PS3.2a - Energy Stores

Gravitational Potential Energy (GPE / E_g)

• Energy that is due to the location of one object relative to another. The energy is stored when the objects are able to fall towards each other. For example, as a marker falls towards the Earth it can cause a change if it hits a sleeping student and wakes them up!

• Earth, or another planet/sun, must be in the system for there to be E_g (a marker can't fall towards itself!).

• We are interested in how energy changes over time. Therefore, it is useful to set a place where the objects can no longer fall any closer together. We call this the "h=0" or "E_g=0" point since the system would not store any E_g here. If your system is capable of storing E_g, you must set an h=0 point. It's convenient to set h=0 at the lowest point in the problem (i.e. many times: the floor).

• Depends on:

  • • • Height - above resting point - h = 0 (often the ground or equilibrium point)

      • Mass - Larger masses have more energy.

      • Gravitational Field - created by the planet the object is near.

• Quantitatively:

  • • • E_g=mgh

Elastic Potential Energy (EPE / E_el)

• Always involves deformation and reformation. Imagine springs stretching and compressing.

• When the object is in a relaxed state E_el=0, because the object is neither stretching or compressing - either of which would increase the amount of E_el stored in the system.

• Depends on:

  • Elasticity of the material - how difficult the material is to stretch or compress.

  • Amount the material is stretched or compressed - measured as a length.

• Quantitatively:

  • E_el=1/2k∆x²

  • In this equation, k represents the "stretchiness" of the spring (spring constant), or the amount it stretches in ratio of the amount of force used to stretch it.

  • ∆x is the spring displacement. This means how much longer or shorter the spring is due to the extension/compression compared to it's relaxed length.

Thermal Energy (E_Diss / E_t)

• Due to temperature (the movement of molecules in an object)

• Since all objects have temperature, all objects store thermal energy. However: we only care about E_t in this class if it increases. In physics, E_t will never decrease. Decreasing E_t is difficult and not something we are studying here.

• Sometimes called dissipated energy because thermal energy tends to spread out. For example: if one object is very warm, it raises the temperature of surrounding objects as the original object's temperature drops.

• Fundamentally E_t is stored in the motion of microscopic objects. The faster atoms vibrate, the warmer the object feels and the more E_t is stored in the object. See: 3D model of a solid.

• In this class: E_t rises if there is friction between objects (they get warmer) or during collisions which also cause both objects temperature to rise.

• At absolute 0 K, E_t=0 but this violates the 3^rd Law of Thermodynamics!

• Depends on:

  • Mass - Amount of material

  • Specific Heat - Ability to change temperature (water has a very high specific heat, aluminum has a low specific heat)

  • Difference in energy between two objects.

• Quantitatively:

  • ∆Q=mC∆T