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Changes in Energy

As before, an object cannot do anything to itself to change the total amount of energy, but the energy can move between potential and kinetic.

Total energy = potential energy + kinetic energy

TE = PE + KE

The total energy may remain constant, but the potential and kinetic energies may not. Think about you car coasting up a hill. The higher it goes, the slower it goes. (kinetic energy changing into potential energy)

Something from the outside of the object is needed to cause a change in the total energy.That?s where work comes in:

W = DTE , but DTE could be the change in potential energy, or kinetic, or both.

EX. Consider shooting an arrow straight into the air.

You pull back on the bowstring (work), increasing the potential energy of the string.
When released, the string moves (potential changing to kinetic), pushing the arrow as it goes (work).
The arrow moves at a fast speed as it comes off the bow (kinetic energy) which slows as the arrow goes up into the air (kinetic changing into potential).
At the top of its flight the arrow is stopped (the total energy is all potential).
As the arrow falls the arrow speeds up (potential changing into kinetic).
when the arrow hits the ground its speed is approximately the same as when it left the bow.(the total energy is all kinetic).

In theory, the work done by you on the bowstring shows up as the maximum potential energy of the arrow. In reality, some of the energy is absorbed into the potential and kinetic energy of the molecules in the string and bow, and the arrow does work on the air as it rises. Each of these reduces the total energy of the arrow, and hence, its maximum height is not as high as it couold have been.

EX. If you use an average force of 150 N to pull a bowstring back a distance of 0.30 m, how
high will a 0.050 Kg arrow rise vertically?

               W = DTE
               W = D(PE + KE)
                                DKE = 0 since the arrow starts from rest and is at rest at the top of the rise
               W = DPE
             F?D = m g h
            150 N (0.30 m) = 0.050 Kg (9.8 m/s² )(h)
                h = 91.8 m

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