A student applies a constant force on a box at an angle to the horizontal, and the box moves in a straight horizontal line on a rough surface. Which statement correctly describes the work done by the applied force on the box?
Only the horizontal component of the applied force, multiplied by the distance moved in the same direction, gives the work done
Work done by a force is defined as the dot product \(W = \vec{F}\cdot\vec{s} = Fs\cos\theta\), where \(\theta\) is the angle between force and displacement.
Only the component of the force along the displacement contributes to work; the perpendicular component does zero work.
Here the displacement is horizontal, so the vertical component of the applied force is perpendicular to the motion and contributes nothing.
Only the horizontal component \(F\cos\theta\) multiplied by the horizontal displacement gives the work done on the box.
Hence, work equals the horizontal component of the applied force times the distance moved in the same direction.
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