The document calculates the strain, stress, and Young's modulus of a rope used for rock climbing. It determines that the strain is 1.9 × 10−3 based on the rope's stretched length. The stress is calculated to be 1.3 × 107 N/m2 by relating the force of a 95 kg climber to the rope's cross-sectional area. Finally, it divides the stress by the strain to determine the rope's Young's modulus is 6.9 × 109 N/m2.

1. 43. (a) If L (= 1500 cm) is the unstretched length of the rope and ∆L = 2.8 cm is the amount it stretches
then the strain is ∆L/L = (2.8 cm)/(1500 cm) = 1.9 × 10−3 .
(b) The stress is given by F/A where F is the stretching force applied to one end of the rope and A is
the cross-sectional area of the rope. Here F is the force of gravity on the rock climber. If m is the
mass of the rock climber then F = mg. If r is the radius of the rope then A = πr2 . Thus the stress
is
2
F mg (95 kg)(9.8 m/s ) 2
= 2 = = 1.3 × 107 N/m .
A πr π(4.8 × 10−3 m)2
(c) Young’s modulus is the stress divided by the strain: E = (1.3 × 107 N/m2 )/(1.9 × 10−3 ) = 6.9 ×
2
109 N/m .