Generator Lifting Lever
A workshop must lift a generator set of mass 240 kg by 0.35 m using a uniform steel plank 4.8 m long as a first-class lever. The fulcrum is placed 1.2 m from the generator end, and the effort is applied vertically downward at the far end. The plank has a mass of 18 kg; its centre of gravity is at its midpoint. Take g = 9.81 m/s2. The workshop floor is level, and the plank is strong enough not to bend. A fitter proposes moving the fulcrum 0.4 m closer to the generator to reduce the effort. A second fitter warns that this will increase the load on the fulcrum and may make the plank unstable. The supervisor also has a 3.0 m ramp available, but the ramp would need a 0.35 m rise over its full length and would let the generator be pushed rather than lifted. The team must compare the lever with the ramp, decide whether moving the fulcrum helps, and explain the trade-off in force and stability. Ignore friction on the ramp.
1. Calculate the ideal effort at the original fulcrum position, ignoring the plank's mass, and state the mechanical advantage.
Read the worked answer
Load force = 240 kg x 9.81 m/s2 = 2,354.4 N.
For a first-class lever, moments about the fulcrum balance: effort x effort arm = load x load arm. Load arm = 1.2 m. Effort arm = 4.8 - 1.2 = 3.6 m.
Effort = 2,354.4 x 1.2 / 3.6 = 784.8 N.
Mechanical advantage = load / effort = 2,354.4 / 784.8 = 3.0, matching the arm ratio 3.6 / 1.2 = 3.0. So the ideal lever reduces the effort to about 785 N, or about 80 kg-force equivalent.
2. Now include the plank's own weight. Does the actual effort rise or fall compared with the ideal value, and why?
Read the worked answer
Plank weight = 18 x 9.81 = 176.58 N. Its centre of gravity is at 2.4 m from the generator end. Since the fulcrum is 1.2 m from that end, the plank's centre of gravity is 2.4 - 1.2 = 1.2 m on the effort side of the fulcrum.
The plank weight therefore acts downward on the effort side and helps the effort. Taking moments: effort x 3.6 + 176.58 x 1.2 = 2,354.4 x 1.2 Effort x 3.6 = 2,825.28 - 211.90 = 2,613.38 Effort = 725.9 N.
The actual effort is lower than the ideal 784.8 N because the plank's own weight supplies part of the clockwise moment. The fulcrum reaction is the sum of downward forces: 2,354.4 + 176.6 + 725.9 = about 3,257 N.
3. Evaluate the proposal to move the fulcrum 0.4 m closer to the generator, and compare the lever with the 3.0 m ramp. Is the second fitter's warning about increased fulcrum load correct?
Read the worked answer
New load arm = 1.2 - 0.4 = 0.8 m. New effort arm = 4.8 - 0.8 = 4.0 m. The plank centre of gravity is now 2.4 - 0.8 = 1.6 m on the effort side.
Effort x 4.0 + 176.58 x 1.6 = 2,354.4 x 0.8 Effort x 4.0 = 1,883.52 - 282.53 = 1,600.99 Effort = 400.2 N.
So the proposal does reduce effort, from about 726 N to about 400 N. The fulcrum reaction becomes 2,354.4 + 176.6 + 400.2 = about 2,931 N, which is lower than the original 3,257 N. The warning about a higher static fulcrum load is therefore not correct for this geometry.
However, the trade-off is real: the plank now overhangs 4.0 m on the effort side and the load sits only 0.8 m from the fulcrum, so the load is closer to the pivot and more prone to slipping or dropping suddenly if control is lost. The effort must also travel farther.
Ramp comparison: ideal mechanical advantage = length / height = 3.0 / 0.35 = 8.57. Push effort = 2,354.4 / 8.57 = about 275 N, lower than either lever arrangement, but the ramp needs clear space and control of the load on the slope. The lever is more compact; the ramp is easier on force.