Question

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. How hard is the spring pulling to lift you?

Answer 1

588 N

Step-by-step explanation:

Hook's Law: Hook's Law states that the Force applied to an elastic material is directly proportional to its extension, provided that the elastic limit is not exceeded.

From Hook's Law,

F = ke................. Equation 1

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

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

Substitute into equation 1

F = 5880(0.1)

F = 588 N

Hence the spring is pulling 588 N hard to lift me

Answer 2

29.4J

Step-by-step 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.

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

= 1/2 (5880)(0.1)2

= 29.4J