13 pts] A block sliding on a flat, frictionless surface with velocity v collides

Question

13 pts] A block sliding on a flat, frictionless surface with velocity v collides into a stationary block. The collision is perfectly elastic, and the two masses are identical. Which happens after the collision? Briefly explain i. The two blocks move away from each other each at half the speed of the block before collision. ii. The initially-sliding block is stationary, and the initially-stationary block moves with velocity v. iii. Both blocks move in the same direction, each with velocity half of v.

Explanation / Answer

When a block with speed v collides with a stationary block of same mass elastically, all of the kinetic energy of the initially sliding is transferred to the stationary block. Hence the stationary block starts moving with speed v while the initially sliding block stays at rest.

This process also conserves momentum.

The initial momentum is m v+ 0 = m v

Final momentum is 0+ m v = m v

Hence the answer is

ii) The initially sliding block is stationary, and the initially stationary block moves with velocity v.

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