Rope-Bridge Descent and Braking Load
During a confidence test, an 80 kg candidate (68 kg body mass plus 12 kg equipment) descends a 12 m rope inclined at 35° to the horizontal. He starts from rest and reaches 3.0 m/s after 4.0 s, then uses a braking hand to hold a steady 3.0 m/s for 6.0 s. The rope outlet is rated at 850 N maximum steady tension. The safety officer also considers an emergency stop from 3.0 m/s to rest in 0.8 s and a heavier candidate with total mass 92 kg. Friction at the pulley and rope is neglected; take g = 9.8 m/s² and sin 35° = 0.574. The trainer tells candidates to grip harder whenever speed rises but does not mention smooth braking. The officer must decide whether each phase stays within the rating and whether the instruction is adequate on an incline.
1. Calculate the rope tension during the acceleration phase and the steady-speed phase for the 80 kg candidate.
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The weight component along the incline is mg sin 35° = 80 × 9.8 × 0.574 = 450 N approximately. During acceleration, a = (3.0 − 0) / 4.0 = 0.75 m/s². The net force down the incline is ma = 80 × 0.75 = 60 N. Tension acts up the incline, so T = 450 − 60 = 390 N. During the steady phase, a = 0, so T = 450 N. Both values are below the 850 N rating: margins are about 460 N and 400 N respectively.
2. Evaluate the emergency stop for the 80 kg candidate and for the 92 kg candidate. Does either exceed the rating?
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An emergency stop from 3.0 m/s to rest in 0.8 s gives deceleration magnitude a = 3.0 / 0.8 = 3.75 m/s² up the incline. The extra force needed is ma. For 80 kg: T = 450 + 80 × 3.75 = 450 + 300 = 750 N, below 850 N by 100 N. For 92 kg: weight component = 92 × 9.8 × 0.574 ≈ 517.5 N; extra force = 92 × 3.75 = 345 N; T ≈ 862.5 N. This exceeds the 850 N rating by about 12.5 N. Therefore the 80 kg emergency stop is within rating but close, while the 92 kg stop is not safe under these assumptions. The heavier candidate needs a longer stopping time, lower speed, or a different setup.
3. Critique the instruction to grip harder whenever speed rises and state a safer braking rule.
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On an incline, the instinct is partly right: to slow a rising speed, the candidate must increase tension so the net force is up the incline. But grip harder whenever speed rises is incomplete and can cause a sudden spike in tension, jerking, or loss of control. A safer rule is: keep a steady descent with light tension near the weight component, watch the speed, and if it exceeds the target, increase grip smoothly and progressively rather than snatching. Emergency stopping should be trained and must stay within the rope rating and stopping-distance limits; a backup belay should be used. The trainer should give a target speed and a smooth-braking technique, not a vague instruction.