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Zorluk: OrtaLevers and Fulcrums

An aviation mechanic is using a manual sheet metal bender. The operating lever pivots on a fixed hinge at its far end. The metal sheet being bent provides resistance against the lever at a point 3 inches3\text{ inches} from the hinge. If the mechanic applies a perpendicular effort force of 50 pounds50\text{ pounds} to the handle at a distance of 24 inches24\text{ inches} from the hinge, which of the following correctly identifies the class of this lever and the resulting force applied to the metal sheet?

  1. Second-class lever; 400 pounds400\text{ pounds}Cevap
  2. B
    Third-class lever; 400 pounds400\text{ pounds}
  3. C
    First-class lever; 350 pounds350\text{ pounds}
  4. D
    Second-class lever; 6.25 pounds6.25\text{ pounds}

Cevap

The mechanism is a second-class lever, and the resulting force applied to the metal sheet is 400 pounds400\text{ pounds}.
In this scenario, the load (metal sheet) is positioned between the fulcrum (hinge) and the effort (mechanic's hand), which defines a second-class lever. The mechanical advantage is found by dividing the effort arm distance (24 inches24\text{ inches}) by the load arm distance (3 inches3\text{ inches}), yielding an MA of 88. Multiplying the applied effort of 50 pounds50\text{ pounds} by the MA of 88 gives a total applied force of 400 pounds400\text{ pounds}.

Adım Adım Çözüm

1
Determine the class of the lever based on the component positions.
The hinge (fulcrum) is at one end, the effort is at the other end, and the metal sheet (load) is between them. This is the definition of a second-class lever.
Correctly identifying the lever class ensures the proper understanding of how forces and distances are distributed.
2
Calculate the Mechanical Advantage (MA) of the lever.
MA=Effort ArmLoad Arm=24 inches3 inches=8MA = \frac{\text{Effort Arm}}{\text{Load Arm}} = \frac{24\text{ inches}}{3\text{ inches}} = 8
Mechanical advantage dictates how much the input effort force will be multiplied by the machine.
3
Calculate the resulting force applied to the load (metal sheet).
Force=Effort Force×MA=50 pounds×8=400 pounds\text{Force} = \text{Effort Force} \times MA = 50\text{ pounds} \times 8 = 400\text{ pounds}
The output force is the product of the input effort force and the mechanical advantage.

Anahtar Kavram

Lever Classification and Mechanical Advantage
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Konular

Levers and Fulcrums

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