Question

the length of nylon rope from which a mountain climber is suspended has a force constant of 1.40*10^4. how much would this rope stretch to break the climbers fall if he freefall 2.00 m before the rope run out of slack

Answer 1

We are given the following values:

Force constant (k) = 1.40 * 10^4 N/m

Freefall distance (h) = 2.00 m

The first thing we need to do is to calculate the potential energy gained by the mountain climber due to his free fall using the formula:

PE = mgh

where PE is potential energy, m is mass, g is acceleration due to gravity (9.81 m/s^2), and h is the height of the fall.

Next, we will use this potential energy to calculate the work done to stretch the rope. This work done will be equal to the potential energy gained during the fall.

PE = 1/2 kx^2

where PE is the potential energy gained during the fall, k is the force constant of the rope, and x is the amount of stretch.

To solve for x, we will rearrange the equation to get:

x = sqrt((2 * PE) / k)

At this point, we have not been given the mass (m) of the climber so we can not find out an exact value for x. If the mass of the climber is provided, we would be able to calculate the potential energy and find the required stretch of the rope.