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Difficulty: HardLevers and Fulcrums

A fisherman holds an 8-foot8\text{-foot} fishing rod. He rests the base of the rod against his waist, which acts as the pivot point (fulcrum). His upper hand pulls upward on the rod at a distance of 2 feet2\text{ feet} from his waist. If a fish pulls downward on the tip of the rod with a force of 20 lbs20\text{ lbs}, what is the required effort force applied by his upper hand to keep the rod balanced, and which class of lever does this represent? (Assume the weight of the rod is negligible).

  1. 80 lbs80\text{ lbs}; Third-class leverAnswer
  2. B
    5 lbs5\text{ lbs}; Third-class lever
  3. C
    60 lbs60\text{ lbs}; First-class lever
  4. D
    80 lbs80\text{ lbs}; Second-class lever

Answer

The required effort force is 80 lbs80\text{ lbs}, and the fishing rod acts as a Third-class lever.
In this scenario, the effort (the upper hand) is located between the fulcrum (the waist) and the load (the fish). This specific arrangement defines a third-class lever. To find the required effort force, set up a torque balance equation: Effort Force×Effort Distance=Load Force×Load Distance\text{Effort Force} \times \text{Effort Distance} = \text{Load Force} \times \text{Load Distance}. Substituting the given values yields Effort Force×2 ft=20 lbs×8 ft\text{Effort Force} \times 2\text{ ft} = 20\text{ lbs} \times 8\text{ ft}. Solving for the effort force gives 160/2=80 lbs160 / 2 = 80\text{ lbs}.

Step-by-Step Solution

1
Identify the locations of the fulcrum, effort, and load on the rod.
The fulcrum is at the base (waist), the effort is applied 2 feet2\text{ feet} from the base, and the load is at the tip, 8 feet8\text{ feet} from the base.
Establishing the sequence and distances of these points is necessary to determine the lever class and torque equations.
2
Determine the class of the lever.
It is a Third-class lever.
Because the effort force (upper hand) is located between the fulcrum (waist) and the load (fish).
3
Set up the torque balance equation.
Effort Force×2 ft=20 lbs×8 ft\text{Effort Force} \times 2\text{ ft} = 20\text{ lbs} \times 8\text{ ft}.
For the lever to be in equilibrium, the torque from the effort must equal the torque from the load.
4
Solve the equation for the effort force.
Effort Force×2=160\text{Effort Force} \times 2 = 160, so Effort Force=80 lbs\text{Effort Force} = 80\text{ lbs}.
To find the specific pulling force the fisherman must exert.

Key Concept

Torque balance and Third-class levers
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Topics

Levers and Fulcrums

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