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Difficulty: MediumWedges

A heavy machinery technician needs to slightly lift a generator weighing 1000 lbs1000\text{ lbs} to slide a permanent leveling mount underneath it. To do this, the technician drives a solid steel wedge under the edge of the generator. If the technician can apply a maximum driving effort of 200 lbs200\text{ lbs} and the wedge has a penetration length of 20 inches20\text{ inches}, what is the maximum thickness the wedge can be to successfully lift the load? (Assume an ideal system with no friction.)

  1. A
    100 inches100\text{ inches}
  2. 4 inches4\text{ inches}Answer
  3. C
    5 inches5\text{ inches}
  4. D
    0.25 inches0.25\text{ inches}

Answer

The maximum thickness the wedge can be is 4 inches4\text{ inches}.
To find the maximum thickness, first determine the required mechanical advantage (MA) by dividing the load force (1000 lbs1000\text{ lbs}) by the effort force (200 lbs200\text{ lbs}), which equals 5. Because the MA of an ideal wedge is equal to its length divided by its thickness, you divide the length (20 inches20\text{ inches}) by the MA (55). This calculation yields a maximum thickness of 4 inches4\text{ inches}.

Step-by-Step Solution

1
Calculate the required Mechanical Advantage (MA) for the task.
MA=Load ForceEffort Force=1000 lbs200 lbs=5MA = \frac{\text{Load Force}}{\text{Effort Force}} = \frac{1000\text{ lbs}}{200\text{ lbs}} = 5
The mechanical advantage determines how much the simple machine must multiply the input force to overcome the load.
2
Relate the mechanical advantage to the geometry of the wedge.
MA=LengthThickness⇒5=20 inchesThicknessMA = \frac{\text{Length}}{\text{Thickness}} \Rightarrow 5 = \frac{20\text{ inches}}{\text{Thickness}}
In an ideal wedge, the ratio of the input distance (penetration length) to the output distance (vertical lift or thickness) equals the mechanical advantage.
3
Solve the equation for the maximum thickness.
Thickness=20 inches5=4 inches\text{Thickness} = \frac{20\text{ inches}}{5} = 4\text{ inches}
Rearranging the formula isolates the unknown variable. A wedge thicker than 4 inches4\text{ inches} would provide an MA of less than 5, making the 200 lbs200\text{ lbs} effort insufficient to lift the generator.

Key Concept

Mechanical Advantage of Wedges
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Topics

Wedges

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