A small car of mass 380 kg is pushing a large truck of mass 900 kg due east on a level road. The car exerts a horizontal force of 1600 N on the truck. What is the magnitude of the force that the truck exerts on the car?

Verified step by step guidance

1. Identify the action and reaction forces involved. According to Newton's Third Law, every action has an equal and opposite reaction. Here, the car exerts a force on the truck, which is the action force.
2. Recognize that the reaction force is the force that the truck exerts on the car. By Newton's Third Law, this force must be equal in magnitude and opposite in direction to the force exerted by the car.
3. Determine the direction of the reaction force. Since the car pushes the truck eastward, the truck's force on the car will be directed westward.
4. Calculate the magnitude of the reaction force. Since the forces are equal and opposite, the magnitude of the force that the truck exerts on the car is the same as the force the car exerts on the truck.
5. Conclude that the magnitude of the force that the truck exerts on the car is 1600 N, directed westward.

Key Concepts

Newton's Third Law of Motion

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that if one object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction on the first object. In this scenario, the force exerted by the car on the truck will be matched by the force exerted by the truck on the car.

Force and Mass

Force is defined as the interaction that causes an object to change its velocity, and it is calculated using Newton's second law, F = ma, where F is force, m is mass, and a is acceleration. In this problem, understanding the masses of the car and truck helps in analyzing the forces at play, particularly how they interact when one object pushes another.

Net Force and Motion

The net force acting on an object is the vector sum of all the forces acting on it. In this case, the net force on the truck is the force exerted by the car minus any opposing forces (like friction). Understanding net force is crucial for determining how the system of the car and truck will move together, as it influences their acceleration and the interaction between the two vehicles.