Question

Two blocks have masses of M and 2M and are initially at rest on a frictionless horizontal counter. The masses are exploded apart by releasing a spring between them. Which of the following is true regarding the speeds of the blocks as they move away from each other?

a. the blocks move away from each other at the same speed.

b. the M block moves away at twice the speed of the 2M block.

c. the M block moves away at four times the speed of the 2M block.

d. the 2M block moves away at twice the speed of the M block.

Answer 1

When two blocks with masses M and 2M are exploded apart by a spring on a frictionless surface, the block with mass M moves away at twice the speed of the block with mass 2M due to conservation of momentum.

Step-by-step explanation:

If two blocks with masses M and 2M are released from a compressed spring on a frictionless surface, the law of conservation of momentum applies to their movement. Since they start from rest, the total initial momentum is zero. After they are exploded apart, the total momentum must remain zero. The momentum of each block is the product of its mass and velocity. Therefore, if block M has a velocity v, then block 2M must have a velocity v/2 in the opposite direction to conserve momentum (Mv + 2M(-v/2) = 0).

So, the block with mass M moves away at twice the speed of the block with mass 2M after the spring is released. This means that option b – the M block moves away at twice the speed of the 2M block – is the correct answer to the question.