The figure shows a 68 kg climber hanging by only the crimp hold of one hand on t

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 Fh and (b) vertical component Fv of the force on each fingertip?

a) number _____________ units ________

b) number _____________ units ________

Explanation / Answer

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

Horizontal force balance: Ff = 4Fh

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

=> aW - hFf = 0

=> aW = 4hFh

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

b) Vertical force balance: 4Fv = W

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.