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## Homework Statement

A child drags a 20kg box across a lawn for 10m anfd along a sidewalk for 30m; the coefficient of friction is 0.25 for the first part of the trip and 0.55 for the second part. If the child always pulls horizontally, how much work does the child do on the box?

## Homework Equations

W = F

_{net,x}[tex]\Delta[/tex]x

## The Attempt at a Solution

The only way that I know how to find a net force is to find the summation of F for part one and the summation of F for part 2. While the problem dioesn't say so, I am going to assume there is constant velocity.

__[tex]\Sigma[/tex]F__

_{x1}=0W

_{x1}=0

P

_{x1}= ?

F

_{f1}= -[tex]\mu[/tex]

_{k1}mg

P

_{x1}- [tex]\mu[/tex]

_{k1}mg = 0

__[tex]\Sigma[/tex]F__

_{y1}=0W

_{y1}= -mg

N

_{1}= mg

mg - mg = 0

__[tex]\Sigma[/tex]F__

_{x2}=0W

_{x2}=0

P

_{x2}= ?

F

_{f2}= -[tex]\mu[/tex]

_{k2}mg

P

_{x2}- [tex]\mu[/tex]

_{k2}mg = 0

__[tex]\Sigma[/tex]F__

_{y2}=0W

_{y2}= -mg

N

_{2}= mg

mg-mg=0

So here is where I get lost. I can find P

_{x1}(49.05N) and P

_{x2}(107.91N). Do I just add them together and plug them into the F portion of the W = F

_{net,x}[tex]\Delta[/tex]x formula, using 40m as my ][tex]\Delta[/tex]x?