Q30P - University Physics with Modern Physics

Question

 A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. When the light turns green, you stomp on the gas and the truck accelerates. To your horror, the box starts to slide towards the back of the truck. Draw clearly labeled free-body diagrams for the truck and for the box. Indicate pairs of forces, if any that are third-law action-reaction pairs. (The horizontal truck bed is not frictionless.)

Step-by-Step Solution

Answer

The free-body diagram of the truck is

                                           

The normal reaction force $\left(\mathrm{N}\right)$ and the weight of the truck $\left(\mathrm{W}\right)$ are the pair of forces that are third-law action-reaction pair and the friction force ${\mathrm{F}}_{\mathrm{f}}$ that acts on the track surface as well as acts on the box surface is also the pair of forces that are third-law action-reaction pair.

The free-body diagram of the box is

                                                             

The normal reaction force $\left({\mathrm{N}}_{\mathrm{b}}\right)$and the weight of the box $\left({\mathrm{W}}_{\mathrm{b}}\right)$ are the pair of forces that are the third-law action-reaction pair.

Step 1: Significance of free-body diagram/Simple diagram:

A free-body diagram is a simple diagram including a box or dot representing a mass with arrows pointing away from the box or dot. The arrows represent the forces acting on the mass. Retarding forces act in the opposite direction of an object's motion.

Step 2: Drawing the free body diagram of the truck

The free-body diagram of the truck is given below.

                                                   

Here, $\mathrm{N}$ is the normal reaction force, $\mathrm{W}$ is the weight of the truck, $\left(\mathrm{W}\right)$ is the friction force that acts on the truck surface and $\mathrm{F}$ is the applied force due to which the truck is moving.

From the above free-body diagram, the normal reaction force $\left(\mathrm{N}\right)$ and the weight of the truck $\left(\mathrm{W}\right)$ are the pair of forces that are the third-law action-reaction pair and the friction force ${\mathrm{F}}_{\mathrm{f}}$ that acts on the truck surface as well as acts on the box surface are also the pair of forces that are third-law action-reaction pair.

Step 3: Draw the free body diagram of the box

The free-body diagram of the box is given below.

                               

Here, ${\mathrm{W}}_{\mathrm{b}}$ is the weight of the box, ${\mathrm{F}}_{\mathrm{f}}$ is the friction force that acts on the box surface that is equal to the friction force acts on the truck surface and ${\mathrm{N}}_{\mathrm{b}}$ is the normal reaction force on the box.

From the above free-body diagram, the normal reaction force $\left({\mathrm{N}}_{\mathrm{b}}\right)$ and the weight of the box $\left({\mathrm{W}}_{\mathrm{b}}\right)$ are the pair of forces that are third-law action-reaction pair.