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Difficulty: EasyLevers and Fulcrums

A demolition worker uses a straight steel bar to pry up a concrete slab. The bar rests on a small block acting as a fulcrum. The distance from the fulcrum to the slab is 1 foot1\text{ foot}, and the distance from the fulcrum to the worker's hands is 4 feet4\text{ feet}. If the worker pushes down with a force of 50 pounds50\text{ pounds}, what is the maximum weight of the slab that can be lifted?

  1. A
    12.5 pounds12.5\text{ pounds}
  2. B
    50 pounds50\text{ pounds}
  3. C
    250 pounds250\text{ pounds}
  4. 200 pounds200\text{ pounds}Answer

Answer

The maximum weight of the slab that can be lifted is 200 pounds200\text{ pounds}.
In a balanced lever system, the torque produced by the worker must equal the torque produced by the load. Torque is calculated as Force multiplied by Distance to the fulcrum. The worker generates an effort torque of 50 pounds×4 feet=200 foot-pounds50\text{ pounds} \times 4\text{ feet} = 200\text{ foot-pounds}. To maintain balance, the load torque must also be 200 foot-pounds200\text{ foot-pounds}. Since the load is 1 foot1\text{ foot} away from the fulcrum, the maximum weight of the slab is 200 foot-pounds/1 foot=200 pounds200\text{ foot-pounds} / 1\text{ foot} = 200\text{ pounds}.

Step-by-Step Solution

1
Determine the mechanical advantage of the lever system.
Mechanical Advantage = 4 feet/1 foot=44\text{ feet} / 1\text{ foot} = 4.
The mechanical advantage of a first-class lever is found by dividing the length of the effort arm by the length of the load arm.
2
Calculate the maximum load weight.
50 pounds×4=200 pounds50\text{ pounds} \times 4 = 200\text{ pounds}.
To find the load that can be lifted, multiply the applied effort force by the mechanical advantage.

Key Concept

Mechanical Advantage and Torque Balance in First-Class Levers
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Topics

Levers and Fulcrums

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