Question

Object 1 pushes on object 2 as the objects move together, like a bulldozer pushing a stone. Assume object 1 does of work on object 2. Does object 2 do work on object 1? Explain your answer. If possible, determine how much work and explain your reasoning.

Short answer

Yes, object 2 works on object 1, and the value of the work done by object 2 on object 1 is.

Step-by-step solution

Given information

The work done by object 1 on object 2,${\mathrm{W}}_{1-2}=15.0\mathrm{J}$

Work done 

When two objects exert an equal amount of force on each other and travel to equal distances, the magnitude of work done would be equal for both objects.

If the direction of force acting on two objects is equal but opposite to each other, then the sum of work done by both objects on each other would be zero.

Work done by object 2 on object 1 

It is given that object 1 pushes on object 2 as both the objects move together; it means that object 1 exerts a certain amount of force on object 2. According to Newton’s third law, object 2 would also exert the same amount of force on object 1 but in the opposite direction. By this law, the work done by object 2 on object 1 would be equal in magnitude but opposite in direction to the work done by object 1 on object 2.

So, the work done by object 2 on object 1 can be calculated as follows:

$\begin{array}{l}{\mathrm{W}}_{2-1}=-{\mathrm{W}}_{1-2}\\ {\mathrm{W}}_{2-1}=-15.0\mathrm{J}\end{array}$

Hence, it is clear object 2 works on object 1, and the value of the work done by object 2 on object 1 is $-15.0\mathrm{J}$.