/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 A car moves along a level road. ... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 24

A car moves along a level road. If the car's velocity changes from \(60 \mathrm{mph}\) due east to \(60 \mathrm{mph}\) due west, the kinetic energy of the car A. remains the same. B. increases. C. decreases. D. first increases, then decreases. E. first decreases, then increases.

Short Answer

Expert verified
A. remains the same.

Step by step solution

01

Understanding the relationship between velocity and kinetic energy

We need to identify the parameters which affect the kinetic energy of a moving object. Kinetic energy is defined by the equation \( K = \frac{1}{2} m v^2 \) where \( K \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its speed. The direction of velocity isn't a factor in this equation.
02

Applying the concept to the situation

In this scenario, the car's velocity changes direction but its speed remains the same (60 mph). Since direction doesn't affect kinetic energy and the speed doesn't change either, we can conclude that the kinetic energy of the car remains unchanged.

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Key Concepts

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

Velocity
In physics, velocity is not just about how fast something is moving. It's a combination of speed and direction. Imagine a car driving north at 60 mph, if it turns around and drives south at 60 mph, although the speed has not changed, the velocity has. This is because velocity is a vector quantity, meaning it has both a magnitude (speed) and a specific direction. Change in either magnitude or direction means a change in velocity.
Change in Direction
Changing direction might seem insignificant if the speed remains constant, but in physics, it represents a significant shift. Whenever an object like a car alters its path, there's a change in its velocity. Although kinetic energy depends only on the magnitude of velocity (speed not the direction), understanding this change helps explain ideas like acceleration and forces acting in different directions. If a car's velocity changes from east to west, you realize that only the direction has flipped.
Speed
Speed is a measure of how fast an object is moving, without considering its direction, and is a scalar quantity. Unlike velocity, speed focuses solely on how quickly an object covers distance. For example, if a car travels 60 mph, its speed remains 60 mph regardless of whether it's moving east, west, or in circles. This attribute of speed plays a crucial role in calculating kinetic energy, as seen in the equation \( K = \frac{1}{2} m v^2 \), where only speed (not direction) is relevant.
Physics Concepts
Physics concepts such as kinetic energy can initially seem complex, but breaking them down simplifies understanding. Important principles to remember include:
  • Kinetic Energy: Relies on mass and speed, not direction.
  • Vectors vs Scalars: Velocity has direction (vector), speed doesn't (scalar).
  • Conservation of Energy: When speed remains same, kinetic energy remains constant, irrespective of direction changes.
In this context, as the car changes direction but maintains its speed, the kinetic energy is unaffected. Understanding these fundamental physics principles equips you with the knowledge to tackle problems involving movement and forces.

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Most popular questions from this chapter

A \(3.0\)-kg block is released up a ramp of angle \(\theta\) equal to \(37^{\circ}\) at initial velocity \(v_{0}\) equal to \(20 \mathrm{~m} / \mathrm{s}\). Between the block and the ramp, the coefficient of kinetic friction is \(\mu_{k}\) equal to \(0.50\) and the coefficient of static friction is \(\mu_{\text {s }}\) equal to \(0.80\). How far up the ramp (in the direction along the ramp) does the block go before it comes to a stop?

A boy swings a ball on a string at constant speed in a circle thar has a circumference equal to \(6 \mathrm{~m}\). What is the work done on the ball by the \(10-N\) rension force in the string during one revolution of the ball? A. \(190 \mathrm{~J}\) B. \(60 \mathrm{~J}\) C. \(30 \mathrm{~J}\) D. \(15 \mathrm{~J}\) E. 0

Analyze the types of energy that are associated with the "circuit" that a snowboarder follows from the bottom of a mountain, to its peak, and back down again. Be sure to explain all changes in energy. \(5 \mathrm{SM}\)

A bicyclist maintains a constant speed of \(4 \mathrm{~m} / \mathrm{s}\) up a hill that is inclined at \(10^{\circ}\) with the horizontal. Calculate the work done by the person and the work done by gravity if the bicycle moves a distance of \(20 \mathrm{~m}\) up the hill. The combined mass of the rider and the bike is \(90 \mathrm{~kg}\).

A \(20-\mathrm{g}\) object is placed against the free end of a spring (k equal to \(25 \mathrm{~N} / \mathrm{m}\) ) that is compressed \(10 \mathrm{~cm}\) (Figure 6-42). Once released, the object slides \(1.25 \mathrm{~m}\) across the tabletop and eventually lands \(1.60 \mathrm{~m}\) from the edge of the table on the floor, as shown. Is there friction between the object and the tabletop? If there is, what is the coefficient of kinetic friction? The sliding distance on the tabletop includes the 10-cm compression of the spring and the tabletop is \(1.00 \mathrm{~m}\) above the floor level.
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