Chapter 10: Q.35 (page 257)

A particle moves from A to D in $F I G U R E E X 10.35$ while experiencing force $\vec{F} = (6 \hat{i} + 8 \hat{j}) N$ . How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

Short Answer

Expert verified

If particle followed path ABD then work done = $50 J$ .

If particle followed path ACD then work done = $50 J$ .

If particle followed path AD then work done = $50 J$ .

Step by step solution

Given information

Force, $\vec{F} = (6 \hat{i} + 8 \hat{j}) N$

Curve followed path,

Explanation :

The force exerted on a mass item that causes it to alter velocity.

When particle follows the path ABD, the work done is

$W_{A B D} = (6 \times 3 + 8 \times 0) + (6 \times 0 + 8 \times 4) = 50 J$

When particle follows the path ACD, the work done is

$W_{A C D} = (6 \times 0 + 8 \times 4) + (6 \times 3 + 8 \times 0) = 50 J$

When particle follows the path AD, the work done is

$W_{A D} = (6 \times 3 + 8 \times 4) = 50 J$

Hence, in all the conditions the work done is same. So, the force is a conservative force.

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A particle moves from A to D in $F I G U R E E X 10.35$ while experiencing force $\vec{F} = (6 \hat{i} + 8 \hat{j}) N$ . How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

Short Answer

Step by step solution

Given information

Explanation :

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A particle moves from A to D in FIGUREEX10.35while experiencing forceF→=(6i^+8j^)N. How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

Short Answer

Step by step solution

Given information

Explanation :

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A particle moves from A to D in $F I G U R E E X 10.35$ while experiencing force $\vec{F} = (6 \hat{i} + 8 \hat{j}) N$ . How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.