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Question

Difficulty: MediumInclined Planes

A worker needs to move a heavy crate into a truck bed that is 33 feet above the ground. The worker is deciding whether to use an 88-foot ramp or a 1212-foot ramp. Assuming friction is negligible, which of the following statements correctly describes the effect of using the 1212-foot ramp instead of the 88-foot ramp?

  1. A
    It requires the same effort force, but increases the total work performed due to the longer distance.
  2. B
    It decreases both the required effort force and the total work performed.
  3. It decreases the required effort force, but the total work performed remains the same.Answer
  4. D
    It increases the required effort force because the crate must be pushed over a greater distance.

Answer

The 1212-foot ramp decreases the required effort force, but the total work performed remains the same.
A longer inclined plane provides a greater Ideal Mechanical Advantage, which means the effort force is reduced. However, because this smaller force must be applied over a proportionally longer distance, the total work done (W=F×dW = F \times d) remains constant. In the absence of friction, the work done equals the work required to lift the load straight up.

Step-by-Step Solution

1
Determine the relationship between ramp length and Ideal Mechanical Advantage (IMA).
IMA is calculated as ramp length divided by vertical height. The 1212-foot ramp has a greater IMA than the 88-foot ramp since both reach the same height of 33 feet.
To establish how the machine alters the required input force.
2
Determine the effect of a greater IMA on effort force.
A higher IMA means less effort force is required to move the same load. Therefore, the 1212-foot ramp requires less effort force.
Effort force is inversely proportional to mechanical advantage.
3
Evaluate the effect of ramp length on total work performed.
Work is the product of force and distance (W=F×dW = F \times d). The smaller force applied over the longer 1212-foot distance equals the larger force applied over the 88-foot distance. Total work remains unchanged.
Simple machines conserve energy; they cannot reduce the total amount of work required.

Key Concept

Work and Force Relationship on Inclined Planes
Estimated Time:1m 0s
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Topics

Inclined Planes

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