The Slipway, the Winch and the Neap Tide
A fishing co-operative on the east coast has a straight concrete slipway 12 m long. The top of the slipway is 1.8 m above the point where a boat floats. Members want to haul a 900 kg pirogue - hull, engine and fuel included - up the slipway with an electric winch rated at 1500 N. From years of moving hand-carts, the co-op's rule of thumb is that friction on the slipway adds about 35 % to the ideal pulling force. Their tide table shows high tides of 0.62 m and 0.68 m this week; three weeks ago the high tides were 1.35 m and 1.40 m. At this week's high tide the water at the foot of the slipway will be about 0.65 m deep, and the loaded pirogue needs 0.85 m of water to float. The co-op meets on Saturday to decide whether to buy the winch, and whether to haul the boat out now or wait.
1. Using g = 10 N/kg, calculate the ideal force needed to pull the boat up the slipway and the force once friction is allowed for. Decide whether the 1500 N winch is adequate, and justify your decision.
Read the worked answer
Step 1 - weight of the boat. W = mg = 900 kg × 10 N/kg = 9000 N. This is the force that must be overcome vertically.
Step 2 - ideal force along the slope (no friction). A slope is a simple machine: it trades force for distance. The fraction of the weight you must pull against is the gradient, height ÷ length = 1.8 ÷ 12 = 0.15. Ideal force = 9000 N × 0.15 = 1350 N.
Step 3 - allow for friction. 1350 N × 1.35 = 1822.5 N, about 1800 N.
Step 4 - compare with the winch. 1822.5 N is about 320 N more than the 1500 N rating - roughly 20 % overload. Even the frictionless figure of 1350 N uses 90 % of the winch's capacity, which leaves no margin for a jammed roller, wet rope or a boat that swings sideways.
Decision: the 1500 N winch is not adequate for this load. Buying it would mean an overloaded motor, a slipping clutch or a parting rope, and a 900 kg boat rolling back down a slope is a fatal hazard. The co-op should not buy it for this job unless the load or the friction is reduced first.
2. Explain why the slipway reduces the force needed but not the work done, and describe two practical ways the co-op could haul the boat with a winch of this size.
Read the worked answer
Force versus work: work done in lifting = weight × vertical height = 9000 N × 1.8 m = 16 200 J. Pulling along the slipway: 1350 N × 12 m = 16 200 J. The same energy is needed; the slope simply spreads it over twelve metres instead of 1.8 m, so each metre needs a smaller force. Friction adds extra work on top: with the 35 % allowance the total is about 16 200 × 1.35 = 21 870 J. So the slipway saves force, not energy.
Way 1 - reduce the mass. Remove the engine, fuel, ice boxes and gear before hauling. If 250 kg is taken off, the mass is 650 kg, weight 6500 N, ideal force 6500 × 0.15 = 975 N, and with friction 975 × 1.35 ≈ 1316 N - comfortably inside the 1500 N rating.
Way 2 - use a block and tackle. A single movable pulley gives two rope sections supporting the load, roughly halving the pull to about 910 N (you pull twice as much rope). A 2:1 system brings even the full 1822 N demand down to about 911 N.
Supporting measures: wet or grease the slipway and keep the rollers turning to cut friction, and pull slowly and steadily rather than snatching. Never stand downhill of the boat or under the rope.
3. Explain why this week's high tides are so much lower than three weeks ago, and advise the co-op on whether to haul the boat out now or wait.
Read the worked answer
Why the tides changed: the tide is driven mainly by the Moon, with a smaller pull from the Sun. At new moon and full moon the Sun, Earth and Moon are in line, so the two pulls add and the tidal range is greatest - these are spring tides. At first quarter and third quarter the Moon is at right angles to the Sun, so the pulls partly cancel and the range is smallest - neap tides. Three weeks ago the high tides were 1.35–1.40 m (spring); this week they are 0.62–0.68 m (neap). A full cycle between spring tides is about two weeks, so three weeks ago was one spring phase and this week is close to the opposite, neap, phase.
The practical problem: at this week's high tide the water at the foot of the slipway will be only about 0.65 m deep, but the loaded pirogue needs 0.85 m to float. The boat would ground before it reached the foot of the slipway, so no winch, however powerful, can help.
Advice: do not buy the winch on the strength of this week's conditions and do not attempt the haul now. Either wait roughly a week for the tides to build back towards spring, or use a crane or a hired heavier winch from the shore. When the haul does happen, it must be timed for high tide, not low, and the boat lightened before it goes on the slipway.