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Difficulty: EasyLevers and Fulcrums

A farmer uses a long, rigid pole to move a 180-pound180\text{-pound} boulder. The pole is positioned over a smaller rock that serves as a fulcrum. The fulcrum is placed exactly 2 feet2\text{ feet} away from the boulder. The farmer pushes down on the opposite end of the pole, which is 6 feet6\text{ feet} away from the fulcrum. What is the minimum downward force the farmer must apply to lift the boulder?

  1. A
    30 pounds30\text{ pounds}
  2. B
    45 pounds45\text{ pounds}
  3. 60 pounds60\text{ pounds}Answer
  4. D
    540 pounds540\text{ pounds}

Answer

The farmer must apply 60 pounds60\text{ pounds} of downward force.
The system acts as a first-class lever. To lift the boulder, the torque (force times distance) on the farmer's side of the fulcrum must match the torque on the boulder's side. The boulder creates a torque of 360 ft-lbs360\text{ ft-lbs} (180 lbs×2 ft180\text{ lbs} \times 2\text{ ft}). To balance this over a 6-foot6\text{-foot} distance, the required force is 360/6360 / 6, which equals 60 pounds60\text{ pounds}.

Step-by-Step Solution

1
Set up the equation for a lever in equilibrium based on the principle of moments.
Effort Force×Effort Distance=Load×Load Distance\text{Effort Force} \times \text{Effort Distance} = \text{Load} \times \text{Load Distance}
For a lever to lift a load, the torque generated by the effort must equal the torque exerted by the load.
2
Substitute the provided values into the equilibrium equation.
Effort Force×6 ft=180 lbs×2 ft\text{Effort Force} \times 6\text{ ft} = 180\text{ lbs} \times 2\text{ ft}
The load is 180 lbs180\text{ lbs} at a distance of 2 ft2\text{ ft}, and the effort is applied at a distance of 6 ft6\text{ ft}.
3
Solve the equation for the Effort Force.
Effort Force=360 ft-lbs6 ft=60 lbs\text{Effort Force} = \frac{360\text{ ft-lbs}}{6\text{ ft}} = 60\text{ lbs}
Dividing the total torque of the load by the effort distance gives the required downward force.

Key Concept

Torque and Mechanical Advantage in 1st Class Levers
Estimated Time:45s
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Topics

Levers and Fulcrums

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