# CONSERVATION OF ENERGY

• Forces can be classified as to whether they are CONSERVATIVE or NON-CONSERVATIVE
• Consider a mass sliding down a frictionless inclined plane of height h. When released from the top, what is the speed at the bottom of the incline?

• How does the speed at the bottom of the incline compare to the speed of an object dropped from a height h?
• A force is CONSERVATIVE if the work done by it on a particle that moves between two points depends only on the positions of the points and not on the path taken.
• For a NON-CONSERVATIVE (dissipative) force the work depends on the path taken.
• POTENTIAL ENERGY can be related to the work done by a conservative force. By lifting an object to a height h, work is done by the lifting force against gravity. Energy is now "stored" and is potentially available in the amount of mgh.
• When conservative forces only are present we can write: KE(initial) + PE(initial) = KE(final) + PE(final)
• When both conservative and non-conservative forces are present this has to be modified to take the work done by non-conservative forces into account: KE(initial) + PE(initial) + W(nc) = KE(final) + PE(final)
• Since the total final mechanical energy (KE + PE) is less than the total initial mechanical energy (KE + PE) when dissipative forces are present, the non-conservative work [W(nc)] is a negative quantity.

EXAMPLE

A spring is stretched 5.0 cm by an external force. If the spring constant, k = 2.0 N/cm

• how much work is done by the external force?
• If a 0.50 kg mass is attached to the spring when it is stretched, what is the speed of the mass as it passes through the equilibrium position after it is released?