Download Energy Conversions: Potential Energy to Kinetic Energy It started as

Energy Conversions: Potential Energy to Kinetic Energy
It started as an almost perfectly round, squishy, but
not yet squished, ball of clay.
Now it is squished - well, half squished.
Energy conversions did it. Energy conversions do
everything. Nothing can happen without them.
In this case gravitational potential energy was
converted to kinetic energy. Kinetic energy was
converted to mechanical work (force acting through a
distance - the floor pushing back against the ball).
Then finally, as is predicted by the 2nd Law of Energy, all of the gravitational potential
energy ended up as low-grade thermal energy.
Warning: In the following discussion there are some simple
Algebra formulas. If you don't know algebra, don't worry
about it. I'll bet you will still get the gist.
As always, the laws of energy were demonstrated to be true,
faithful, and reliable as the US Coast Guard (in which the
author once served).
How to Smash a Clay Ball
Our friend Clayton wanted to demonstrate how to convert
gravitational potential energy to kinetic energy.
The first thing he did was pick the round ball off the floor and
lift it over his head. To do that, his hand had to exert a force on the ball through the
distance H shown in the picture. That means work was done on the ball by his hand. The
amount of work is force times the distance the force is exerted.
Energy is now concentrated in the ball as gravitational potential energy. The force of gravity
is pushing the ball toward the ground, but the ball can't move because Clayton's hand is
exerting an equal force on it in the opposite direction. The ball is not moving. No energy is
being converted. Nothing is happening.
To move the ball upward, the upward force on the ball (shown by green arrow) had to be
greater than the downward gravitational force (yellow arrow).
If the ball is not moving it is in equilibrium. The forces are equal and balanced.
Lifting the ball is like winding a spring. But instead of concentrating the work into a spring,
Clayton has concentrated the work into the ball. Potential energy can be thought of as
concentrated energy waiting for its chance to flow or move to a less concentrated form (see
2nd Law of Thermodynamics).
To lift the ball, Clayton's muscles converted concentrated food energy into work and heat.
He had to lift his body weight when he bent over to pick up the ball; and also had to lift the
weight of his arm in addition to the weight of the ball. Since the human body and its
muscles are no more efficient than human-made machines, only about 25% or so of the
food energy was converted to work to lift the ball. The rest of the food energy was
converted into low-grade thermal energy that heated his muscles a little, then moved into
the surrounding air. It will never be of much use to us earthlings again.
Clayton's body used more energy to raise the ball than is now stored in the ball - about 5
times more energy by my estimate. That is always the way it is. We can never break even
(see the 2nd Law of Thermodynamics made easy - unless you already visited it above).
So Clayton has managed to concentrate and store
energy in the ball, though in the process five times
more "spread-out" thermal energy was generated than
ended up being concentrated in the ball. Darn that
second law.
We call the stored energy, potential energy. To be
even more specific we can call it gravitational potential
energy. This tells us it is not energy stored in a spring
or in chemical bonds. It has the potential to be
converted into the energy of motion if we get the hand
force out of its way.
How much gravitational energy is stored in the ball?
In this situation the ball has the potential to fall from Clayton's hand to the ground. If there
was a deep hole under Clayton's hand it could fall farther. But in this case it can only fall the
distance H to the ground. The potential energy in each case depends on how far the object
can fall (not how much energy it took to raise it).
When Clayton lets go of the ball it will fall the distance H, before its exciting, but short, trip
will be stopped by the ground. All the time the ball is falling, gravity will be pushing (or
pulling?) on it with a force equal to 9.8 m/sec^2 (meters per second squared) times the
mass of the ball. The gravitational force on the ball is constant no matter how fast or slow
the ball moves. Gravity will exert a force I labeled Fg on the ball for a distance H. Work is
force times distance. The work done on the ball, therefore, is Fg times H. That's it! That's
how much potential energy is stored in the ball.
Potential Energy (PE) concentrated in the ball equals Force of Gravity times the distance the
ball will fall, or PE = Fg x H.
If you remember Newton's laws of motion, you will remember that Force equals mass times
acceleration. In the case of gravity we know exactly what the force is if we know the mass
of the object. We lable the acceleration caused by the force of gravity, g.
