Chapter 9: Q. 42 (page 613)

In the definition of work given in this section, what is the work done if F is orthogonal to $\vec{A B} ?$

Short Answer

Expert verified

There will be no work done ifFis orthogonal to $\vec{A B} .$

Step by step solution

Step 1. Given Information

We have to find what will be the work done ifFis orthogonal to $\vec{A B} .$

Step 2. Finding the work done

As we know the work done by a constant force Fin moving an object from a point, A to a point B is defined as $W = F \cdot \vec{A B} .$

Now, let F constant force is moving an object from point Ato point B,and the angle between the force vector and displacement vector is $θ .$

We know the work done is localid="1646819766257" $W = F \cdot \vec{A B} . . . . . . (a)$

As we know if uand vare two nonzero vectors, the angle $θ, 0 \leq θ \leq π,$ between uand vis determined by the formula

$\cos θ = \frac{u \cdot v}{||u|| ||v||}$

Thus, $\cos θ = \frac{F \cdot \vec{A B}}{||F|| ||\vec{A B}||}$

Step 3. F is orthogonal to AB→

So, $θ = 90^{\circ}$

$\cos 90^{\circ} = \frac{F \cdot \vec{A B}}{||F|| ||\vec{A B}||} 0 = F \cdot \vec{A B} . . . . . . . . (b)$

From (a) and (b) we get,

$W = 0$

Therefore there will be no work done if F is orthogonal to $\vec{A B} .$

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In the definition of work given in this section, what is the work done if F is orthogonal to $\vec{A B} ?$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the work done

Step 3. F is orthogonal to AB→

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In the definition of work given in this section, what is the work done if F is orthogonal toAB→?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the work done

Step 3. F is orthogonal to AB→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Calculus

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the definition of work given in this section, what is the work done if F is orthogonal to $\vec{A B} ?$