9. Work & Energy
Net Work & Work-Energy Theorem
Problem 7.99a
Textbook Question
Textbook QuestionStretchable ropes are used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length ℓ is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height ℓ above the anchor point, he slips and falls under the force of gravity for a distance 2ℓ , after which the rope becomes taut and stretches a distance x as it stops the climber (see Fig. 7–37). <IMAGE>
Assume a stretchy rope behaves as a spring with spring constant k.
(a) Applying the work-energy principle, show that
x = mg/k [ 1 + √1 + (4kℓ/mg)]
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