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Difficulty: EasyInclined Planes

A delivery crew needs to load a 600 lb600\text{ lb} safe into the back of a moving truck that sits 4 ft4\text{ ft} above the ground. They deploy a straight, uniform ramp that is 16 ft16\text{ ft} long. Assuming friction is negligible, what is the ideal effort force, in pounds, required to push the safe up the ramp?

Answer: 150 lbs

Answer

150
By using a ramp, the distance over which the force is applied increases, which proportionally decreases the required force. A 16-foot ramp lifting an object 4 feet provides a mechanical advantage of 4 (16 divided by 4). Therefore, pushing a 600-pound load requires only one-quarter of the weight in force, which is 150 pounds.

Step-by-Step Solution

1
Calculate the Ideal Mechanical Advantage (IMA) of the ramp.
IMA = 16 / 4 = 4
The mechanical advantage of an inclined plane is the ratio of its length to its vertical height.
2
Calculate the ideal effort force required to move the load.
Effort Force = 600 / 4 = 150 lbs
The required effort force is the total load divided by the mechanical advantage.

Key Concept

Ideal Mechanical Advantage of an Inclined Plane
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Topics

Inclined Planes

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