# Work on a Sliding Box

## Homework Statement

A box of mass m is sliding along a horizontal surface.
Part A) The box leaves position x=0 with a speed v0. The box is slowed by a constant frictional force until it comes to rest at a position x=x1. Find Ff, the magnitude of the average frictional force that acts on the box. (express in terms of m, v0, and x1.
I found the correct answer to part A...(Ff=(mv02)/2x1)

Part B) After the box comes to rest at a position x1, a person starts pushing the box giving it a speed v1. When the box reaches position x2 (where x2>x1), how much work Wp has the person done on the box? Assume that the box reaches x2 after a person has accelerated it from rest to speed v1. Express the work in terms of m,v0,x1,x2, and v1.

W=ΔKE
W=F*d

## The Attempt at a Solution

So I figured that the total work would be the work done in part A (-(mv02)/2x1)*(x1)
added to the work done between x1 and x2:
-(mv02(x2-x1))/2x1

however when I add these two solutions, it tells me that the answer needs to include v1. So then I thought to solve for v1 by setting the work done between x1 and x2 equal to the change in kinetic energy between that time frame which gave me:

KE = (mv12)/2 = work between x1 and x2

v02=(x1v12)/-(x2-x1)

so that allowed me to have v1 in my final answer...but mastering physics is still telling me it's incorrect.

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