The Conservation of Energy

Robert Drach

What do we already Know??

• Kinetic Energy: Depends on an objects motion.• KE = 1/2 mv2

• Potential Energy: Depends on an object’s position.• PE = mgh (gravitational potential energy)

What do we already Know?

• WORK– Work is done to an object by an external

force.– Work is measured in Joules, just like

energy!

• Where do we go from here?

What is a closed system?

• Just what it sounds like!

• In a closed system, no energy enters or leaves.

• For example: no work is done by an external force.

Conservation of Energy

• In closed systems, all energy is conserved.

• This includes Potential Energy, and Kinetic Energy.

• E = PE + KE

• In a closed system, this total E will not change.

• Kinetic Energy can take many forms:– Translational KE (1/2 mv2)

– Vibrational – Rotational

• Potential Energy can also take many forms: – Gravitational Potential– Spring Potential

• No matter what type of potential or kinetic energy we use, E is always conserved.

• EX: Throwing a ball of mass m.

• Immediately after the ball is thrown:– h = 0, --> PE = mgh = 0– All the energy is kinetic energy.

• When the ball reaches the top of its climb:– It temporarily stops, so KE = 0– It has a height, h, so PE = mgh.

h = h

v = 0

• What happens at the bottom of the fall?

• Obviously, it has stopped.

• Obviously, it has no height.

• So KE + PE = 0

• So what happened to conservation?!?

h = 0

v = 0

• When the ball hits the ground:– The ground exerts a force on the ball.– The ball and the ground heat up.– The ball makes a THUD.

• These are all manifestations of energy.

• But since the energy is no longer in the ball, we can no longer say it is conserved!