Question

A rope that is 6 m long can sustain a maximum tension of 700 Newtons before breaking. A person stands with the rope angled 45 degrees from the vertical and swings off a ledge in a circular arc. What is the maximum mass the person can have, in order to not break the rope. Answer in kilograms.

Answer 1

T = maximum tension force in the rope = 700 N

L = length of the rope = 6 m

= Angle = 45 deg

h = height dropped

height dropped to reach the bottom is given as

h = L (1 - Cos)

h = (6) (1 - Cos45)

h = 1.76 m

Using conservation of energy

Kinetic energy gained = Potential energy lost

(0.5) m v2 = mgh

v = sqrt(2gh)

v = sqrt(2(9.8)(1.76))

v = 5.873 m/s

At the bottom, force equation for the motion of the person is given as

T - mg = m v2/L

T = mg + m v2/L

T = mg + m v2/L

700 = 9.8 m + (5.873)2 m/6

m = 45.02 kg