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Shown above is an Astro-Blaster toy. This toy consists of a set of 4 rubber balls that can be stacked on a plastic rod. The balls are stacked in order of size with the largest at the bottom. The masses of the balls decrease with their size, so that for the example shown the balls have masses of about 68 g, 28 g, 10 g and 4 g respectively. When the stack is dropped to the ground, the balls undergo a series of elastic collisions which causes the top ball (the small red ball) to launch upward to a height considerably larger than the original drop height. Assuming that all the collisions are elastic and that the assembly hits the ground moving at a speed v, find the speed of the red ball as it launches up from the top in terms of v and find the fraction of the initial kinetic energy deposited in each ball (ignoring subsequent collisions and friction due to the rod).
Systems: We will consider three separate collisions: the bottom ball with the second ball, the second with the third, and the third with the top. For each collision, we will consider the system to be made up of the two balls that are colliding. We will assume that each collision is instantaneous, so that external forces will provide negligible impulse.
Models: Momentum and Impulse plus Mechanical Energy and Non-Conservative Work.
Approach: