After a fall, a 75 kg rock climber finds himself dangling from the end of a rope that had been 18 m long and 11 mm in diameter but has stretched by 2.1 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus.

(A) Strain = 0.0012

(b) Stress

(c) Young's modulus    

Explanation:

Mass of the rock m = 75 kg

So weight of the rock

Length of the rope l = 18 m

Diameter of the rope d = 11 mm

Change in length of rope

So radius r = 5.5 mm = 0.0055 m

Cross sectional area

(a) Strain is equal to ratio change in length to original length

So strain

(b) Stress

(c) Young's modulus is equal to ratio of stress and strain

So young's modulus

c. newton's third law of motion