Problem 20 - University Physics with Modern Physics

Question

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?

Step-by-Step Solution

Answer

The force exerted by the truck on the car is 1600 N.

Step 1: Identify the Forces Involved

To solve this problem, let's first identify the forces acting on the two vehicles. The car exerts a force on the truck, and by Newton's Third Law, the truck will exert an equal and opposite force on the car. The force the car exerts on the truck is 1600 N, directed east.

Step 2: Apply Newton's Third Law

According to Newton's Third Law, every action has an equal and opposite reaction. Therefore, the force that the truck exerts on the car is equal in magnitude but opposite in direction to the force the car exerts on the truck.

Step 3: Conclusion - Determine the Force

Based on Newton's Third Law, since the car exerts 1600 N on the truck, the truck will exert a force of 1600 N on the car, in the opposite direction (west).

Key Concepts

Action and Reaction Forces

Newton's Third Law introduces the concept of action and reaction forces, which are essential in understanding interactions between objects. When two bodies interact, they apply forces to one another. These forces are known as action and reaction forces. Imagine pushing a heavy object, like a large truck, with a smaller vehicle, such as a car. The car exerts a force on the truck – this is the action force. According to Newton's Third Law, the truck responds by exerting a force back on the car – the reaction force.

Here's what you should remember:

• Action and reaction forces are always present when two bodies interact.
• These forces act on different bodies, not on the same object.
• They have the same strength but point in opposite directions.

Understanding these pairs of forces helps clarify how objects move or remain in balance in various situations.

Force Magnitude

The magnitude of a force is a measure of its strength, often expressed in Newtons (N). In our example, the car exerts a force with a magnitude of 1600 N on the truck. This tells us how strong the push from the car is.

Here are some important points about force magnitude:

• The magnitude indicates the entire amount of force without regard to its direction.
• It shows how much influence one object has on another when they interact.
• In calculations, such as determining the effect of forces, magnitude plays a crucial role.

Knowing the magnitude of forces can help you compare their influences and predict how objects will behave under their effects.

Horizontal Force

A horizontal force acts parallel to the ground. In the scenario of the car and truck on a level road, the force exerted by the car is horizontal. This means it's not aimed up or down but straight forward.

Here's why understanding horizontal forces is crucial:

• Horizontal forces typically move objects across surfaces without affecting their weight.
• They can make objects slide, accelerate, or decelerate along a path.
• Since these forces are parallel to the surface, they don't directly counteract gravity, which acts vertically.

Recognizing when forces are horizontal helps you understand their direct impact on an object's movement across a plane.

Equal and Opposite Forces

The principle of equal and opposite forces is at the heart of Newton's Third Law. This law states that the forces two bodies exert on each other are equal in magnitude but opposite in direction. In our exercise, this means that while the car pushes on the truck with a force of 1600 N, the truck pushes back on the car with a force of the same magnitude, 1600 N, directed west instead of east.

Key points to remember about equal and opposite forces include:

• This principle explains why objects don’t accelerate despite the applied forces – the forces balance each other out.
• It's crucial for understanding equilibrium and motion.
• In most interactions, observing these forces can tell us about the balance and motion of the objects involved.

Comprehending this concept is vital for solving problems related to object motion and interaction in physics.