2. A hanging chair is suspended on a spring from the ceiling. The 5880 N/m spring stretches

from 15 cm long to 25 cm long when you sit in the chair

a) How hard is the spring pulling to lift you?

b) How hard does gravity pull down on you?

c) How massive are you?

a) = 29.4J

b) F = 588 N

c) = 60 Kg

Explanation:

Force constant of the spring (k) = 5880 N/m

Change in length of the spring (x) = 25 - 15 = 10 cm 0.1m

This work done on the spring as it is stretched (or compressed) can be recovered. This is stored work that can be used to do work on something else by this spring. That means the stretched (or compressed) spring has energy - - potential energy. This is spring potential energy or elastic potential energy.

a) Work done in pulling the body W = 1/2kx²

= 1/2 (5880) (0.1) 2

= 29.4J

b) From Hook's Law,

F = ke

Where F = applied force, k = spring constant, e = extension.

Given: k = 5880 N/m, e = 25-15 = 10 cm = 0.1 m.

Substitute into the formula above

F = 5880 (0.1)

F = 588 N

c) By using the formula, F = - kx

Hence mg = kx

Thus m x 9.8 = 5880 x0.1

Hence mass of the body

m = 5880 x0.1/9.8

= 60 Kg