How to Calculate Velocity and Distance for Block on Slab with Friction

[Beckaze]

Homework Statement

The problem says: A small block of mass Mb = 0.5 kg is placed on a slab with mass Ms = 3.0 kg. Initially the slab is at rest and the block has a speed of V(initial)= 4m/s. The coefficient of kinetic friction between the block and the slab is .2 and there is no friction between the slab and the horizontal surface. At some moment later, before the block reaches the right end of the slab, both the block and the slab have the same speed Vfinal.

A)Calculate Vfinal
B) Calculate the distance the slab has traveled at the moment it reaches Vfinal
C)Calculate the work done by friction on the slab from the beginning of its motion until it reaches Vfinal

Homework Equations

The Attempt at a Solution

A) I tried 1/2 Mb vinital^2 = 1/2 Mb+s Vfinal^2 and i got 1.511 m/s but I feel like I missed a step with the friction. I don't know if it comes into play with the velocity.

 

[collinsmark]

Hello Beckaze,

Welcome to Physics Forums!

You are correct about missing something with the friction. Because of the friction, kinetic energy is not conserved. In short, your attempted solution for part A is not valid.

On a positive note, you know that linear momentum is conserved, so you might want to start with that, for part A.

 

[Beckaze]

thanks so much for the help