Question

Figure 9-30 shows a snapshot of block 1 as it slides along an x-axis on a frictionless floor before it undergoes an elastic collision with stationary block 2. The figure also shows three possible positions of the center of mass (com) of the two-block system at the time of the snapshot. (Point Bis halfway between the centers of the two blocks.) Is block 1 stationary, moving forward, or moving backward after the collision if the com is located in the snapshot at (a) A, (b) B, and (c) C?

Short answer

1. After a collision at A, block 1 is moving forward
2. After a collision at B, block 1 is stationary
3. After a collision at C, block 1 is moving backward.

Step-by-step solution

The given data

Figure showing the snapshot of block 1 sliding along the x-axis which undergoes an elastic collision with block 2

Understanding the concept of the center of mass

Using the concept of center of mass, we can find answers for the collision of block 1 at positions a), b), and c). Using the concept of center of mass we can guess the direction of the motion of the bodies after the collision.

a) Calculation of the situation of block 1 at A

If the center of mass of the blocks is at A, the mass of block 1 will be greater than that of block 2. Hence, after collision block 1 will move forward.

c) Calculation of the situation of block 1 at B

If the center of mass of the blocks is at B, the mass of block 1 will be equal to the mass of block 2. Hence, after collision block 1 will become stationary.

c) Calculation of the situation of block 1 at C

If the center of mass of the blocks is at C, the mass of block 2 will be greater than that of block 1. Hence, after collision block 1 will move backward.