See Fig. 9-32 below: A block on a horizontal floor is initially either stationar
ID: 1907226 • Letter: S
Question
See Fig. 9-32 below: A block on a horizontal floor is initially either stationary, sliding in the positive direction of an x axis, or sliding in the negative direction of that axis. Then the block explodes into two pieces that slide along the x axis. Assume the block and the two pieces form a closed, isolated system. Six choices for a graph of the momenta of the block and the pieces are given, all versus time t. Determine which choices represent physically impossible situations.
Explanation / Answer
In every one of these graphs, you see a single line bracketing into two lines. This represents the explosion into two pieces. It is a physically impossible scenario if the momenta of the two pieces is greater than or less than the momentum of the block. The easiest way to do it is to assign values along the y axis (the p-axis). Let each horizontal line going upwards by 1, 2, 3 etc. In (A) you have an initial momentum of 3. It then breaks into two pieces, one has a momentum of 5 the other has a momentum of 1. This adds to 6. So A is impossible. In (B) you have an initial momentum of 1. One piece then has a momentum of 2, and the other has a momentum of -1. This adds to 1. B is possible. In (C) the initial momentum is -2. The two pieces have a momentum of +2 and -5. This adds to -3. A system cannot have LESS momentum than it started with in an isolated system. Impossible. In (D) the initial momentum is zero (so the block is stationary). The two pieces are then shown as having equal and opposite momenta - this is possible since it adds to zero. Doing this same analysis for (e) and (f), you find they are both impossible. The only possible graph here is D and B. A, C, E, and F are all impossible because the final momentum of the two pieces does not equal the momentum of the block before it exploded.