and so on. The amount of mechanical energy does decline, but when you include all
forms of energy, the overall energy stays constant.
There is a caveat to the law of conservation of energy. Albert Einstein demonstrated
that there is a relationship between mass and energy. Mass can be converted into
energy, as it is inside the Sun or a nuclear reactor, and energy can be converted into
mass. It is the sum of mass and energy that remains constant. Our current focus is on
much less extreme situations.
Using the principle of conservation of energy can have many practical benefits, as
automotive engineers are now demonstrating. When it comes to energy and cars, the
focus is often on how to cause the car to accelerate, how fast they will reach say a
speed of 100 km/h.
Of course, cars also need to slow down, a task assigned to the brakes. As conventional
cars brake, the energy is typically dissipated as heat as the brake pads rub on the
rotors. Innovative new cars, called hybrids, now capture some of the kinetic energy and
convert it to chemical energy stored in batteries or mechanical energy stored in
flywheels. The engine then recycles that energy back into kinetic energy when the car
needs to accelerate, saving gasoline.
Ef = Ei
PEf + KEf = PEi + KEi
E= total energy
KE= kinetic energy
PE= potential energy
6.17 - Sample problem: conservation of energy
Sam is jumping up and down on a trampoline. He bounces to a maximum height of 0.25 m above the surface of the trampoline. How fast will
he be traveling when he hits the trampoline? We define Sam’s potential energy at the surface of the trampoline to be zero.
Variables
What is the strategy?
- Use the law of conservation energy, to state that Sam’s total energy at the peak of his jump is the same as his total energy at the
surface of the trampoline. Simplify this equation, using the facts that his kinetic energy is zero at the peak, and his potential energy is
zero at the surface of the trampoline. - Solve the resulting equation for his speed at the bottom.
Physics principles and equations
The definition of gravitational potential energy
PE = mgh
The definition of kinetic energy
KE = ½ mv^2
Total energy is conserved in this isolated system.
Ef = Ei
Sam is at the peak of his jump.
Calculate Sam's speed when he
reaches the trampoline's surface.
Sam’s height at peak h = 0.25 m
Sam’s speed at peak vpeak = 0 m/s
Sam’s speed at bottom v