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Chapter 7: Problem 9

A \(1000 \mathrm{kg}\) car pushes a \(2000 \mathrm{kg}\) truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N. Rolling friction can be neglected. 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?

Short Answer

Expert verified
The magnitude of the force of the car on the truck is 4500 N, and the magnitude of the force of the truck on the car is also 4500 N.

Step by step solution

01

Understand the situation and identify forces

The car is applying a force of 4500N to the ground to move the truck. According to Newton's third law, the ground also applies an equal and opposite force to the car. Hence, the force of the car on the ground is equal to the force of the ground on the car, which is 4500N. This force is assuming to be distributed equally between the car and the truck.
02

Determine the force of the car on the truck

The force that the car applies to the truck is the same as the force that the ground applies to the car and truck system, considering that there is no friction. Therefore, the magnitude of the force of the car on the truck is 4500N.
03

Determine the force of the truck on the car

According to Newton's third law of motion, the force that the truck exerts on the car is equal and opposite to the force that the car exerts on the truck. Therefore, the magnitude of the force of the truck on the car is also 4500N.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Forces in Physics
Forces are a fundamental part of physics and can be thought of as pushes or pulls that cause objects to move or change their motion. In the scenario of the car and truck, the force being applied is known as an external force. The car uses its engine to push against the ground, creating a forward force. This force is essential to initiate motion. When we talk about forces, it's important to remember:
  • Forces can cause acceleration, which means a change in the speed or direction of an object's motion.
  • They have both magnitude (how strong) and direction (which way they're pushing or pulling).
In our case, the car exerts a force of 4500 N against the ground, which plays a key role in moving the truck. This force overcomes any resistance, starting the motion of the two vehicles together.
Frictionless Motion
Frictionless motion is an idealized concept, where we assume there is no resistance from surfaces when objects move. It helps us understand basic physical principles without the complexity added by real-world friction. In our problem, we assume rolling friction is negligible, which simplifies the interaction between the car and truck. This means the full force exerted by the car's wheels is used to push the truck without any reduction due to friction. Here's what you should know about frictionless motion:
  • Friction normally opposes motion, making it harder for objects to slide over each other.
  • Without friction, an object would continue moving at a constant speed unless another force is applied.
Applying the concept of frictionless motion makes solving physics problems simpler, as it allows forces to be directly used to calculate movement without losses.
Force Interaction
Force interaction is a key component of understanding how objects affect each other in the realm of physics. According to Newton's Third Law of Motion, every action force has an equal and opposite reaction force. In the exercise:
  • The car exerts a force on the truck, which is 4500 N.
  • Simultaneously, the truck exerts an equal force of 4500 N back on the car, but in the opposite direction.
This interaction ensures that forces always come in pairs. Newton's Third Law helps us understand that forces are mutual - one object cannot apply a force without experiencing one in return. So, despite the different masses of the car and truck, the forces they exert on each other stay balanced, allowing for predictable motion.

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Most popular questions from this chapter

\(A 4.0 \mathrm{kg}\) box is on a frictionless \(35^{\circ}\) slope and is connected via a massless string over a massless, frictionless pulley to a hanging \(2.0 \mathrm{kg}\) weight. The picture for this situation is similar to Figure P7.39. a. What is the tension in the string if the \(4.0 \mathrm{kg}\) box is held in place, so that it cannot move? b. If the box is then released, which way will it move on the slope? c. What is the tension in the string once the box begins to move?

A Federation starship \(\left(2.0 \times 10^{6} \mathrm{kg}\right)\) uses its tractor beam to pull a shuttlecraft \(\left(2.0 \times 10^{4} \mathrm{kg}\right)\) aboard from a distance of \(10 \mathrm{km}\) away. The tractor beam exerts a constant force of \(4.0 \times 10^{4} \mathrm{N}\) on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

A 100 g ball of clay is thrown horizontally with a specd of \(10 \mathrm{m} / \mathrm{s}\) toward a \(900 \mathrm{g}\) block resting on a rictionless surface. It hits the block and sticks. The clay exerts a constant force on the block during the 10 ms it takes the clay to come to rest relative to the block. After 10 ms, the block and the clay are sliding along the surface as a single system. a. What is their speed after the collision? b. What is the force of the clay on the block during the collision? c. What is the force of the block on the clay?

a. How much force does an 80 kg astronaut exert on his chair while sitting at rest on the launch pad? b. How much force does the astronaut exert on his chair while accelerating straight up at \(10 \mathrm{m} / \mathrm{s}^{2} ?\)

Shows a \(200 \mathrm{g}\) hamster sitting on an \(800 \mathrm{g}\) wedge shaped block. The block, in turn, rests on a spring scale. a. Initially, static friction is sufficient to keep the hamster from moving. In this case, the hamster and the block are effectively a single \(1000 \mathrm{g}\) mass and the scale should read \(9.8 \mathrm{N}\). Show that this is the case by treating the hamster and the block as separaie objects and analyzing the forces. b. An extra-fine lubricating oil having \(\mu_{s}=\mu_{k}=0\) is sprayed on the top surface of the block, causing the hamster to slide down. Friction between the block and the scale is large enough that the block does not slip on the scale. What does the scale read as the hamster slides down?
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