Chapter 7, Problem 52A

A car of mass m cruises along the highway at a constant velocity v. The tires push back-ward on the road with a force f. The reaction to this force provides the forward force on the car. Wind resistance against the car is R.

a. Using symbols, what is the net force on the car?

b. Using symbols, what is the acceleration of the car?

c. A friend says that since the car is moving forward, there must be a net forward force, which means f must be greater than R, even at constant velocity. What do you say to enlighten your friend?

To determine

To Find: The net force on the car.

Explanation of Solution

Given:

Mass of the car, m

The car moves at constant velocity, v

The tires push back on the tire with force, f

Wind resistance, $R$

Formula Used:

Newton’s Second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is the mass a is the acceleration .

Calculation:

Since the car moves at constant velocity. Therefore, net force on the car would be zero.

  $f-R=0$

To determine

To Find: The acceleration of the car.

Explanation of Solution

Given:

Mass of the car, m

The car moves at constant velocity, v

The tires push back on the tire with force, f

Wind resistance, $R$

Formula Used:

Newton’s Second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is the mass a is the acceleration .

Calculation:

Since the car moves at constant velocity. Therefore, net force on the car would be zero and thus acceleration would also be zero.

  $\begin{array}{l}v=\text{constant}\\ a=0\\ \frac{f-R}{m}=0\end{array}$

To determine

Whether there can be net forward force pushing the car forward if the velocity is constant.

Explanation of Solution

Introduction:

Newton’s Second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is the mass a is the acceleration .

Calculation:

The car moves forward at constant velocity. This means that its acceleration of the car is zero. From Newton’s second law of motion, if acceleration is zero, it implies that net force on the car is zero.