The greatest instantaneous acceleration a person can survive is 25g. where g is
ID: 1899377 • Letter: T
Question
The greatest instantaneous acceleration a person can survive is 25g. where g is the acceleration of free fall. A climber's rope should be selected such that, if the climber falls when the rope is attached to a fixed point on a vertical rock, the fall will be survived. A climber of mass m is attached to a rope which is attached firmly to a rock face at B as shown in figure M6. when at a point A, a distance L above B, the climber falls.
A particular rope has a breaking strength of 25 times the weight of a climber and obeys Hooke's law until breaking, when it has stretched by 20% of its length. Determine whether this rope is suitable.
Explanation / Answer
Help: 1/2 mv^2=mgx+1/2 Fx During free fall loss of p.e. = gain of k.e. When the rope becomes taut the maximum deceleration (which can be equal to 25g) occurs, at max. extension and velocity = zero; here the k.e. and further loss of gravitational p.e. are stored as elastic strain energy in the rope. An energy equation in terms of extension e in the rope when the climber's fall is stopped gives the maximum force in the rope. Relating this to the maximum deceleration gives:e>= L /6 (b) The given breaking strength is insufficient to decelerate the climber beyond 25g so this is 0K. But will the rope break? Another energy balance shows that the extension is only 18.7%: the rope is fine.
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