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Difficulty: MediumLevers and Fulcrums

A person uses a straight-handled snow shovel to lift a 20-pound20\text{-pound} load of snow. The person's top hand acts as a stationary pivot (fulcrum) at the very end of the handle. Their lower hand applies an upward lifting effort 10 inches10\text{ inches} down the shaft from the top hand. If the center of the snow load is located 40 inches40\text{ inches} further down the shaft from the lower hand, what is the upward lifting force required by the lower hand to hold the shovel horizontally?

  1. A
    4 lbs4\text{ lbs}
  2. B
    20 lbs20\text{ lbs}
  3. C
    80 lbs80\text{ lbs}
  4. 100 lbs100\text{ lbs}Answer

Answer

100 lbs100\text{ lbs}
In a third-class lever, the effort is located between the fulcrum and the load. The distance from the fulcrum to the effort is 10 inches10\text{ inches}, and the distance from the fulcrum to the load is 10+40=50 inches10 + 40 = 50\text{ inches}. Setting the torques equal gives FE×10=20×50F_E \times 10 = 20 \times 50. Solving for FEF_E results in 100 lbs100\text{ lbs}.

Step-by-Step Solution

1
Identify the lever class and the locations of the fulcrum, effort, and load.
The shovel acts as a third-class lever. Fulcrum is at the top hand, effort is applied at the lower hand, and load is at the snow.
This establishes the pivot point for calculating torque (moments).
2
Determine the effort arm (dEd_E) and the load arm (dLd_L).
dE=10 inchesd_E = 10\text{ inches}. The load arm dLd_L is the total distance from the fulcrum to the load: 10 inches+40 inches=50 inches10\text{ inches} + 40\text{ inches} = 50\text{ inches}.
Torque is always calculated as force multiplied by the distance from the fulcrum.
3
Apply the principle of moments (Torque equilibrium) to find the effort force (FEF_E).
FE×dE=FL×dL⇒FE×10=20×50⇒FE×10=1000⇒FE=100 lbsF_E \times d_E = F_L \times d_L \Rightarrow F_E \times 10 = 20 \times 50 \Rightarrow F_E \times 10 = 1000 \Rightarrow F_E = 100\text{ lbs}.
For the shovel to be held horizontally in equilibrium, the upward torque from the effort must equal the downward torque from the load.

Key Concept

Third-Class Levers and Torque Balance
Estimated Time:1m 0s
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Topics

Levers and Fulcrums

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