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 slammed on the brakes and your car is skidding to a

stop while going down a ${20}^o$hill.

Short answer

The car is moving downwards of a hill that is slanted at an angle of ${20}^o.$The motion diagram states the velocity of the car till it stops while going down the hill. Also the free-body diagram represents all the forces acted on the car while moving.

Step-by-step solution

Motion diagram

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

* Model the car as a dot and assume the mass of the car is concentrated into a single point.

* The hill is slanted at an angle of ${20}^o$.

* The speed of the car is decreasing moving along downward the hill.

* The frame between the dots are decreasing as the speed of the car is decreasing due to the skidding of the car.

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

Thus, the motion-diagram of the car 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. Here, the object is the car.
2. Now we have to draw the image of the person and encircle it.
3. The following forces are acting on the car:

• The long-range gravitational force is acted the on the car directly downwards.
• The contact force- frictional force is acted on the car due to the uneven surface of the hill.
• The normal force that is a contact force is acted perpendicular to the surface of the hill.

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 climber and draw the vector of the forces.
• Represent the object (here, the car) as a dot at the origin of the coordinate axes considering the particle model.
• Here, a static frictional force ${\overrightarrow{f}}_k$is acted parallel to the surface of the hill along negative x-axis.
• A normal force is acted perpendicular to the surface of the hill along y-axis.
• A long range gravitational force ${\overrightarrow{F}}_G$is acted downwards along negative y-axis.

The car is slowing down as it moves downwards due to a net force acting parallel to the hill directed opposite of its motion as shown here: