Lifting a Crate onto a Dock
A dock crew uses a single fixed pulley system to raise a 90 kg crate from a boat to a quay 4.0 m above. A rope passes over the pulley and two sailors pull horizontally on the free end, each able to sustain a steady force of 300 N. The pulley has noticeable friction, estimated at 15% of the load's weight, and the rope is rated to 1200 N. Take g = 9.8 m/s². The crate must be raised at constant speed. One sailor argues that a movable pulley would let them lift it with less effort; another worries about rope strength and about whether two people pulling horizontally can actually do the job.
1. Determine the total force needed at the rope to raise the crate at constant speed with the fixed pulley, and check the rope rating.
Read the worked answer
Weight of crate = 90 × 9.8 = 882 N.
Friction = 0.15 × 882 = 132.3 N.
Total rope tension needed = 882 + 132.3 ≈ 1014 N.
Rope rating is 1200 N, so the tension is within rating (margin ≈ 186 N). The two sailors together can supply 600 N, which is less than 1014 N - with the fixed pulley alone they cannot raise it at constant speed.
2. Evaluate the movable-pulley proposal: what effort would be needed, and what new risk appears?
Read the worked answer
A single movable pulley (with the fixed one as a direction change) gives a mechanical advantage of 2, so the ideal effort is about 1014 / 2 ≈ 507 N. That is within the sailors' combined 600 N, so the lift becomes feasible.
The trade-off: the rope must be pulled roughly twice as far (≈ 8 m) to raise the crate 4 m, and the tension in the segment holding the movable pulley equals the load share, so the rope still carries about 1014 N in the loaded segment - close to the 1200 N rating, leaving little margin. The judgement is that the movable pulley solves the force problem but demands more rope travel and careful monitoring of the rating; a second check on friction under load is prudent.