/*! 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 11 If the net work done on a partic... [FREE SOLUTION] | 91影视

91影视

Log out

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 = 螖K where W is the work done, and 螖K 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: 螖K = 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 螖K: 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 = 卤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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 car does the work \(W_{\text {car }}=7.0 \cdot 10^{4} \mathrm{~J}\) in traveling a distance \(x=2.8 \mathrm{~km}\) at constant speed. Calculate the average force \(F\) (from all sources) acting on the car in this process.

A father pulls his son, whose mass is \(25.0 \mathrm{~kg}\) and who is sitting on a swing with ropes of length \(3.00 \mathrm{~m}\), backward until the ropes make an angle of \(33.6^{\circ}\) with respect to the vertical. He then releases his son from rest. What is the speed of the son at the bottom of the swinging motion?

How much work is done against gravity in lifting a \(6.00-\mathrm{kg}\) weight through a distance of \(20.0 \mathrm{~cm} ?\)

Two railroad cars, each of mass \(7000 . \mathrm{kg}\) and traveling at \(90.0 \mathrm{~km} / \mathrm{h},\) collide head on and come to rest. How much mechanical energy is lost in this collision?

A car of mass \(m\) accelerates from rest along a level straight track, not at constant acceleration but with constant engine power, \(P\). Assume that air resistance is negligible. a) Find the car's velocity as a function of time. b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens. c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of \(12.0 \mathrm{~m} / \mathrm{s}^{2} .\) Both cars have identical masses of \(1000 . \mathrm{kg} .\) The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is \(0.250 \mathrm{mi}\)
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Space Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Atoms and Radioactivity

Read Explanation

Energy Physics

Read Explanation

Translational Dynamics

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.