Blocks, Collisions, and Friction

[minimario]

Homework Statement

A block of mass m lying on a rough horizontal surface is given an initial velocity of v_0. After traveling a distance d, it makes a head-on elastic collision with a block of mass 2m. How far does the second block move before coming to rest? (Assume that the coefficient of friction, μk, is the same for both blocks.)

Homework Equations

In an elastic collision, the total momentum, mv, is conserved.
In addition, ## v_{1i} - v_{2i} = -(v_{1f} - v_{2f}) ## in an elastic collision.

The Attempt at a Solution

I don't know how the friction is going to work in this problem, but if you let the coefficient be equal to 0 for both blocks, the 2nd block never stops

 

[ehild]

What happens if the coefficient of kinetic friction is not zero?
What is the velocity of the first block just before the collision? Apply work-energy theorem.
What is the velocity of the second block just after the elastic collision? Apply both conservation of momentum and conservation of energy.
The blocks move on after the collision subjected to friction, so they stop after traveling some distance.