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Difficulty: EasyInclined Planes

A construction worker needs to push a heavy wheelbarrow up to a raised foundation that is 2 m2\text{ m} above the ground. The worker has three different sturdy wooden planks available to use as a ramp. Arrange the following planks in order from the LEAST amount of effort force required to the MOST amount of effort force required.

  1. 1A plank with a length of 10 m10\text{ m}
  2. 2A plank with a length of 8 m8\text{ m}
  3. 3A plank with a length of 4 m4\text{ m}

Answer

The planks should be ordered from longest (10 m10\text{ m}) to shortest (4 m4\text{ m}). The 10 m10\text{ m} plank requires the least effort, the 8 m8\text{ m} plank requires a moderate amount, and the 4 m4\text{ m} plank requires the most effort.
The effort force needed to move an object up a ramp is inversely proportional to the ramp's length when the vertical height is fixed. The 10 m10\text{ m} plank provides the most gradual slope (highest mechanical advantage) and therefore requires the least effort force. As the plank length decreases to 8 m8\text{ m} and then 4 m4\text{ m}, the slope becomes steeper, reducing the mechanical advantage and requiring increasingly more effort force. Thus, ordering from least to most effort force is synonymous with ordering from longest to shortest plank.

Step-by-Step Solution

1
Recall the formula for the Ideal Mechanical Advantage (IMA) of an inclined plane.
IMA=Length of the slopeHeight of the incline\text{IMA} = \frac{\text{Length of the slope}}{\text{Height of the incline}}
This formula helps us determine how much a ramp multiplies the input force.
2
Determine the relationship between length, IMA, and effort force.
Since the height (2 m2\text{ m}) is constant for all three planks, a longer plank results in a higher IMA. A higher IMA means less effort force is required to push the load.
Understanding this inverse relationship allows us to rank the effort force without doing complex calculations.
3
Rank the planks based on length to determine the required effort force.
Longest plank (10 m10\text{ m}) = Highest IMA = Least effort force. Shortest plank (4 m4\text{ m}) = Lowest IMA = Most effort force.
The question asks to order from LEAST effort force to MOST effort force, which corresponds to ordering from longest ramp to shortest ramp.

Key Concept

For an inclined plane of a given height, increasing the length of the plane increases its mechanical advantage, which proportionally decreases the effort force required to move a load up the plane.
Estimated Time:45s
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Topics

Inclined Planes

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