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Ramp Feasibility for a 180 lb Crate

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Ramp Feasibility for a 180 lb Crate

A worker must slide a 180 lb crate up a straight ramp onto a platform 3.0 ft high. The ramp is 12.0 ft long. The worker can push with a sustained force of 90 lb. Friction between the crate and ramp is estimated at a constant 40 lb for this setup. The crew is considering shortening the ramp to 9.0 ft to save space, or using a longer ramp if the push is too hard. Assume the crate moves at constant speed and the ramp itself is light. The supervisor wants a feasibility check before building anything.

1. Using the 12.0 ft ramp, what push is required, and can the worker do it alone?

Read the worked answer

The ideal mechanical advantage of a ramp is length ÷ height:

  • MA = 12.0 ÷ 3.0 = 4.

The ideal push is the load divided by MA:

  • 180 ÷ 4 = 45 lb.

Friction adds 40 lb, so the actual push needed is:

  • 45 + 40 = 85 lb.

The worker can sustain 90 lb, so the job is feasible with only 5 lb of margin. It would work, but it leaves little room for a heavier crate or rougher ramp surface.

2. If the ramp is shortened to 9.0 ft, can the same worker still push the crate?

Read the worked answer

With a 9.0 ft ramp and the same 3.0 ft height:

  • MA = 9.0 ÷ 3.0 = 3.
  • Ideal push = 180 ÷ 3 = 60 lb.
  • Adding the same estimated 40 lb of friction gives 60 + 40 = 100 lb.

100 lb exceeds the worker's 90 lb sustained push by 10 lb. The crate would not be moved steadily by this worker alone under the stated assumptions. Shortening the ramp saves space but makes the push harder because the ramp is steeper and has less mechanical advantage.

3. What is the minimum ramp length that keeps the required push at or below 90 lb, assuming friction stays 40 lb?

Read the worked answer

Let L be the ramp length. The push required is:

  • (180 × 3.0) ÷ L + 40 ≤ 90.

Simplify:

  • 540 ÷ L ≤ 50.
  • L ≥ 540 ÷ 50 = 10.8 ft.

So the ramp must be at least about 10.8 ft long. The existing 12.0 ft ramp works; the proposed 9.0 ft ramp does not. A 10.8 ft ramp would meet the limit exactly, so in practice a little longer than 10.8 ft would be safer.