Question

A 1000 kg car pushes a 2000 kg truck that has a dead battery. When the driver steps on the
accelerator, the drive wheels of the car push backwards against the ground with a force of 4500 N.
(a) What is the magnitude of the force of the car on the truck?
(b) What is the magnitude of the force of the truck on the car?

Answer 1

Concepts and reason

The concepts used to solve this problem are Newton’s second law and the third law of motion.

Use the concept of Newton’s second law to find the acceleration of the system and the force acting on the truck due to the car.

Use the concept of Newton’s third law to find the force acting on the car due to the truck.

Fundamentals

Newton’s second law states that the net force acting on an object is directly proportional to the product of mass and acceleration of the object.

Expression for Newton’s second law is as follows:

Here, the force of the car is , mass of the car is , and the acceleration is .

Newton’s third law states that “For every action, there is an equal and opposite reaction.

(a)

The total mass of the car and truck system is given below:

Here, the total mass of the car and truck is , the mass of the car is , and the mass of the truck is .

Substitute for and for .

Expression for the net force acting on the system is as follows:

Rearrange the expression for .

Substitute for and for .

The free body diagram for the system is given below:

Here, is the force acting on the car due to the truck and is the force acting on the truck due to the car.

The free body diagram of the truck is given below:

Expression for the force of car acting on the truck is as follows:

Substitute for and for .

(b)

The free body diagram of the car is as follows:

Newton’s third law states that “For every action, there is an equal and opposite reaction.

For the action-reaction force to be cancelled out between the car and the truck, the car should have the same amount of force acting on the truck as the force acting on the car due to the truck.

Therefore, the force on the car due to the truck is given below:

Ans: Part a

The force acting on the truck due to the car is .

Part b

The force acting on the car due to the truck is .