Math Help - Energy

1. Energy

I'm struggling to understand concepts involving potential energy and kinetic energy. Could someone briefly explain these energies in terms of particles dangling from elastic strings. If potential energy is stored energy why has my tutor given me the equations

potential energy = mgh

stored energy = $\frac{1}{2}\frac{\lambda x^2}{l}$

Also before i delve into simple harmonic motion, is it true to say SHM is sort of an extension of hooke's law?

2. Originally Posted by djmccabie
I'm struggling to understand concepts involving potential energy and kinetic energy. Could someone briefly explain these energies in terms of particles dangling from elastic strings. If potential energy is stored energy why has my tutor given me the equations

potential energy = mgh

stored energy = $\frac{1}{2}\frac{\lambda x^2}{l}$

Also before i delve into simple harmonic motion, is it true to say SHM is sort of an extension of hooke's law?
Yes. Simple Harmonic Motion is governed by an equation which is equivalent to Hooke's Law.

Potential energy is the energy that is required to move a body back to what we call the 'reference' position. With regards to a spring, the reference position is the position where the spring is in mechanical equilibrium.

If we move the spring from the reference position, the stiffness of the spring produces a force which is proportional to the distance we move it from the reference position. If we hold it at a position from the reference position, then it had potential energy which tries to move it back to the reference position.

In a spring, this energy is stored as elastic potential energy. Which is the 2nd equation you gave for 'stored' energy.

E = mgh, is the equation for the gravitational potential energy. (The energy which comes about as the result of the force of gravity, which attempts to pull a body towards the reference position, which, in the case of gravity, is the centre of mass of the body)

[tex] E = \frac{\lambda x^2}{2l} is the equation for elastic potential energy.

There are many types of potential energy. Gravitational, elastic, nuclear, electrostatic. And they are each governed by their own equations.