Question

A bag of groceries is on the seat of your car as you stop for

a stop light. The bag does not slide. Draw a motion diagram, a

force-identification diagram, and a free-body diagram for the bag.

Short answer

The motion diagram states the velocity of the grocery bag along with the car before stopping and also the direction of acceleration.

The free-body diagram represents the forces acting on the bag of groceries while it was moving with the car and remains fixed when the car stops.

Step-by-step solution

Motion diagram

• Consider the particle model for the diagram of the motion.
• Represent the bag on the seat of the car as a dot and assume the mass of the bag is concentrated into a single point considering the particle model.
• Consider the shape or size of the bag does not affect the velocity of it according to the particle model.
• The grocery bag is in motion along with the car and when the car stops for a spotlight, it also stops with the car without sliding.
• The frame between two consecutive dots is decreasing as the car is moving forward.
• The velocity vector is directed along left to right and the acceleration vector is directed opposite to the motion of the car.

Therefore, the motion diagram of the bag should be as follows:

Force-identification diagram

To identify the forces acted on the rock, we have to follow the given steps:

• We have to consider the grocery bag in which the force is acting upon.
• Now we have to draw the image of the object and encircle it. Here the object is the grocery bag that is kept on the car seat.
• Following forces are acting on the bag:

1. A long-range gravitational force is acted straight downward the bag kept on the car seat.
2. A normal force that is equal to the force of gravity is acting on the bag vertically upward.
3. As the car is slowing down at a stop, the bag is accelerating to the opposite direction of motion but the bag is not sliding off. So, there must be a static frictional force between the car seat and the bag that keep the bag at one place as given in the image below:

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 object and draw the vector of the forces.
• Represent the object (here, the bag) as a dot at the origin of the coordinate axes considering the particle model.
• A long range gravitational force is acting on the rock which defines its weight.
• A normal force equal to the force of gravity is acting on the bag, vertically upward direction.
• The bag is not sliding across the seat. A static friction force acts in the opposite direction of motion prevents the slipping.
• Thus, the net force acts in the opposite direction in which the bag was moving with the car before stopping as follows: