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Chapter 3: Problem 8

A net force must be acting when an object a. accelerates. b. changes direction but not speed. c. changes speed but not direction. d. all of the above

Short Answer

Expert verified
Option (d): all of the above.

Step by step solution

01

Understanding the Problem

Determine under what conditions a net force must be acting on an object.
02

Analyzing Acceleration

According to Newton's second law of motion, a net force must act on an object for it to accelerate. When an object accelerates, its velocity changes, indicating the presence of a net force.
03

Changing Direction

When an object changes direction but not speed, it also accelerates because acceleration is a vector quantity that includes changes in direction. Therefore, a net force must be acting.
04

Changing Speed

When an object changes its speed but not direction, it accelerates since acceleration refers to any change in the velocity (which includes speed). A net force is required for this change.
05

Consolidation

Each scenario describes a situation where acceleration occurs, either through speed, direction, or both. Therefore, a net force must be present in all scenarios. This matches option (d).

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Key Concepts

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

Understanding Acceleration
Acceleration refers to the rate at which an object's velocity changes over time. It's important to note that velocity involves both speed and direction. Therefore, an object can be accelerating even if its speed remains constant, as long as its direction is changing.
According to Newton's second law of motion, whenever there is acceleration, there must be a net force acting on the object. This is because force, mass, and acceleration are directly related. If an object is accelerating, its velocity is changing, which means a force must be causing this change.
  • Speeding up: When an object gains speed, it accelerates.
  • Slowing down: When an object decreases its speed, it also accelerates (sometimes called deceleration).
  • Changing direction: Even at a constant speed, changing direction means acceleration.
Net Force and Its Impact
The term 'net force' refers to the overall force acting on an object when all individual forces are combined. This combined force determines whether and how an object will accelerate.
If the forces acting on an object are balanced, the net force is zero, meaning there will be no acceleration. However, if there is an unbalanced force, or a net force, the object will accelerate in the direction of the net force.
  • Net force causes acceleration, changing the object's speed or direction.
  • Balanced forces result in no change in motion (constant velocity).
  • Unbalanced forces are necessary for an object to change its state of motion.
    • How Velocity Change Relates to Net Force
    Velocity change is another way to think about acceleration. When an object's velocity changes, whether in speed, direction, or both, it indicates that a net force is acting on it.
    This concept can be understood by breaking it down:
    • Change in speed: If an object speeds up or slows down, it means its velocity is changing, thus there is acceleration and a net force at play.
    • Change in direction: Even if an object maintains a constant speed, a change in its direction means there is acceleration, hence a net force causing this change in direction.
    In any case where velocity changes, Newton's second law of motion assures us that a net force must be causing this acceleration. Whether it's moving faster, slower, or turning, the presence of a net force is essential.

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    Most popular questions from this chapter

    Suppose you read in the newspaper that a new planet has been found. Its average speed in orbit is \(33 \mathrm{km} / \mathrm{s}\). When it is closest to its star it moves at \(31 \mathrm{km} / \mathrm{s}\), and when it is farthest from its star it moves at \(35 \mathrm{km} / \mathrm{s}\). This story is in error because a. the average speed is far too fast. b. Kepler's third law says the planet has to sweep out equal areas in equal times, so the speed of the planet cannot change. c. Kepler's second law says the planet must move fastest when it is closest, not when it is farthest away. d. using these numbers, the square of the orbital period will not be equal to the cube of the semimajor axis.

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