A rock climber has fallen while descending a cliff face and landed on a ledge 10 m below the cliff top where you are standing. You have attached a rope to pull the injured climber up to safety. However, you are not sure if the rope can withstand the generated tension without snapping. Is it best to pull the climber up quickly, slowly, or does it make no difference? Explain your answer.
2006-08-26 23:39:50 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
As slowly as possible at first, acceleration requires additional force. You may increase your rate of pulling so long as you do not increase the acceleration
Newton's second law
2006-08-26 23:50:07 · answer #1 · answered by john a 2 · 0⤊ 0⤋
It makes a difference. Of course you want to avoid "jerking" the rope, and take up the tension slowly at the start. After that, you want to avoid a lot of accelerations and decelerations, so you should pull smoothly.
It is important to realize that if a steady upward velocity be achieved, the force exterted on the rope is the same whether that velocity is high or low, and is equal only to the force exerted on the climber by gravity. It is only accelerations that exert a force on the rope greater than the force of gravity, so the best course of action is to accelerate the climber gradually and smoothly (a constant low rate of acceleration; a constant force slightly greater than the weight of the climber) all the way up, to achieve a "high" upward velocity to minimize the time the climber is in jeopardy.
To put an exact figure on the rate of acceleration, we would have to know detailed specifications of the rope.
2006-08-26 23:58:52 · answer #2 · answered by ? 6 · 0⤊ 0⤋
The best answer is none of those (I'm a rock climber myself and do mountain rescue).
In any situation like that the key is to life the load *smoothly*, if you jerk the rope then you shock-load it which exerts a lot more force and so increases the risk of it snapping. Assuming you take up the tension on the rope and life smoothly then the speed at which you lift will not have much effect on the rope - unless you were to lift at a really fast speed.
You could argue that lifting slowly causes sustained tension which causes stress on the inner core of the rope over a longer period of time but you could also argue that lifting quicker has to overcome greater resistance. On that basis both options are right and wrong.
2006-08-26 23:54:20 · answer #3 · answered by Trevor 7 · 0⤊ 0⤋
Tension in the rope
= force to be applied to pull the climber up against gravity and with an acceleration a
= mg+ma
So tension will be more for larger acceleration
Hence it would be advisable to pull slowly.
Assumption : the breaking strength of the rope is indepedent of the duration of application of the force which I believe holds in practice.
2006-08-27 05:03:47 · answer #4 · answered by rabi k 2 · 0⤊ 0⤋
Slowly slowly, "catchee", climber. Fishermen will tell you it is possible to catch fish of weights greater than the breaking strain of the line they are using, which is always mono filament, using a multi stranded rope makes the task a lot easier.
2006-08-27 00:46:33 · answer #5 · answered by djoldgeezer 7 · 0⤊ 0⤋