Load Capacity and Overload Decision
A small shop owner needs to move a 480 lb electric motor onto a truck bed 3 ft off the ground. She has a 12 ft steel ramp rated for 600 lb safe working load and a hand winch rated at 500 lb pulling capacity, mounted at the top of the ramp. The ramp angle will be roughly 15 degrees. A helper suggests skipping the winch and just pushing the motor up with two people. One worker can push with about 120 lb of force; the second can add 100 lb. Rolling friction of the motor on the ramp is negligible. The motor's center of gravity sits 1.5 ft above the ramp surface, and the ramp is 3 ft wide.
1. Using the ramp angle, estimate the force needed to hold the motor steady on the ramp and determine whether the two workers can push it up without the winch.
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The component of weight along a 15° incline is W·sin(15°) = 480 lb × 0.259 ≈ 124 lb. The combined push force is 120 + 100 = 220 lb, which exceeds 124 lb, so the two workers can push it up the ramp with margin. Note that the winch's 500 lb capacity is far above the required 124 lb, so either method is feasible from a force standpoint.
2. Check whether the motor could tip sideways during the move and state what that implies for the plan.
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Tipping sideways depends on the lateral force and the height of the center of gravity (1.5 ft) versus half the ramp width (1.5 ft). The tipping threshold is roughly when lateral force × 1.5 ft exceeds weight × 1.5 ft, i.e., a lateral force near 480 lb - far above any realistic sideways nudge. So sideways tipping is not the controlling hazard. The practical risks are the motor rolling back down the ramp and the ramp's 600 lb rating versus the 480 lb load, leaving only a 120 lb margin. A strap or winch as a backup is still prudent.
3. If the owner instead raises the ramp angle to 30° to shorten the run, how does the required force change and does the winch remain adequate?
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At 30°, the along-ramp weight component is 480 × sin(30°) = 480 × 0.5 = 240 lb. The winch at 500 lb still exceeds this, and the two workers (220 lb combined) would now fall short, so the winch becomes necessary. The ramp's 600 lb rating is unaffected by angle, but the higher angle increases the rollback hazard and the force on the winch anchor.