Question

The length of nylon rope from which a mountain climber is suspended has a force constant of 1.4x10⁴ N/m.

How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.4 m before the rope starts to stretch?

Answer 1

The nylon rope would stretch approximately 137.2 cm when the climber free-falls 1.4 m before the rope starts to stretch.

Step-by-step explanation:

To determine how much the nylon rope will stretch when the climber free-falls, we can use the principle of conservation of energy. When the climber free-falls 1.4 m, their potential energy is converted into elastic potential energy stored in the stretched nylon rope. The equation to calculate the amount of stretch in the rope is given by: D = (1/2)kx^2, where D is the stretch, k is the force constant of the rope, and x is the initial displacement.

Substituting the given values: D = (1/2)(1.4x10^4 N/m)(1.4 m)^2 = 13720 cm, or 137.2 m.

Therefore, the nylon rope would stretch approximately 137.2 cm when the climber free-falls 1.4 m before the rope starts to stretch.