Examkin

Question

Difficulty: MediumWedges

A forestry worker uses a high-impact plastic felling wedge to direct the fall of a large tree. The wedge has a length (penetration depth) of 15 cm15\text{ cm} and a maximum heel thickness of 3 cm3\text{ cm}. If the worker strikes the wedge with a sledgehammer, applying an average effort force of 450 N450\text{ N}, what is the theoretical maximum lifting force (in Newtons) exerted by the wedge? Assume 100%100\% efficiency.

Answer: 2250 N

Answer

2250 Newtons
The correct theoretical maximum lifting force is found by first determining the mechanical advantage of the wedge (length divided by thickness), which is 5. Multiplying this mechanical advantage by the input effort force (450 N) yields an output force of 2250 N.

Step-by-Step Solution

1
Identify the formula for the Ideal Mechanical Advantage (IMA) of a wedge.
IMA=LengthThickness\text{IMA} = \frac{\text{Length}}{\text{Thickness}}
The mechanical advantage of a wedge is determined by the ratio of its penetration length to its maximum separation thickness.
2
Calculate the IMA using the given dimensions.
IMA=15 cm3 cm=5\text{IMA} = \frac{15\text{ cm}}{3\text{ cm}} = 5
Substituting the length (15 cm15\text{ cm}) and thickness (3 cm3\text{ cm}) into the formula gives a mechanical advantage multiplier of 5.
3
Calculate the theoretical maximum output force.
Output Force=IMA×Input Force=5×450 N=2250 N\text{Output Force} = \text{IMA} \times \text{Input Force} = 5 \times 450\text{ N} = 2250\text{ N}
The output force is the product of the mechanical advantage and the applied effort force, assuming ideal conditions.

Key Concept

Ideal Mechanical Advantage (IMA) of Wedges
Rate this question

Topics

Wedges

More questions from this topic