Problems 51 and 52 show the free-body diagrams of two interacting systems. For each of these, you are to

a. Write a realistic problem for which these are the correct freebody diagrams. Be sure that the answer your problem requests is consistent with the diagrams shown.

b. Finish the solution of the problem.

The given $FIGUREP7.52$follows and describes a roller is sliding over the block moving in forward force $F.$

Now we are ready to write the newton's second law for roller

$$\begin{gathered} \sum _i{\left(F_{onroller}\right)}_{i,x}=-F-2.94N=m_r{a}_r \\ \sum _i{\left(F_{onroller}\right)}_{i,y}=9.8N-9.8N=0 \end{gathered}$$

For the block

$$\begin{gathered} \sum _i{\left(F_{onblock}\right)}_{i,x}=F-9.8N=m_b{a}_b \\ \sum _i{\left(F_{onblock}\right)}_{i,y}=19.6N-19.6N=0 \end{gathered}$$

Therefore, the unknown force acting on the block when roller sliding down on the block, braking is $F=9.8N-2.94N=6.86N$,

Consistent with the diagrams shown here, the following explanations are given.

The roller is interacting twice with the block—a friction force parallel to the surface of the block and a normal force perpendicular to this surface. The block interacts similarly with the level surface, but notice that the roller does not interact with the ground; there’s no contact between them.

The two interactions within the system are each an action/reaction pair, so this is a total of four forces. You can also see four external forces crossing the system boundary, so the free-body diagrams should show a total of eight forces.