Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 11

If the net work done on a particle is zero, what can be said about the particle's speed?

Short Answer

Expert verified
Answer: If the net work done on a particle is zero, the magnitude of the particle's speed does not change. The particle's final speed is either equal to or opposite in direction to its initial speed.

Step by step solution

01

Recall the Work-Energy Theorem

The Work-Energy Theorem states that the work done on an object is equal to the change in its kinetic energy: W = ΔK where W is the work done, and ΔK is the change in kinetic energy.
02

Express the Kinetic Energy in Terms of Speed

The kinetic energy (K) of an object can be expressed in terms of its mass (m) and speed (v) as follows: K = \dfrac{1}{2}mv^2 Thus, the change in kinetic energy can be expressed as: ΔK = K_f - K_i= (\dfrac{1}{2}mv_f^2 )- (\dfrac{1}{2}mv_i^2 ) where K_f is the final kinetic energy, K_i is the initial kinetic energy, v_f is the final speed, and v_i is the initial speed.
03

Set the Work Done to Zero

Given that the net work done on the particle is zero, we set W = 0 and substitute the expression for ΔK: 0 = (\dfrac{1}{2}mv_f^2 )- (\dfrac{1}{2}mv_i^2 )
04

Solve for the Relationship between Speeds

We can now solve for the relationship between the final and initial speeds: 0 = \dfrac{1}{2}m(v_f^2 - v_i^2 ) Since the mass cannot be zero, we have: 0 = v_f^2 - v_i^2 v_f^2 = v_i^2 Taking the square root of both sides, we get: v_f = ±v_i
05

Interpret the Result

If the net work done on a particle is zero, then the particle's final speed (v_f) is either equal to or opposite in direction to its initial speed (v_i). The magnitude of the particle's speed does not change when the net work done on it is zero.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A bullet moving at a speed of \(153 \mathrm{~m} / \mathrm{s}\) passes through a plank of wood. After passing through the plank, its speed is \(130 \mathrm{~m} / \mathrm{s}\). Another bullet, of the same mass and size but moving at \(92 \mathrm{~m} / \mathrm{s}\), passes through an identical plank. What will this second bullet's speed be after passing through the plank? Assume that the resistance offered by the plank is independent of the speed of the bullet.

A \(1500-\mathrm{kg}\) car accelerates from 0 to \(25 \mathrm{~m} / \mathrm{s}\) in \(7.0 \mathrm{~s}\) What is the average power delivered by the engine \((1 \mathrm{hp}=746 \mathrm{~W}) ?\) a) \(60 \mathrm{hp}\) c) \(80 \mathrm{hp}\) e) \(180 \mathrm{hp}\) b) \(70 \mathrm{hp}\) d) \(90 \mathrm{hp}\)

A horse draws a sled horizontally across a snowcovered field. The coefficient of friction between the sled and the snow is \(0.195,\) and the mass of the sled, including the load, is \(202.3 \mathrm{~kg}\). If the horse moves the sled at a constant speed of \(1.785 \mathrm{~m} / \mathrm{s}\), what is the power needed to accomplish this?

Supppose you pull a sled with a rope that makes an angle of \(30.0^{\circ}\) to the horizontal. How much work do you do if you pull with \(25.0 \mathrm{~N}\) of force and the sled moves \(25.0 \mathrm{~m} ?\)

A small blimp is used for advertising purposes at a football game. It has a mass of \(93.5 \mathrm{~kg}\) and is attached by a towrope to a truck on the ground. The towrope makes an angle of \(53.3^{\circ}\) downward from the horizontal, and the blimp hovers at a constant height of \(19.5 \mathrm{~m}\) above the ground. The truck moves on a straight line for \(840.5 \mathrm{~m}\) on the level surface of the stadium parking lot at a constant velocity of \(8.90 \mathrm{~m} / \mathrm{s}\). If the drag coefficient \(\left(K\right.\) in \(\left.F=K v^{2}\right)\) is \(0.500 \mathrm{~kg} / \mathrm{m}\), how much work is done by the truck in pulling the blimp (assuming there is no wind)?
See all solutions

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Read Explanation

Modern Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Physical Quantities And Units

Read Explanation

Energy Physics

Read Explanation

Classical Mechanics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free