Question

The length of nylon rope from which a mountain climber is suspended has a force constant of 1.52 ✕ 10⁴N/m.

(a)

What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 86.0 kg?

(b)

How much would this rope stretch (in cm) to break the climber's fall if he free-falls 2.00 m before the rope runs out of slack? Hint: Use conservation of energy.

(c)

Repeat both parts of this problem in the situation where twice this length of nylon rope is used.

frequency (in Hz)

stretch length (in cm)

Update: Im getting the stretch length of part c wrong. All the other answers i got to be 2.16 Hz, 53 cm, 1.496 Hz for a, b, and first part of c respectively, which are right.

Answer 1

C)

0.5 kx^2 - mgx - 2mg = 0

0.5 x (0.5 x 15200) x^2 - (86 x 9.8)x - (2 x 86 x 9.8) = 0

3800 x^2 - 843.66 x - 1687.32 = 0

X = 78.65 cm

Comment in case any doubt please rate my answer....