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Difficulty: HardLevers and Fulcrums

A hydraulic piston is attached to a hinged ramp 22 feet away from the hinge (the fulcrum) and pushes perpendicularly to close it. A 200200-pound heavy crate is positioned on the ramp 88 feet away from the hinge. Assuming the weight of the ramp itself is negligible, how much effort force must the hydraulic piston apply to balance the crate, and which class of lever does this mechanism represent?

  1. 800 pounds; Third-class leverAnswer
  2. B
    50 pounds; Second-class lever
  3. C
    800 pounds; Second-class lever
  4. D
    50 pounds; Third-class lever

Answer

800 pounds; Third-class lever
The correct answer accurately identifies the system as a third-class lever because the effort (the piston) is located between the fulcrum (the hinge) and the load (the crate). Using the principle of moments, the torque from the load is 200 pounds×8 feet=1600 lb-ft200 \text{ pounds} \times 8 \text{ feet} = 1600 \text{ lb-ft}. To balance this, the piston must apply an equal opposing torque at a distance of 22 feet: 1600÷2=800 pounds1600 \div 2 = 800 \text{ pounds}.

Step-by-Step Solution

1
Identify the lever class based on the arrangement of components.
The arrangement is Fulcrum (hinge) - Effort (piston at 2 ft) - Load (crate at 8 ft).
Because the effort is applied between the fulcrum and the load, this is by definition a third-class lever.
2
Set up the torque balance equation to find the effort force.
Effort×Effort Arm=Load×Load Arm\text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm}
For the lever to be balanced, the clockwise torque must equal the counterclockwise torque.
3
Substitute the known values into the equation and solve for Effort.
Effort×2=200×8\text{Effort} \times 2 = 200 \times 8, which simplifies to 2E=16002\text{E} = 1600. Solving for E gives 800800 pounds.
A third-class lever always has a mechanical advantage of less than 1, requiring an effort force greater than the load.

Key Concept

Torque Balance and Third-Class Levers
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Topics

Levers and Fulcrums

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