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Difficulty: MediumWedges

A shipwright uses a steel wedge to precisely align a heavy hull plate. The wedge has a length of 24 cm24\text{ cm} and a maximum heel thickness of 4 cm4\text{ cm}. If the shipwright strikes the heel, applying an average effort force of 600 N600\text{ N}, what is the theoretical maximum lateral lifting force exerted by the wedge on the hull plate?

  1. A
    2400 N2400\text{ N}
  2. B
    100 N100\text{ N}
  3. 3600 N3600\text{ N}Answer
  4. D
    600 N600\text{ N}

Answer

3600 N3600\text{ N}
The mechanical advantage (IMA) of a wedge is calculated by dividing its length by its maximum thickness. In this case, 24 cm/4 cm=624\text{ cm} / 4\text{ cm} = 6. The theoretical maximum lateral force is the effort force multiplied by the IMA, which is 600 N×6=3600 N600\text{ N} \times 6 = 3600\text{ N}.

Step-by-Step Solution

1
Calculate the ideal mechanical advantage (IMA) of the wedge.
IMA=24 cm4 cm=6IMA = \frac{24\text{ cm}}{4\text{ cm}} = 6
The IMA of a wedge is the ratio of its penetration length to its maximum thickness.
2
Calculate the theoretical maximum lateral force.
Fout=6×600 N=3600 NF_{\text{out}} = 6 \times 600\text{ N} = 3600\text{ N}
The output lateral force is the product of the applied effort force and the mechanical advantage.

Key Concept

The ideal mechanical advantage of a wedge is determined by the ratio of its length to its thickness.
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Topics

Wedges

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