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Chapter 4: Problem 29

\(\bullet\) The driver of a car traveling at 65 mph suddenly hits his brakes on a horizontal highway.(a) Make a free-body diagram of the car while it is slowing down. (b) Make a free-body diagram of a passenger in a car that is accelerating on a freeway entrance ramp.

Short Answer

Expert verified
Draw free-body diagrams with forces labeled for both scenarios.

Step by step solution

01

Understanding the Problem

We have two distinct scenarios to analyze. First, we need to create a free-body diagram of a car slowing down due to braking on a horizontal highway. Second, we need to draw a free-body diagram depicting a passenger in a car that is accelerating on a freeway entrance ramp.
02

Car Slowing Down - Free Body Diagram

For the car slowing down, we identify the forces acting on it: 1. **Weight ( W )**: The force due to gravity acting downwards on the car. Formula: W = mg , where mg g is the acceleration due to gravity (9.8 m/s ^2). 2. **Normal Force ( N )**: The support force exerted perpendicular to the surface (highway) by the ground on the car. 3. **Frictional Force ( F_f )**: The force exerted by the brakes, acting opposite to the direction of motion (deceleration). In the free-body diagram, these forces should be represented as: - W pointing vertically downwards. - N pointing vertically upwards, balancing the weight. - F_f pointing horizontally opposite to the direction of motion.
03

Passenger Accelerating - Free Body Diagram

For the passenger in an accelerating car: 1. **Normal Force ( N_p )**: Directed upwards, this represents the force exerted by the car seat on the passenger. 2. **Weight ( W_p )**: The gravitational force acting downwards. 3. **Inertial Force ( F_i )**: A fictitious force that acts in the opposite direction to the acceleration due to the resistance experienced by the passenger. This isn't an actual force but useful in a non-inertial reference frame to analyze motion. In the free-body diagram: - W_p acts vertically downward. - N_p acts vertically upward, equal in magnitude to W_p. - F_i points horizontally in the direction opposite to the acceleration of the car.

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Key Concepts

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

Normal Force
When an object is placed on a surface, like a car on a road, the ground exerts an upward force known as the normal force. This force is perpendicular, or "normal," to the surface. It's what keeps the object from sinking into the ground. For a car on a flat horizontal highway, the normal force perfectly balances the weight of the car, so the car doesn't move vertically but stays steady on the road.
  • The normal force equals the gravitational force if the surface is flat and horizontal.
  • It acts perpendicular to the ground plane.
In the car slowing down scenario, the normal force counteracts the weight force. Similarly, when a passenger is accelerating inside the vehicle, the normal force from the car seat acts upward, supporting the passenger's weight, ensuring that they do not fall downward.
Weight Force
The weight force is a fundamental concept in physics. It鈥檚 the force exerted by the earth's gravity on an object. Weight is calculated using the equation \[ W = mg \] where \( m \)is the object's mass and \( g \)is the acceleration due to gravity, averaged at approximately 9.8 \( m/s^2 \) on the surface of the earth.
  • Weight acts downwards towards the center of the Earth.
  • It is directly proportional to the mass of the object.
In both the scenarios of a car braking on a highway and a passenger accelerating in a car, the weight force acts downward. For the car, it is the gravity's pull on the entire vehicle, and for the passenger, it pulls them down onto the seat of the car.
Frictional Force
Frictional force is the resistance that one surface or object encounters when moving over another. It acts opposite to the direction of motion and is crucial for activities like driving, as it helps the car slow down and stop.
  • Frictional force is essential for braking in vehicles.
  • It helps in controlling motion by resisting unwanted movement.
In the braking car scenario, the frictional force is due to the interaction between the car鈥檚 tyres and the road surface. This force is what allows the car to decelerate when the brakes are applied. Without sufficient friction, stopping would be impossible, which is why vehicles have trouble stopping on icy roads.
Inertial Force
Inertial force is not an actual force but a useful concept in physics. When observing motion from a non-inertial (accelerating) frame of reference, such as being inside an accelerating car, we often introduce "fictitious" forces to simplify analyses. This helps in understanding how objects behave in rapidly changing frames.
  • In an accelerating car, passengers feel as though they are pushed backwards due to inertial force.
  • It appears in the opposite direction to acceleration.
For the passenger in our example, the inertial force acts opposite to the car鈥檚 acceleration direction. This is why passengers feel as though they are being pushed into their seat when the car speeds up quickly.
Forces in Physics
Forces, fundamentally, are interactions that cause objects to accelerate, decelerate, or maintain their motion. Understanding forces is crucial to comprehending how the physical world operates. They can be contact forces, like the normal and frictional forces, or non-contact forces, like gravitational or electromagnetic forces.
  • Forces are vector quantities, which means they have both magnitude and direction.
  • They play an essential role in determining the motion of objects.
In our exercise, various forces interact with one another. The normal and weight forces generally act vertically, while frictional and inertial forces act horizontally. Mastering these concepts enhances our understanding of everyday phenomena, like driving a car or even sitting inside one as it speeds up or slows down.

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Most popular questions from this chapter

BIO Bacterial motion. A bacterium using its flagellum as propulsion can move through liquids at a rate of 0.003 \(\mathrm{m} / \mathrm{s} .\) For a \(50 \mu \mathrm{m}-\) long bacterium, that is the equivalent of 60 cell lengths per second. Bacteria of that size have a mass of approximately \(1 \times 10^{-12} \mathrm{g}\). The viscous drag on a swimming bacterium is so great that if it stops beating its flagellum it will stop within a distance of 0.01 \(\mathrm{nm} .\) What is the acceleration that stops the bacterium? A. \(1.2 \times 10^{4} \mathrm{m} / \mathrm{s}^{2}\) B. \(5 \times 10^{5} \mathrm{m} / \mathrm{s}^{2}\) C. \(6 \times 10^{5} \mathrm{m} / \mathrm{s}^{2}\) D. \(9 \times 10^{5} \mathrm{m} / \mathrm{s}^{2}\)

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A truck is pulling a car on a horizontal highway using a horizontal rope. The car is in neutral gear, so we can assume that there is no appreciable friction between its tires and the highway. As the truck is accelerating to highway speeds, draw a free-body diagram of (a) the car and (b) the truck. (c) What force accelerates this system forward? Explain how this force originates.

A hockey puck with mass 0.160 \(\mathrm{kg}\) is at rest on the horizontal, frictionless surface of a rink. A player applies a force of 0.250 \(\mathrm{N}\) to the puck, parallel to the surface of the ice, and continues to apply this force for 2.00 \(\mathrm{s}\) . What are the position and speed of the puck at the end of that time?
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