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Difficulty: HardWedges

A heavy-duty steel wedge is used to split a solid masonry block. The wedge has a penetration length of 24 cm24\text{ cm} and a maximum width (thickness) of 4 cm4\text{ cm} at its head. A pneumatic tool applies a constant downward driving effort force of 850 N850\text{ N} to the head of the wedge. Due to high surface resistance, the wedge operates with a mechanical efficiency of 60%60\%. What is the total lateral separating force exerted on the masonry block by the wedge? (Enter your answer as a number in Newtons)

Answer: 3060 N

Answer

3060
The correct lateral separating force is found by determining the wedge's Ideal Mechanical Advantage (24 cm/4 cm=624\text{ cm} / 4\text{ cm} = 6), adjusting for energy lost to friction by applying the 60%60\% efficiency (6×0.60=3.6 AMA6 \times 0.60 = 3.6\text{ AMA}), and multiplying this actual advantage by the input force (850 N×3.6=3060 N850\text{ N} \times 3.6 = 3060\text{ N}).

Step-by-Step Solution

1
Calculate the Ideal Mechanical Advantage (IMA) of the wedge.
IMA=6IMA = 6
The IMA of a wedge is defined as the ratio of its penetration length to its maximum thickness (24 cm/4 cm24\text{ cm} / 4\text{ cm}).
2
Determine the Actual Mechanical Advantage (AMA).
AMA=3.6AMA = 3.6
Because the wedge operates at 60%60\% efficiency due to friction, the actual mechanical advantage is the IMA multiplied by the efficiency (6×0.606 \times 0.60).
3
Calculate the total lateral separating force.
3060 N3060\text{ N}
The output force is the product of the input effort force and the Actual Mechanical Advantage (850 N×3.6850\text{ N} \times 3.6).

Key Concept

Mechanical Advantage and Efficiency of Wedges
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Topics

Wedges

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