You are rearranging the furniture in your living room. In doing so, you push a 2

Question

You are rearranging the furniture in your living room. In doing so, you push a 28 kg sofa to the left a total distance of 2 m and then you push it back to the right a distance of 1 m. The coefficient of kinetic friction between the sofa and the hardwood floor is 0. Please show work.

a.) What is the work done by friction in moving the sofa?

b.)Suppose that you had instead simply moved the sofa to its final position by moving it directly 1 m to the left. What is the work done by friction in this case? c.)From the results you obtained in Parts A and B, what can you conclude about the nature of the friction force? Is it a conservative force? Explain

Explanation / Answer

in moving a distance 2m

work done is W1 = -mu_k*m*g*S = -0.2*9.81*28*2 = -109.872 J

and next to 1m work done is w2 = -0.2*28*9.81*1 = - 54.936 J

A) W = W1+W2 = -54.936-109.872 = -164.808 J

B) W3 = -mu_k*m*g*S = -0.2*28*9.81*1 = -54.936 J

C0 since Workdone in part A is not equal to work done on part B

then the frictional force is a non conservative force since it depends upon the path

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