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Difficulty: MediumInclined Planes

Arrange the following material handling tasks in order from the LEAST amount of effort force required to the GREATEST amount of effort force required. (Assume frictionless ramps)

  1. 1Task A: Moving a 120 lb120\text{ lb} crate up a 12 ft12\text{ ft} long ramp to a 3 ft3\text{ ft} high dock.
  2. 2Task D: Rolling a 200 lb200\text{ lb} drum up a 5 ft5\text{ ft} long ramp to a 1 ft1\text{ ft} high pallet.
  3. 3Task C: Sliding a 100 lb100\text{ lb} box up an 8 ft8\text{ ft} long ramp to a 4 ft4\text{ ft} high platform.
  4. 4Task B: Pushing a 180 lb180\text{ lb} cart up a 6 ft6\text{ ft} long ramp to a 2 ft2\text{ ft} high step.

Answer

The correct sequence from least to greatest effort force is: Task A (30 lbs30\text{ lbs}), Task D (40 lbs40\text{ lbs}), Task C (50 lbs50\text{ lbs}), Task B (60 lbs60\text{ lbs}).
Task A requires 30 lbs30\text{ lbs} of force, Task D requires 40 lbs40\text{ lbs}, Task C requires 50 lbs50\text{ lbs}, and Task B requires 60 lbs60\text{ lbs}. Ordering these mathematically from lowest to highest yields Task A, Task D, Task C, and Task B.

Step-by-Step Solution

1
Calculate the Ideal Mechanical Advantage (IMA) for each ramp.
Task A: 12/3=412/3 = 4. Task B: 6/2=36/2 = 3. Task C: 8/4=28/4 = 2. Task D: 5/1=55/1 = 5.
The IMA determines how much the ramp multiplies the applied force, calculated as the length of the ramp divided by its height.
2
Calculate the required effort force for each task.
Task A: 120/4=30 lbs120/4 = 30\text{ lbs}. Task B: 180/3=60 lbs180/3 = 60\text{ lbs}. Task C: 100/2=50 lbs100/2 = 50\text{ lbs}. Task D: 200/5=40 lbs200/5 = 40\text{ lbs}.
Effort force equals the load's total weight divided by the IMA of the ramp.
3
Order the tasks from least effort to greatest effort.
Task A (30 lbs30\text{ lbs}) < Task D (40 lbs40\text{ lbs}) < Task C (50 lbs50\text{ lbs}) < Task B (60 lbs60\text{ lbs}).
The question specifically asks for the sequence starting with the lowest force and ending with the highest.

Key Concept

Ideal Mechanical Advantage and Effort Force on an Inclined Plane
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Topics

Inclined Planes

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