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Example · Example 1

Q.A force of 20 N20\ \text{N} acts on a block, making an angle of 60∘60^\circ with the horizontal, and displaces the block through 4 m4\ \text{m} along the horizontal floor. Find the work done by the force.

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✓ Free question

Given: force F=20 NF = 20\ \text{N}, displacement d=4 md = 4\ \text{m}, angle between them θ=60∘\theta = 60^\circ.

By definition, the work done by a constant force is W=Fdcos⁡θ=20×4×cos⁡60∘=20×4×0.5=40 JW = Fd\cos\theta = 20 \times 4 \times \cos 60^\circ = 20 \times 4 \times 0.5 = 40\ \text{J}

Only the horizontal component of the force, Fcos⁡θ=20cos⁡60∘=10 NF\cos\theta = 20\cos60^\circ = 10\ \text{N}, actually acts along the direction of the block's motion; the vertical component, Fsin⁡60∘F\sin60^\circ, does no work at all since it is perpendicular to the (horizontal) displacement.

✓Final answer

The work done by the force is 40 J40\ \text{J}.

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