Spring causes blocks to slide

[mmiller9913]

Homework Statement

. Block A has a mass m and block B has a mass 2m. Block A is pressed against a spring to compress the spring by a distance x. It is then released such that the block eventually separates from the spring and it slides across a surface where the friction coefficient is µk. The same process is applied to block B. Which one of the following statements concerning the distance that each block slides before stopping is correct?a) Block A slides one-fourth the distance that block B slides.

b) Block A slides one-half the distance that block B slides.

c) Block A slides the same distance that block B slides.

d) Block A slides twice the distance that block B slides.

e) Block A slides four times the distance that block B slides.

Homework Equations

W= delta K
K= 1/2mv^2
Fx=-KX
W= -1/2Kx^2

The Attempt at a Solution

I'm really not sure how to start. I'm not sure if both bocks start out with the same velocity? I'm guessing it's d just by making an educated guess. but is there a way to prove this?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[jbsteele]

The answer is b) Block A slides one-half the distance that block B slides. This can be explained by the conservation of energy. Since the two blocks have different masses, the kinetic energy of block B will be higher than that of block A when the blocks are released from the spring (assuming they start with the same velocity). This means that the gravitational potential energy of block B will be converted to kinetic energy at a higher rate than that of block A. Thus, block B will have a greater magnitude of velocity and will slide farther than block A before coming to a stop.