/*! 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} Q61P How much work is done by a force... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 7: Q61P (page 175)

How much work is done by a force $\overset{鈫�}{F} = (2 x N) \hat{i} + (3 N) \hat{j}$ ,with x in meters, that moves a particle from a position $\overset{鈫�}{r_{i}} = (2 m) \hat{i} + (3 m) \hat{j}$ to a position $\overset{鈫�}{r_{f}} = - (4 m) \hat{i} + (3 m) \hat{j}$ ?

Short Answer

Expert verified

Work done by the applied force is $- 6 J$

Step by step solution

01

Given information

It is given that,

$F_{a p p} = (2 x N) \hat{i} + (3 N) \hat{j} \overset{鈫�}{r_{i}} = (2 m) \hat{i} + (3 m) \hat{j} \overset{鈫�}{r_{f}} = - (4 m) \hat{i} - (3 m) \hat{j}$

02

Determining the concept

This problem deals with the variable forces. When the direction and the amount of force vary throughout the motion, variable forces occur. To solve this problem, usetheconcept of variable forces. Work done due to variable forces can be found by using integration.

Formula:

The work done is given by,

$W = 鈭� F_{x} . d x + 鈭� F_{y} . d y$

Where,

$F_{x,} F_{y}$ Are the forces in x and y direction, dx and dy are small displacements.

03

Determining the work done by the applied force (Wapp).

Using the above formula, writethetotal work done as,

$W = {鈭�}_{x i}^{x f} F_{x} d x + {鈭�}_{y i}^{y f} F_{y} d y$

Substituting the value of forces and from the given data,

$W = {鈭�}_{2}^{- 4} 2 脳 d x + {鈭�}_{3}^{- 3} 3 d y W = {[x^{2}]}_{2}^{- 4} + {[3 y]}_{3}^{- 3} W = 16 - 4 - 9 - 9 W = - 6 J$

Work done by the applied force is $- 6 J$

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

An initially stationary 2.0kgobject accelerates horizontally and uniformly to a speed of10 m/sin3.0 s. (a) In that 3.0 sinterval, how much work is done on the object by the force accelerating it? What is the instantaneous power due to that force (b) at the end of the interval and (c) at the end of the first half of the interval?

A can of bolts and nuts is pushed 2.00 m along an x axis by a broom along the greasy (frictionless) floor of a car repair shop in a version of shuffleboard. Figure 7-26 gives the work Wdone on the can by the constant horizontal force from the broom, versus the can鈥檚 position x. The scale of the figure鈥檚 vertical axis is set by W_S=6 J. (a) What is the magnitude of that force? (b) If the can had an initial kinetic energy of 3.00 J, moving in the positive direction of the x axis, what is its kinetic energy at the end of the 2.00 m?

A bead with mass $1.8 脳 10^{- 2} kg$ is moving along a wire in the positive direction of an x axis. Beginning at time t=0, when the bead passes through x=0 with speed 12 m/s, a constant force acts on the bead. Figure 7-24 indicates the bead鈥檚 position at these four times: t₀=0, t₁=1.0 s, t₂=2.0 s, and t₃=3.0 s. The bead momentarily stops at t=3.0 s. What is the kinetic energy of the bead at t=10 s ?

A father racing his son has half the kinetic energy of the son, who has half the mass of the father. The father speeds up by $1.0 m / s$ and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son?

A cord is used to vertically lower an initially stationary block of mass M at a constant downward acceleration of $\frac{g}{4}$ .When the block has fallen a distance d , find

(a) the work done by the cord鈥檚 force on the block,

(b) the work done by the gravitational force on the block,

(c) the kinetic energy of the block, and

(d) the speed of the block.

See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Linear Momentum

Read Explanation

Energy Physics

Read Explanation

Dynamics

Read Explanation

Famous Physicists

Read Explanation

Scientific Method Physics

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.