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Work, Energy, and Power — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power3 Marks
Question
A block of mass M is pulled along a horizontal surface by applying a force at an angle with horizontal. Coefficient of friction between block and surface is u. If the block travels with uniform velocity, find the work done by this applied force during ú displacement d of the block.
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Answer

The forces acting on the block are shown in Figure. As the block moves with uniform velocity the forces add up to zero.

$\therefore\text{F}\cos\theta=\mu\text{N}\cdots\text{(i)}$

$\text{F}\sin\theta+\text{N}=\text{mg}\cdots\text{(ii)}$

Eliminating N from equation (i) and (ii),

$\text{F}\cos\theta=\mu(\text{Mg}-\text{F}\sin\theta)$

$\text{F}=\frac{\mu\text{Mg}}{\cos\theta+\mu\sin\theta}$

Work done by this force during a displacement d

$\text{W}=\text{F}.\text{d}\cos\theta=\frac{\mu\text{Mgd}\cos\theta}{\cos\theta+\mu\sin\theta}$

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