To determine The mass of the rock for the climber to be saved. Explanation The free-body diagram of the climber is shown in figure 1. Write the equation for the y-component of the net force on the climber. Σ F → c y = m c a → c (I) Here, Σ F → c y is the y-component of the net force on the climber, m c is the mass of the climber and a → c is the acceleration of the climber. Write the equation for Σ F → c y . Σ F → c y = T → c − F → g c Here, T → c is the rope tension on the climber and F → g c is the weight of the climber. Put the above equation in equation (I). T → c − F → g c = m c a → c (II) Write the equation for F → g c . F → g c = m c g Here, g is the acceleration due to gravity. Put the above equation in equation (II). T → c − m c g = m c a → c (III) The free-body diagram of the rock is shown in figure 2. Write the equation for the x-component of the net force net force on the rock. Σ F → r x = m r a → r (IV) Here, Σ F → r x is the x-component of the net force on the rock, m r is the mass of the rock and a → r is the x-component of the acceleration of the rock. Write the equation for Σ F → r x . Σ F → r x = T → r Here, T → r is the rope tension on the rock. Put the above equation in equation (IV). T → r = m r a → r (V) The rock has no vertical acceleration. Write the equation for the y-component of the net force net force on the rock. Σ F → r y = 0 (VI) Here, Σ F → r y is the y-component of the net force on the rock. Write the equation for Σ F → r y . Σ F → r y = n → − F → g r Here, F → g r is the weight of the rock and n → is the normal force from the surface. Put the above equation in equation (VI). n → − F → g r = 0 (VII) Write the equation for F → g r

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ISBN: 9780134988559

Author: Wolfson, Richard

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Chapter 5, Problem 31E

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The mass of the rock for the climber to be saved.

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