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Difficulty: MediumWork, Energy and Power

A crate is pulled along a smooth horizontal floor by a constant force of 80 N80\text{ N} applied at an angle of 60∘60^\circ to the horizontal. If the crate moves through a displacement of 15 m15\text{ m} along the floor, what is the work done by the applied force?

  1. 600 J600\text{ J}Answer
  2. B
    1039 J1039\text{ J}
  3. C
    1200 J1200\text{ J}
  4. D
    300 J300\text{ J}

Answer

600 J600\text{ J}
The work done by a constant force applied at an angle θ\theta to the direction of motion is given by W=Fscos⁡θW = F s \cos\theta. Substituting F=80 NF = 80\text{ N}, s=15 ms = 15\text{ m}, and cos⁡(60∘)=0.5\cos(60^\circ) = 0.5 gives W=80×15×0.5=600 JW = 80 \times 15 \times 0.5 = 600\text{ J}.

Step-by-Step Solution

1
Identify the given physical quantities
Force F=80 NF = 80\text{ N}, displacement s=15 ms = 15\text{ m}, angle θ=60∘\theta = 60^\circ
Extract parameters required for the work formula.
2
Apply the work formula for a force at an angle
W=Fscos⁡θW = F s \cos\theta
Only the component of force parallel to the displacement does work on the object.
3
Substitute the values and compute the result
W=80×15×cos⁡(60∘)=1200×0.5=600 JW = 80 \times 15 \times \cos(60^\circ) = 1200 \times 0.5 = 600\text{ J}
Calculates the effective work done by the applied force.

Key Concept

Work Done by a Constant Force at an Angle
Estimated Time:1m 0s
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Topics

Work, Energy and Power

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