Question

Problems 42 through 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram.

You’ve just kicked a rock on the sidewalk and it is now sliding

along the concrete.

Short answer

The motion diagram represents the velocity of the rock while it is sliding along the concrete sidewalk. Also the free-body diagram represents all the forces acted on the rock after it is kicked.

Step-by-step solution

Motion diagram

* Consider the particle model for the diagram of the motion.

* Represent the rock as a dot and assume the mass of the car is concentrated into a single point considering the particle model.

* The frame between the dots are decreasing as the speed of the rock is slowing down due to the frictional force acted on it.

* The acceleration vector$\overrightarrow{a}$is directed opposite to the direction of motion.

Thus, the motion-diagram of the rock sliding along the concrete is given below:

Force-identification diagram

To identify the force acted on the car, we have to follow the given steps:

1. We have to consider the object in which the force is acting upon.
2. Now we have to draw the image of the object (here, the object is the rock) and encircle it.
3. The following forces are acting on the object:

• The long-range gravitational force is acted the on the rock directly downwards.
• The kinetic frictional force is acted between the rock and the concrete sidewalk due to the rough surface of the sidewalk.
• The normal reaction force that is a contact force is acted perpendicular to the surface of the concrete sidewalk.

Thus, the force-identification diagram should be as follows:

Free-body diagram

The free body diagram is a pictorial representation of an object under some forces where the objects act as the particle and the forces acting on the object.

To draw a free-body diagram, we have to follow some steps as given below:

• Draw a coordinate system.
• Identify all the forces acting on the rock that is being kicked and draw the vector of the forces.
• Represent the rock as a dot at the origin of the coordinate axes considering the particle model.
• A static frictional force ${\overrightarrow{f}}_k$is acted parallel to the surface of the concrete sidewalk along negative x-axis.
• A normal force localid="1650311162336" $\overrightarrow{n}$is acted perpendicular to the sidewalk along y-axis.
• A long range gravitational force is acted downwards along negative y-axis.
• The net force is acted on the rock acting parallel to the sidewalk and it is equal to the kinetic friction acting opposite of its motion.

Therefore, the free-body diagram of the rock that is being kicked, sliding along a concrete sidewalk is given below: