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Difficulty: EasyInclined Planes

A homeowner needs to move a 300 lb300\text{ lb} refrigerator onto a porch that is 2 feet2\text{ feet} above ground level. They place a straight, frictionless wooden ramp that is 6 feet6\text{ feet} long from the ground to the porch edge. How much effort force is required to push the refrigerator up the ramp?

  1. A
    150 lbs150\text{ lbs}
  2. B
    300 lbs300\text{ lbs}
  3. 100 lbs100\text{ lbs}Answer
  4. D
    900 lbs900\text{ lbs}

Answer

100 lbs100\text{ lbs}
To find the force required to push an object up a frictionless ramp, first find the ramp's Ideal Mechanical Advantage (IMA). The IMA is the ramp's length divided by its vertical height (6 ft/2 ft=36\text{ ft} / 2\text{ ft} = 3). The effort force needed is the object's weight divided by this mechanical advantage (300 lbs/3=100 lbs300\text{ lbs} / 3 = 100\text{ lbs}).

Step-by-Step Solution

1
Calculate the Ideal Mechanical Advantage (IMA) of the ramp.
IMA=LengthHeight=6 ft2 ft=3\text{IMA} = \frac{\text{Length}}{\text{Height}} = \frac{6\text{ ft}}{2\text{ ft}} = 3
The IMA tells us how many times easier the ramp makes the task compared to lifting the object straight up.
2
Calculate the required effort force.
Effort Force=WeightIMA=300 lbs3=100 lbs\text{Effort Force} = \frac{\text{Weight}}{\text{IMA}} = \frac{300\text{ lbs}}{3} = 100\text{ lbs}
An inclined plane reduces the necessary force by a factor equal to its mechanical advantage.

Key Concept

Ideal Mechanical Advantage and Effort Force of an Inclined Plane
Estimated Time:1m 0s
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Topics

Inclined Planes

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