The figure shows a 60 kg climber hanging by only the crimp hold of one hand on t

Question

The figure shows a 60 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 = 2.2 m directly below her crimped fingers but do not provide any support. Her center of mass is distance a = 0.25 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 horizontal component F_h, and vertical component F_v of the force on each fingertip?

Explanation / Answer

a)

here

net force along along x axis and net force along y axis

Fnet , x = -Fn + 4 * Fh = 0

Fnet , y = -Fg + 4 * Fv = 0

Fv = Fg / 4

Fv = 60 * 9.8 / 4 = 147 N

b)

in this first we calculate the torque around origin

Tnet = Fn(0) + 4 *Fv(0) - 4*Fh * H + Fg * a = 0

Fh = Fg * a /(4 * H)

Fh = 60*9.8 * 0.25 / ( 4 * 2.2)

Fh = 16.7 N

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