Question

Step 1: Before the collision, the total momentum is pbefore = mv0 + 0 where m is the ball’s mass and v0 is the ball’s speed. The pendulum is not moving so its contribution to the total momentum is zero. After the collision, the total momentum is pafter = (m + M) V, where m is the ball’s mass, M is the pendulum mass, and V is the velocity of the pendulum with the ball stuck inside (see the picture on the next page).

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Using conservation of momentum we have: pbefore = pafter, so

M v0 = (m + M) V (*)
1) The friction force between the ball and the pendulum during the ball’s capture is very large (the ball gets stuck inside the pendulum very quickly). Why does not this very large friction force affect the conservation of momentum during the ball’s capture?

Step 2: At this point, we still have two unknowns, V and vo. In order to find the launch speed v0 we need to know V, the speed of the pendulum and ball after the collision. It can be found by using conservation of energy after the ball is captured and the pendulum with the trapped ball swings upward (relatively slow process – step 2).



Right after the collision, the ball and pendulum have zero potential energy while their kinetic energy is 1/2 (M + m) V 2. When they reach the highest point of the swing, the kinetic energy is zero and potential energy is (M + m)gh, with h being the maximum deflection height. Kinetic energy has been converted into potential energy. Conservation of energy gives:

½ (M + m) V 2 = (M + m)gh (**)
Hence, V = (2gh)1/2. Substituting V to the momentum equation (*) and solving for v0, we obtain   

v0 = ((M + m) /m) (2gh)1/2 (***)

2) Why cannot we use conservation of momentum when the pendulum-ball system swings upward yet we can use the conservation of mechanical energy?
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Experimental data (ballistic pendulum):

The mass of the ball m was measured on a balance. The pendulum mass M was measured by hanging the pendulum from a spring scale (not a very precise measuring tool).

m = 60.5 +/- 0.1 g M = 210 +/- 10 g

The maximum deflection angle of the pendulum was determined using the angular scale attached to the device (see the picture on page 1).

θ = 35˚ +/- 1˚

The height maximum deflection h can be calculated as follows:

h = r (1 – cosθ)

In the above formula, r is the distance from the pivot to the center of the pendulum bob (and θ is the maximum deflection angle). r was measured using a meter stick:

r = 30.0 +/- 0.1 cm

3) Prove the formula h = r (1 – cosθ) with a drawing and trigonometry in your lab report.

4) Calculate v0 using the equations given above (the equation for the height h and equation (***)).

Answer 1

1. Because friction force between balls are internal force and work done by net internal force is zero .Hence net internal friction is zero so it not effect conservation of momentum .

2 . Because when it traveling upward gravity is acting which is a external force . Hence we not able to apply conservation of momentum but we can apply energy conservation .

3 .