So, according to Newton,
Fg = Mb x g (Mass of the ball times acceleration caused by gravity, g)
Now we can show a formula that always works to calculate the amount of gravitational
potential energy concentrated in an object a distance H above the ground:
PE = Mb x g x H
(Potential Energy equals Mass of object times g times Height above ground)
In this case the ball weighs 0.5 kilograms (kg). Clayton is holding it 2 meters (m) above the
ground. The acceleration caused by the force of gravity on earth is always 9.8 meters per
second squared (m/s^2).
So,
PE = 0.5 kg x 2 m x 9.8 m/s^2 = 9.8 Joules
That's not a lot energy, but if your nose had to absorb it, I think it would hurt.
Gravity never stops pulling the ball toward the earth. The force is constant whether the ball
is falling fast or slow. That means the rate of acceleration of the ball is constant also.
The ball speeds up (accelerates) until it hits the ground. It goes faster and faster,
until...thud! It comes to a smashing stop.
When the ball hits the ground, it has fallen the distance H. Now its kinetic energy equals the
potential energy at the start of its fall.
After falling the distance H, the kinetic energy equals the potential energy of Mass of the
ball times the acceleration due to gravity times the height, H.
So,
KE = (Mb x V^2)/2 = Mb x g x H
See? The Kinetic Energy at the end of the trip, is exactly equal to the Potential Energy at
the beginning of the trip.
If you know a little algebra you will be able to solve for V, the velocity of the ball. If not,
take my word for it.
Here is the answer:
V = (2gH)^1/2
...which means that after falling the distance H, the velocity of the ball is equal to "the
square root of 2 times g times H". There you have it. Isn't that cool? If you know the mass
of the ball and the Height it is going to fall, you can calculate how fast it will be going after
falling that distance.
A Word About Air Resistance
All of the above is a bit idealized. If you are not on the moon, or in a vacuum (gasping for
air), then air resistance will eventually slow down the ball and mess up your calculations. As
every sky diver knows, air resistance will eventually push back as hard on the ball (or the
free falling sky diver) as gravity is pulling on it. The ball will stop speeding up
(accelerating). This point is called terminal velocity, which doesn't mean the ball has died. It
means the ball is falling at a constant speed and has stopped accelerating. In a vacuum like
outer space, the ball would keep accelerating until something, like a planet perhaps, got in
its way.
Even if air resistance slows down the ball, the potential energy is the same (Mb x g x H).
But if air resistance is in the way, not all of the potential energy can be converted to kinetic
energy. Some of the energy has to be used to push the air molecules out of the way. When
that happens, the energy of the air molecules is increased. The air is actually "heated" up
by the falling ball.
But for relatively short distances, we can say the air resistance is negligible (doesn't have
much effect) and our calculation is pretty accurate.
The Final Conversion - Predictable as Always
Finally, the ball hits the ground. What happens to the kinetic energy? As we learned in the
pages on the First Law of Energy, the energy doesn't disappear. It has to go somewhere.
All of that kinetic energy gets turned, rather quickly, through a work process, into thermal
energy. The ball is smashed as the ball pushes on the floor and the floor pushes back on the
ball. Work is done on the ball. If the ball hits dirt, maybe some work is done on the dirt as it
also is pushed on by the ball. The internal friction of the molecules in the clay causes the
clay to heat up.
That's right, the ball actually gets hotter. The kinetic energy has, now, all been converted to
low-grade thermal energy. The air was heated up a little by the falling ball, and the ball was
heated up by the internal friction of the molecules as they were pushed around during the
"smashing process".
All of the potential energy was finally converted into thermal energy. As we learned in the
section on the 2nd Law of Energy, this is what happens to mechanical energy. All of it can
be, and is eventually, converted to low-grade thermal energy.
Once again the Laws of Thermodynamics have predicted the final end of all energy
conversions.
Summary
The amount of gravitational potential energy concentrated in an object is determined by
how far it will fall (which I called H), how much mass it has (M), and the acceleration due
to the force of gravity, g (it would be different on the moon than on earth).
When an object is allowed to fall, the concentrated gravitational potential energy is
converted into the kinetic energy of motion. If there is no air resistance, or other
restrictions, all of the potential energy will be converted to kinetic energy when the object
has fallen the distance H.
The formulas to calculate potential energy and kinetic energy of an object are simple and
accurate, but it takes most of us a little practice to get good at it.