Question

The figure shows a 68 kg climber hanging by only the crimp hold of one hand on the edge of a shallow horizontal ledge in a rock wall. (The fingers are pressed down to gain purchase.) Her feet touch the rock wall at distance H

= 1.7 m directly below her crimped fingers but do not provide any support. Her center of mass is distance a = 0.30 m from the wall. Assume that the force from the ledge supporting her fingers is equally shared by the four fingers. What are the values of the (a) horizontal component F_h and (b) vertical component F_v of the force on each fingertip?

L. com

a) number _____________ units ________

b) number _____________ units ________

Answer 1

a) Lets assume the horizontal force applied by the rock wall at the feet is F_f .

Horizontal force balance: F_f = 4F_h

Torque about the edge of ledge is zero for the climber to be in equilibrium.

=> aW - hF_f = 0

=> aW = 4hF_h

=> F_h = aW/4h = 0.30 * (68 * 9.81) / (4 * 1.7) = 29.4 N

b) Vertical force balance: 4F_v = W

=> F_v = W/4 = (68 * 9.81) / 4 = 166.8 N