Ramp Versus Direct Lift
A worker must load a 60 kg crate onto a platform 1.2 m high. Lifting it directly would need a force equal to its weight, so the worker uses a wooden ramp 3.0 m long. A spring balance shows that a steady pull of 280 N along the ramp moves the crate at constant speed. The pull takes 6.0 s. The worker's safety guideline says no single person should pull with more than 300 N on this task. Take g = 10 N/kg. The ramp is smooth but not frictionless, and the crate's centre of mass rises by the full 1.2 m. A second worker suggests making the ramp shorter (2.0 m) to save space, saying 'a shorter ramp is easier because there is less distance to walk.' The supervisor wants calculations before agreeing to the change.
1. Calculate the useful work done on the crate, the work input by the worker, and the efficiency of the ramp.
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The useful work is the gain in gravitational potential energy: W_out = mgh = 60 kg × 10 N/kg × 1.2 m = 720 J.
The work input is the force along the ramp multiplied by the distance moved along it: W_in = F × d = 280 N × 3.0 m = 840 J.
Efficiency = useful work ÷ input work × 100 = 720 ÷ 840 × 100 ≈ 85.7%. About 120 J is transferred to the surroundings, mainly by friction and small deformations, so the ramp is not perfectly efficient.
2. Calculate the mechanical advantage and decide whether the current ramp meets the 300 N guideline. Then evaluate the suggestion to shorten the ramp to 2.0 m.
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Mechanical advantage = load ÷ effort. The load is the crate's weight, 60 × 10 = 600 N. MA = 600 N ÷ 280 N ≈ 2.14. The ideal MA for a frictionless ramp is length ÷ height = 3.0 ÷ 1.2 = 2.5; the measured MA is lower because of friction.
The current ramp needs 280 N, which is below the 300 N guideline, so it is acceptable, though only just.
A 2.0 m ramp is not safer. The ideal effort would be 720 J ÷ 2.0 m = 360 N even before friction is counted. With friction the real effort would be higher than 360 N, clearly above 300 N. A shorter ramp means a steeper slope, so the same height is gained over less distance and the force needed rises. The suggestion should be rejected.
3. Explain why the ramp's efficiency is less than 100% and give one practical change that would raise efficiency without exceeding the 300 N limit.
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Efficiency is below 100% because some input work is not stored as gravitational potential energy. Friction between the crate and the ramp, friction in any rollers, and slight deformation of the crate or ramp all convert some work into thermal energy and sound. The crate may also be pulled slightly sideways, so not all the effort contributes to lifting.
A practical improvement is to smooth or lubricate the ramp surface, or use clean rollers, so friction is reduced. The same 280 N effort would then move the crate with less loss, or a smaller effort could produce the same useful work, raising efficiency. The ramp should not be made shorter to improve efficiency; that increases the required effort. Any change should be tested with the spring balance to confirm the pull stays below 300 N.