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Difficulty: EasyWork, Energy, and Power

A shop crane lifts a replacement motor vertically through a distance of 4 meters4\text{ meters}, performing 2000 J2{}000\text{ J} of work. What constant upward force is exerted by the crane?

  1. A
    8000 N8{}000\text{ N}
  2. 500 N500\text{ N}Answer
  3. C
    500 kg500\text{ kg}
  4. D
    500 W500\text{ W}

Answer

The constant upward force exerted by the crane is 500 N500\text{ N}.
Work equals force multiplied by distance (W=F×dW = F \times d). Dividing the total work of 2000 J2{}000\text{ J} by the vertical distance of 4 meters4\text{ meters} yields a constant force of 500 N500\text{ N}.

Step-by-Step Solution

1
State the formula relating work, force, and distance.
W=F×dW = F \times d
Work is defined as force applied over a parallel distance.
2
Rearrange the equation to solve for force.
F=WdF = \frac{W}{d}
Isolating force allows direct calculation from known work and distance values.
3
Substitute the given values (W=2000 JW = 2{}000\text{ J} and d=4 md = 4\text{ m}) into the rearranged formula.
F=2000 J4 m=500 NF = \frac{2{}000\text{ J}}{4\text{ m}} = 500\text{ N}
Carrying out the division yields the magnitude of force in newtons.

Key Concept

Work and Force Relationship
Estimated Time:45s
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Topics

Work, Energy, and Power

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