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Difficulty: MediumWedges

A stonemason uses a steel wedge to fracture a granite boulder. The wedge has a penetration length of 160 mm160\text{ mm} and tapers to a maximum width (thickness) of 20 mm20\text{ mm}. Assuming an ideal mechanical system with zero friction, if the mason applies a downward effort force of 450 N450\text{ N} to the head of the wedge, what is the maximum lateral outward force, in Newtons, that the wedge exerts on the stone?

Answer: 3600 N

Answer

3600
The correct lateral outward force is 3600 N. This is found by first determining the ideal mechanical advantage (IMA) of the wedge, which is its length divided by its thickness (160 / 20 = 8). Multiplying this IMA by the input effort force (450 N) gives the total ideal output force exerted on the stone.

Step-by-Step Solution

1
Calculate the Ideal Mechanical Advantage (IMA) of the wedge.
IMA=160 mm20 mm=8IMA = \frac{160\text{ mm}}{20\text{ mm}} = 8
The mechanical advantage of a wedge is determined by the ratio of its penetration length to its maximum thickness.
2
Calculate the output resistance force.
Output Force=450 N×8=3600 NOutput\ Force = 450\text{ N} \times 8 = 3600\text{ N}
In an ideal machine, the output force is equal to the input effort force multiplied by the mechanical advantage.

Key Concept

Mechanical Advantage of a Wedge
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Topics

Wedges

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