Work Done By A Constant Force

Question

A warehouse worker pushes a crate along a level floor by applying a 50 N force directed at 60 degrees above the horizontal, displacing it 8 m. How much work does the applied force do?

RankGuru · Accepted Answer

Work done by a constant force equals the product of the force magnitude, the displacement, and the cosine of the angle between them, written $W = Fd\cos	heta$. Only the component of force along the displacement transfers energy to the body; the perpendicular component does no work. Here the horizontal displacement is along the floor, so the relevant component of the 50 N force is $50\cos 60^\circ = 25	ext{ N}$. Multiplying by the 8 m displacement gives $W = 25 	imes 8 = 200	ext{ J}$. The option 400 J wrongly uses the full force without the cosine factor. The option 346 J mistakenly uses $\cos 30^\circ$, effectively swapping the angle. The option 100 J halves the correct displacement contribution and has no physical basis. This follows the NCERT definition of the scalar product of force and displacement. As a plausibility check, since the force is tilted away from the motion, the work must be less than the $400	ext{ J}$ a fully horizontal force would deliver, and $200	ext{ J}$ satisfies that bound.

Work Done By A Constant Force

Select the correct option:

🔒 Solution Hidden from View

More work, energy and power Practice Questions

A gardener pushes a lawn roller with a force of 150 N directed at 60 degrees below the horizontal, m...

A rubber ball is dropped from a height of 2 m onto a hard floor and rebounds to a height of 1.28 m a...

A satellite moves in a perfectly circular orbit around the Earth under the gravitational pull direct...

A cyclist of total mass 70 kg rides up a slope inclined at 30 degrees to the horizontal at a steady ...

A small stone tied to a string is whirled in a vertical circle of radius 2 m. What is the minimum sp...

Two bodies of different masses possess the same magnitude of linear momentum while moving in a strai...

A ball is thrown vertically upward and returns to the same height from which it was launched on a wi...

A stone of mass 0.5 kg is dropped from rest at a height of 8 m above the ground. Ignoring air resist...

A weightlifter raises a barbell of mass 80 kg from the floor to a height of 2 m above the floor in 4...

A 2 kg lump of clay moving at 6 m/s strikes and sticks to a 4 kg block initially at rest on a fricti...

A car engine delivers a constant power of 50 kW while the car moves at a steady speed of 25 m/s alon...

A wooden crate of mass 10 kg is dragged 5 m up a rough incline by a force, and friction exerts a con...

About This Question

Solution