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Difficulty: MediumLevers and Fulcrums

A hinged lifting ramp is supported by a vertical hydraulic cylinder. The hinge acts as the fulcrum at one end of the ramp. The hydraulic cylinder applies an upward force exactly 3 feet3\text{ feet} from the hinge. A heavy crate weighing 600 lbs600\text{ lbs} rests on the ramp exactly 12 feet12\text{ feet} from the hinge. Assuming the ramp is horizontal and ignoring its weight, how much upward force must the hydraulic cylinder exert to keep the ramp in equilibrium?

  1. 2400 lbs2400\text{ lbs}Answer
  2. B
    1800 lbs1800\text{ lbs}
  3. C
    800 lbs800\text{ lbs}
  4. D
    150 lbs150\text{ lbs}

Answer

2400 lbs2400\text{ lbs}
In this third-class lever setup, the fulcrum is at one end (the hinge), the effort is applied in the middle, and the load is at the other end. To maintain equilibrium, the upward torque must equal the downward torque. The load torque is 600 lbs×12 feet=7200 ft-lbs600\text{ lbs} \times 12\text{ feet} = 7200\text{ ft-lbs}. To find the required effort force, divide the total torque by the effort distance from the fulcrum (3 feet3\text{ feet}). Therefore, 7200/3=2400 lbs7200 / 3 = 2400\text{ lbs}.

Step-by-Step Solution

1
Identify the lever configuration and locate the fulcrum.
The hinge is the fulcrum. The effort is applied at 3 feet3\text{ feet} from the fulcrum, and the load is at 12 feet12\text{ feet} from the fulcrum. This makes it a third-class lever.
Correctly identifying the distances from the pivot point is necessary for torque calculations.
2
Calculate the torque exerted by the load.
600 lbs×12 feet=7200 ft-lbs600\text{ lbs} \times 12\text{ feet} = 7200\text{ ft-lbs}
Torque is equal to force multiplied by the perpendicular distance from the fulcrum.
3
Set up the equilibrium equation and solve for the required effort force.
Feffort×3 feet=7200 ft-lbsF_{effort} \times 3\text{ feet} = 7200\text{ ft-lbs}. Solving for FeffortF_{effort} yields 7200/3=2400 lbs7200 / 3 = 2400\text{ lbs}.
For the ramp to be in equilibrium, the upward torque provided by the hydraulic cylinder must equal the downward torque of the load.

Key Concept

Torque balance in third-class levers
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Topics

Levers and Fulcrums

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