Q. 1 Work as an integral of force and... [FREE SOLUTION]

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 $x = \frac{蟺}{2}$ 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 $x = \frac{蟺}{2}$ 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 $x = \frac{蟺}{2}$ 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

$W = {鈭�}_{0}^{蟺 / 2} x \sin x d x$

Firstly solving the integral

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

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

$W = {[- x \cos x + \frac{x^{2}}{2} \cos x]}_{0}^{蟺 / 2} W = [(- \frac{蟺}{2} \cos \frac{蟺}{2} + \frac{{(\frac{蟺}{2})}^{2}}{2} \cos \frac{蟺}{2}) - (0 \cos 0 + \frac{{(0)}^{2}}{2} \cos 0)] W = [(- \frac{蟺}{2} 脳 0 + \frac{蟺^{2}}{4 路 2} 脳 0) - (0 \cos 0 + \frac{{(0)}^{2}}{2} \cos 0)] W = [(0 + 0) - (0 + 0)] W = 0$

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91影视

Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to $x = \frac{蟺}{2}$ 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

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91影视

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=蟺2 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

Logic and Functions

Pure Maths

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

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 $x = \frac{蟺}{2}$ if the force acting on the object at a given value of x is role="math" localid="1650297715748" $F (x) = x \sin x$ .