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 Homework Statement
 I can never quite remember when solving problems with elastic materials whether I should be using Hooke's Law or conservation of energy. Below are two sample problems.
 Homework Equations

Hooke's Law: ##F=kx##
Elastic Potential Energy: ##E_e=\frac{1}{2}kx^2##
Gravitational Potential Energy: ##E_g=mgh##
Here are the two questions I want to compare:
1. A student of mass 62 kg stands on an upholstered chair containing springs, each of force constant 2.4 × 10^{3} N/m. If the student is supported equally by six springs, what is the compression of each spring?
2. A 0.20kg ball attached to a vertical spring of force constant 28 N/m is released from rest from the unstretched equilibrium position of the spring. Determine how far the ball falls, under negligible air resistance, before being brought to a momentary stop by the spring.
I can get the right answer for both questions, by using Hooke's law for number 1 and conservation of energy for question 2. My question is if I didn't know what the answers were, how would I choose the method? By using the incorrect method I'm off by a factor of two in both cases (bigger in 1 and smaller in 2).
1. A student of mass 62 kg stands on an upholstered chair containing springs, each of force constant 2.4 × 10^{3} N/m. If the student is supported equally by six springs, what is the compression of each spring?
2. A 0.20kg ball attached to a vertical spring of force constant 28 N/m is released from rest from the unstretched equilibrium position of the spring. Determine how far the ball falls, under negligible air resistance, before being brought to a momentary stop by the spring.
I can get the right answer for both questions, by using Hooke's law for number 1 and conservation of energy for question 2. My question is if I didn't know what the answers were, how would I choose the method? By using the incorrect method I'm off by a factor of two in both cases (bigger in 1 and smaller in 2).