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Difficulty: MediumLevers and Fulcrums

A carpenter uses a claw hammer to extract a stubborn nail from a wooden board. The hammer functions as a first-class lever, pivoting on the curve of its head. The perpendicular distance from the pivot point to the nail is 6 cm6 \text{ cm}, and the carpenter applies an effort force on the handle at a perpendicular distance of 24 cm24 \text{ cm} from the pivot point. If the nail requires a resistance force of 480 N480 \text{ N} to be pulled out, what minimum effort force must the carpenter apply?

  1. A
    96 N96 \text{ N}
  2. B
    160 N160 \text{ N}
  3. 120 N120 \text{ N}Answer
  4. D
    384 N384 \text{ N}

Answer

The minimum effort force required is 120 N120 \text{ N}.
In a first-class lever system in equilibrium, the effort torque must equal the resistance torque (Effort Force × Effort Arm = Resistance Force × Resistance Arm). Plugging in the given values yields: Effort Force × 24 cm = 480 N × 6 cm. Solving for the Effort Force gives 120 N.

Step-by-Step Solution

1
Identify the type of lever and the location of the fulcrum.
The claw hammer is acting as a first-class lever. The pivot point (fulcrum) is located between the applied effort (the carpenter's hand) and the load (the nail).
Correctly identifying the lever setup is necessary to assign the proper lengths to the effort arm and resistance arm.
2
Determine the length of the effort arm and the resistance arm.
The effort arm is the distance from the pivot to the hand (24 cm24 \text{ cm}). The resistance arm is the distance from the pivot to the nail (6 cm6 \text{ cm}).
Torque is calculated using the distance from the pivot point to where the force is applied.
3
Calculate the mechanical advantage (MA) of the lever.
MA=Effort ArmResistance Arm=246=4MA = \frac{\text{Effort Arm}}{\text{Resistance Arm}} = \frac{24}{6} = 4.
The mechanical advantage indicates how much the lever multiplies the applied force.
4
Calculate the required effort force to overcome the resistance.
Effort Force=Resistance ForceMA=4804=120 N\text{Effort Force} = \frac{\text{Resistance Force}}{MA} = \frac{480}{4} = 120 \text{ N}.
The effort force multiplied by the mechanical advantage must equal the resistance force to balance the torques.

Key Concept

Torque Balance and Mechanical Advantage in First-Class Levers
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Topics

Levers and Fulcrums

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