A small ball of mass m is aligned above a larger ball of mass M = 0.79 kg (with a slight separation), and the two are dropped simultaneously from height h = 2.0 m. (Assume the radius of each ball is negligible relative to h).

(a) If the larger ball rebounds elastically from the floor and then the small ball rebounds elastically from the larger ball, what value of m results in the larger ball stopping when it collides with the small ball?

I'm not understanding what it's asking here... I'm assuming that momentum is conserved (even after the big ball bounces) so for the other ball to cause a collision which results in the big ball stopping the mass should be the same because the speeds are going to be equal, but that is not correct.

To understand what the question is asking, let's break it down step by step:

1. Initially, both balls are dropped simultaneously from a height of 2.0 m, which means they both have the same initial potential energy.

2. The larger ball hits the floor and rebounds elastically, which implies that both the kinetic energy and momentum of the larger ball are conserved. In an elastic collision, the speed and direction of the ball after the collision are the same as before the collision.

3. The small ball then hits the larger ball, which is now moving upwards after the bounce from the floor. We need to find the mass of the small ball that will cause the larger ball to stop when they collide.

4. Since the collision between the small ball and the larger ball is also elastic, both momentum and kinetic energy are conserved. However, the velocities of the two balls will change after the collision.

5. Note that the rebounding of the larger ball from the floor does not affect the collision between the small ball and the larger ball in terms of conservation laws. Momentum will be conserved both before and after the larger ball bounces.

Now, let's find the solution:

Let's assume the velocity of the larger ball after the bounce from the floor is v1, and the velocity of the small ball after the collision is v2.

Considering the conservation of momentum:

Initial momentum = Final momentum

(0.79 kg) * 0 - (0.79 kg) * v1 = (0.79 kg + m) * v2

Since the larger ball should stop (v1 = 0) when it collides with the small ball:

0 - (0.79 kg) * 0 = (0.79 kg + m) * v2

0 = (0.79 kg + m) * v2

Now, considering the conservation of kinetic energy:

Initial kinetic energy = Final kinetic energy

(0.79 kg) * 0^2 = (0.79 kg + m) * v2^2

0 = (0.79 kg + m) * v2^2

We can see that the equations indicate that the velocity of the small ball after the collision (v2) should be zero for the larger ball to stop.

So, we now have the equation:

0 = (0.79 kg + m) * 0^2

0 = 0.79 kg + m

Solving for m:

m = -0.79 kg

However, since mass can't be negative, this means that there is no mass of the small ball (m) that will cause the larger ball to stop when they collide.

Therefore, the answer is that there is no value of m that results in the larger ball stopping when it collides with the small ball.