A logistics team needs to roll a heavy generator weighing 900\text{ lbs} from the ground o… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics team needs to roll a heavy generator weighing $900\text{ lbs}$ from the ground onto a raised platform that is $5\text{ feet}$ high. If the team can apply a maximum combined push force of $150\text{ lbs}$ parallel to the ramp surface, what is the minimum ramp length required to accomplish this task? Assume ideal conditions with zero friction.

Answer: 30 feet

Answer

The minimum ramp length required is

30\text{ feet}

In an ideal frictionless system, the ratio of the load force to the effort force equals the ratio of the ramp length to its height. A load of

900\text{ lbs}

requiring only

150\text{ lbs}

of effort means the system needs a mechanical advantage of

6

. Since the height is

5\text{ feet}

, the ramp must be

6

times longer than the height, which is

30\text{ feet}

Step-by-Step Solution

Calculate the required Ideal Mechanical Advantage (IMA).

IMA = \frac{\text{Load}}{\text{Effort}} = \frac{900\text{ lbs}}{150\text{ lbs}} = 6

The mechanical advantage indicates how many times the machine multiplies the effort force. We need a mechanical advantage of 6 to move the

900\text{ lbs}

load with only

150\text{ lbs}

of force.

Calculate the required ramp length using the IMA and the given height.

IMA = \frac{\text{Length}}{\text{Height}} \Rightarrow 6 = \frac{\text{Length}}{5\text{ feet}} \Rightarrow \text{Length} = 6 \times 5 = 30\text{ feet}

For an inclined plane in ideal conditions, the mechanical advantage is also the ratio of the ramp's length to its vertical height.

Key Concept

The relationship between effort force, load, ramp length, and vertical height on an ideal inclined plane (Ideal Mechanical Advantage).

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic