When we say something is conserved, we mean it remains constant.

Mass is a conserved quantity.

The motion of many objects involves a combination of potential and kinetic energy.

The two types of potential energy (gravitational and elastic) plus kinetic energy form a quantity called mechanical energy.

ME = KE + ΣPE

The other types of energy form nonmechanical energy.

Mechanical energy is often conserved.

MEi = MEf

An example of this is a pendulum.

Example: A diver steps off the edge of a platform that is 10-m above the water. What is his velocity when he hits the water?

Example: If the diver weighs 500 Newtons, what is his kinetic energy when he hits the water?

Example: What is the potential energy of the 500 N diver while on the 10 m platform?

Example: Compare the two answers. Can you make some sense of the results?

MEi = MEf

This is only true if there is no friction.

MEi = MEf

1/2 mv2i + mghi

= 1/2 mv2

f + mghf

Example: Starting from rest, a child slides down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Her mass is 25.0 kg.

How should we do this problem?

If the slope if this slide were constant, we could use the kinematic equations to solve this problem.

But, we don't know the slope, or if it is constant (acceleration may not be constant).

But, comparing energy is not affected by the shape of the path, so we don't need the slope.We just remember that MEi = MEf.

Example: Starting from rest, a child slides down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Her mass is 25.0 kg.

Mechanical energy is not conserved in the presence of friction. (Total energy is conserved, but not mechanical.)

Power is the rate at which work is done.

P = W/Δt

Since W = Fd and P = Fd/t and d/t = v,

P = Fv is also true.

The SI unit of power is the watt, which is equal to one joule per second.

Machines with different power ratings do the same work in different time intervals.

Example: Superman is "more powerful than a speeding locomotive." What does this mean?

Example: A 193 kg curtain needs to be raised 7.5 m, at a constant speed, in a time as close to 5.0 s as possible. The power ratings for three motors are 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best?