Chapter 14: Q. 1 (page 1095)

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to $x = \frac{π}{2}$ if the force acting on the object at a given value of x is role="math" localid="1650297715748" $F (x) = x \sin x$ .

Short Answer

Expert verified

The work done in moving an object along the x-axis from the origin to $x = \frac{π}{2}$ is $0$ .

Step by step solution

Step 1.Given Information

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to $x = \frac{π}{2}$ if the force acting on the object at a given value of x is data-custom-editor="chemistry" $F (x) = xsinx$ .

Step 2. The work done is W=∫0π/2F(x)dx

$W = \int_{0}^{π / 2} x \sin x d x$

Firstly solving the integral

$W = \int x \sin x d x W = [x \int \sin x d x - \{\int \frac{d}{d x} (x) (\int \sin x d x)\}] W = [- x \cos x - \{- \frac{x^{2}}{2} \cos x\}] W = [- x \cos x + \frac{x^{2}}{2} \cos x]$

Step 3. Now solving the integral W=-xcosx+x22cosx0π/2

$W = {[- x \cos x + \frac{x^{2}}{2} \cos x]}_{0}^{π / 2} W = [(- \frac{π}{2} \cos \frac{π}{2} + \frac{{(\frac{π}{2})}^{2}}{2} \cos \frac{π}{2}) - (0 \cos 0 + \frac{{(0)}^{2}}{2} \cos 0)] W = [(- \frac{π}{2} \times 0 + \frac{π^{2}}{4 \cdot 2} \times 0) - (0 \cos 0 + \frac{{(0)}^{2}}{2} \cos 0)] W = [(0 + 0) - (0 + 0)] W = 0$

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to $x = \frac{π}{2}$ if the force acting on the object at a given value of x is role="math" localid="1650297715748" $F (x) = x \sin x$ .

Short Answer

Step by step solution

Step 1.Given Information

Step 2. The work done is W=∫0π/2F(x)dx

Step 3. Now solving the integral W=-xcosx+x22cosx0π/2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to x=π2 if the force acting on the object at a given value of x is role="math" localid="1650297715748" F(x)=xsinx.

Short Answer

Step by step solution

Step 1.Given Information

Step 2. The work done is W=∫0π/2F(x)dx

Step 3. Now solving the integral W=-xcosx+x22cosx0π/2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to $x = \frac{π}{2}$ if the force acting on the object at a given value of x is role="math" localid="1650297715748" $F (x) = x \sin x$ .