Answer:
The total work done by friction is -2 · μ · m · g · D
Explanation:
Hi there!
The work done by a force is calculated as follows:
W = F · d · cos θ
Where:
W = work.
F = force that does the work.
d = displacement.
θ = angle between the displacement and the force.
If the force is horizontal, as in this case, cos θ = 1
The friction force is calculated as follows:
Ffr = μ · m · g
Where:
μ = friction coefficient.
m = mass of the object.
g = acceleration due to gravity.
Then, in this case, the work done by friction when pushing the block from A to B will be:
W AB = -Ffr · D
W AB = - μ · m · g · D
Notice that the friction force is negative because it is opposite to the pushing force P.
When the block is pushed from B to A, the work done by friction will be:
W BA = Ffr · (-D)
W BA = -μ · m · g · D
Now, the displacement is negative and the friction force is positive (in the opposite direction to -P).
The total work done by friction will be:
W AB + W BA = - μ · m · g · D - μ · m · g · D = -2 μ · m · g · D
