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Zorluk: OrtaLevers and Fulcrums

An angler is reeling in a catch and holds the fishing rod perfectly horizontal. The butt of the rod is braced firmly against the angler's waist, which acts as the pivot point. The angler's top hand applies an upward lifting force 2 feet2 \text{ feet} away from the waist. If the fish creates a constant downward pull of 15 lbs15 \text{ lbs} at the rod's tip, which is exactly 8 feet8 \text{ feet} away from the pivot point, how much upward effort force must the angler's top hand exert to maintain the rod's horizontal position? (Assume the weight of the rod itself is negligible.)

  1. A
    120 lbs120 \text{ lbs}
  2. 60 lbs60 \text{ lbs}Cevap
  3. C
    45 lbs45 \text{ lbs}
  4. D
    3.75 lbs3.75 \text{ lbs}

Cevap

60 lbs60 \text{ lbs}
In a third-class lever, the effort is located between the fulcrum and the load. To maintain equilibrium, the effort torque must equal the load torque. Since the effort arm (2 feet2 \text{ feet}) is one-quarter the length of the load arm (8 feet8 \text{ feet}), the mechanical advantage is 0.250.25. Therefore, the required effort force must be four times the load force (15 lbs×4=60 lbs15 \text{ lbs} \times 4 = 60 \text{ lbs}).

Adım Adım Çözüm

1
Identify the lever class and pivot point.
The waist is the fulcrum, the top hand is the effort, and the fish is the load. This is a third-class lever.
Understanding the arrangement is required to correctly measure distances for the torque equation.
2
Calculate the torque exerted by the load (the fish).
Load Torque=15 lbs×8 ft=120 lb-ft\text{Load Torque} = 15 \text{ lbs} \times 8 \text{ ft} = 120 \text{ lb-ft}.
Torque is the product of force and distance from the fulcrum.
3
Set the effort torque equal to the load torque to find the required force.
Effort×2 ft=120 lb-ft\text{Effort} \times 2 \text{ ft} = 120 \text{ lb-ft}, which means Effort=60 lbs\text{Effort} = 60 \text{ lbs}.
For the rod to remain horizontally stable, the opposing torques must be perfectly balanced.

Anahtar Kavram

Third-Class Levers and Torque Equilibrium

Alternatif Yöntem

Calculate the Mechanical Advantage (MA) first: MA=Effort ArmLoad Arm=28=0.25\text{MA} = \frac{\text{Effort Arm}}{\text{Load Arm}} = \frac{2}{8} = 0.25. Then find the effort using Effort=LoadMA=150.25=60 lbs\text{Effort} = \frac{\text{Load}}{\text{MA}} = \frac{15}{0.25} = 60 \text{ lbs}.
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Levers and Fulcrums

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