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Difficulty: EasyLevers and Fulcrums

A construction worker uses a straight steel bar to lift a 150-pound150\text{-pound} concrete slab. A metal pipe is placed underneath the bar to serve as a pivot point (fulcrum). If the slab rests on the bar 3 feet3\text{ feet} from the fulcrum, and the worker applies downward force on the opposite end at a distance of 9 feet9\text{ feet} from the fulcrum, how much force is required to perfectly balance the slab?

  1. A
    37.5 lbs37.5\text{ lbs}
  2. 50 lbs50\text{ lbs}Answer
  3. C
    150 lbs150\text{ lbs}
  4. D
    450 lbs450\text{ lbs}

Answer

The correct force required is 50 lbs50\text{ lbs}.
According to the principle of levers, a system is balanced when the input torque equals the output torque (F1×d1=F2×d2F_1 \times d_1 = F_2 \times d_2). The concrete slab generates 450 lb-ft450\text{ lb-ft} of torque (150 lbs×3 ft150\text{ lbs} \times 3\text{ ft}). Dividing this torque by the effort arm distance of 9 feet9\text{ feet} yields a required downward effort force of 50 lbs50\text{ lbs}.

Step-by-Step Solution

1
Set up the torque balance equation for a first-class lever.
Forceeffort×Distanceeffort=Forceload×DistanceloadForce_{effort} \times Distance_{effort} = Force_{load} \times Distance_{load}
For a lever to be perfectly balanced, the torque applied by the worker must equal the torque exerted by the load.
2
Calculate the torque of the load.
150 lbs×3 ft=450 lb-ft150\text{ lbs} \times 3\text{ ft} = 450\text{ lb-ft}
Torque is calculated by multiplying the weight of the object by its distance to the fulcrum.
3
Solve for the required effort force.
450 lb-ft/9 ft=50 lbs450\text{ lb-ft} / 9\text{ ft} = 50\text{ lbs}
Dividing the total load torque by the length of the effort arm determines the exact force the worker needs to apply.

Key Concept

Torque balance in first-class levers (Law of Levers)
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Topics

Levers and Fulcrums

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