Q. 56

Expert-verified
Found in: Page 130

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# If a car stops suddenly, you feel “thrown forward.” We’d like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there’s nothing for you to hold onto. a. Draw a picture and identify all of the forces acting on you as the car travels at a perfectly steady speed on level ground. b. Draw your free-body diagram. Is there a net force on you? If so, in which direction? c. Repeat parts a and b with the car slowing down. d. Describe what happens to you as the car slows down. e. Use Newton’s laws to explain why you seem to be “thrown forward” as the car stops. Is there really a force pushing you forward? f. Suppose now that the bench is not slippery. As the car slows down, you stay on the bench and don’t slide off. What force is responsible for your deceleration? In which direction does this force point? Include a free-body diagram as part of your answer.

Part a

The pictorial representation shows the given situation and the forces acting on you while sitting on the bench in the car.

Part b

The free-body diagram shows the forces acting on you while sitting on the bench in the car. The net force on you is zero.

Part c

The forces remain the same which implies that the pictorial representation and the free-body diagram remain unchanged.

Part d

The car slows down because of some new contact force on the car. But there is no new contact force on you. No horizontal forces are acting on you. You do not slow down and you continue at constant velocity until something in the picture changes for you.

Part e

According to Newton’s first law, if the net force on you is zero, then you continue to move in a straight line with a constant velocity. That is what happens to you when the car slows down.

You continue to move forward with a constant velocity.

Part f

The free-body diagram for the given situation shows the forces acting on you while sitting on the bench in the car as the car slows down.

See the step by step solution

## Given information

You are sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there’s nothing for you to hold onto.

## Part a

• You are sitting on a bench driving along to the right.
• Both you and the bench are moving at a constant speed, so there are no horizontal forces.
• There is a force on you due to gravity, which is acting in a downward direction.
• There is a contact force between you and the bench, which is acting in an upward direction.
• As you are not accelerating up or down the net vertical force on you is zero, which implies that the two vertical forces are equal in magnitude.
• As per the given situation, the bench is very slippery which means there is no frictional force.
• Thus, the force diagram includes only the normal force up, the gravitational force down, and no horizontal force.
• The pictorial representation is shown below

## Part b

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, follow the steps 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, you sitting on a bench) as a dot at the origin of the coordinate axes considering the particle model.
• A long-range gravitational force is acting on you.
• The free body diagram is shown below

## Part c

• The car (and therefore the bench) slows down.
• The forces remain the same which implies that the pictorial representation and the free-body diagram remain unchanged.
• Pictorial representation and the free-body diagram are shown in steps 2 and 3 respectively.

## Part d

• The car slows down because of some new contact force on the car.
• But there is no new contact force on you. Thus, the force diagram for you remains unchanged.
• No horizontal forces are acting on you.
• You do not slow down and you continue at constant velocity until something in the picture changes for you.

## Part e

The net force on you has remained zero because the net vertical force is zero and there are no horizontal forces at all.

According to Newton’s first law, if the net force on you is zero, then you continue to move in a straight line with a constant velocity. That is what happens to you when the car slows down.

You continue to move forward with a constant velocity.

## Part f

• Suppose now the bench is not slippery. That implies there is a frictional force between the bench and you. This force is certainly horizontal, that is, parallel to the surface of the bench.
• The car is slowing down and you are staying on the bench. That means you are slowing down with the bench. Your velocity to the right is decreasing (you are moving right and slowing down), so you are accelerating to the left.
• By Newton’s second law, that means the force producing the acceleration must be to the left. That force is the force of static friction.
• When the car accelerates, that is, increases in speed to the right and you accelerate with it, then your acceleration is to the right and the frictional force must be to the right.
• The free-body diagram is shown below