m₂ = the mass at rest
Velocity of mass 1, initially  = v_1i
Velocity of mass 2, initially = 0
Velocity of mass 1, final = v_1f
Velocity of mass 2, final = v_2f

The total momentum of the system before = momentum of cart 1 + momentum of cart 2 = m₁ v_1i + 0
The total momentum of the system after = momentum of cart 1 + momentum of cart 2 = m₁v_1f + m₂v_2f

So: m₁v_1i = m₁v_1f + m₂ v_2f

In addition, we know that if no energy is lost, then conservation of energy holds true also:

1/2 m ₁v_1i² + 0 = 1/2 m₁v_1f ² + 1/2 m₂v_2f²

Combining these equations we can determine the velocity of the second cart in terms of the velocity of the first cart.

v _2f = 2v_1i / (1 + m₂/m₁)

We can also find out what percentage of the total energy went into the second cart.
The total energy = initial kinetic energy of the first cart = 1/2 m1v1i2
The energy of the second cart after the collision = 1/2 m2v2f2
The fraction of the energy transferred = TE = m₂v_2f ² / m₁v_1i²

Procedure:
(151 class -- please take a moment to clean your air track, as you are the first class of the day)

1. Level your air track in the manner that we discussed in the Air Track experiment (do this very thoroughly!!)
2. You will be assigned mass 1 and mass 2 for your group.
3. Measure the mass of your two carts (do not trust previous student labels!)
4. Place mass 2 in the middle of the air track at rest
5. Set mass 1 at the end of the track, and give it an arbitrary velocity. (You may wish to practice these next few steps a few times without making a record). 
6. Start the spark timer for mass 1 once you are clear of the track.
7. Stop the spark timer for mass 1 when it approaches mass 2, and start the spark timer for mass 2
8. Stop the spark timer for mass 2 when it reaches the end of the track.
9. Repeat steps 4-7 four more times.
10. Calculate the TE ratio and SDM of the TE and write your value on the board.
11. Plot the class TE on Figure 1, page 65.
    

Important!
1) The masses should never actually touch. As we learned last time, that causes a great deal of lost energy. Instead the magnets should repel the carts.

bad collision	good collision

2) Do not record any accelerations! (Acceleration can be seen easily on the spark tape when the dots become closer together or further apart).

3) Recall that the time elapsed between dots is 0.1 s. So if you count 9 dots (as in the picture above), a time of 0.8 s has elapsed since the first dot was made.

Data:
Mass of Cart 1, m1 = _____________+/- _______
Mass of Cart 2, m2 = _____________+/- _______

Trial	Cart 1: Distance Measured (    )	Cart 1: Time elapsed (     )	Cart 1: Velocity (    )	Cart 2: Distance Measured (    )	Cart 2: Time elapsed (     )	Cart 2: Velocity (    )	TE = m2v2f2 / m1v1i 2
1
2
3
4
5

Your average TE= ___________+/- _______

Class Data:

Group	m2/m1	TE
I
II
III
IV
V
VI
VII
VIII
IX
X

Assignments:
1.  Answer question 3 on pg. 67.