You have probably discussed **kinetic energy**
in an earlier physics course.
Kinetic energy, or KE for short,
is just one of many different types
of energy.

Q: Can you name any other types of energy? Try to be specific.

Kinetic energy is the energy a body has due to its motion. The formula for calculating the kinetic energy of a body (in the non-relativistic regime) is pretty simple:

The SI units of energy are **Joules**:

Q: I toss a rubber ball of massm = 0.2 kggently across the room atv = 5 m/s. What is the ball's kinetic energy, in Joules? Q: Crazy Ellie fires a 125-grain cartridge from her Smith and Wesson .357 Magnum handgun (one grain is approx 0.065 grams). The bullet leaves the muzzle of the gun atv = 440 m/s. What is the bullet's kinetic energy, in Joules?

Sometimes, people use other units to describe
energy.
For example, if one measures mass in grams,
distance in centimeters, and time in seconds --
the **cgs system**, which is sometimes used
by astronomers --
then the units of energy are **ergs**.

High-energy physicists often use a unit of energy
called the **electron-Volt**, or **eV**.
If you let an electron accelerate across an
electric potential of 1 Volt, then the kinetic energy
it gains by the end of its journey is
one eV.

Q: The mass of an electron is 9.1 x 10^(-31) kg. The velocity it gains by the time it reaches the positive grid is about 593,000 m/s. How many Joules are in one eV? How many eV are in one Joule? Q: I toss a rubber ball of massm = 0.2 kggently across the room atv = 5 m/s. What is the ball's kinetic energy, in eV? The Large Hadron Collider at CERN will give protons a kinetic energy of about 7 TeV. a) which is larger: KE of rubber ball, or KE of proton in LHC? b) by what factor is the winner's KE larger than the loser's KE?

Well, one of the most useful aspects of KE, and energy in general, is that one can SOMETIMES use it to solve very complicated problems in a simple way. In some situations, the mechanical energy of an object (or a system of objects) remains constant from start to end, no matter what complex paths it takes and no matter what sort of forces act on it. The mechanical energy is just the sum of KE and potential energy.

Consider a roller coaster ride.
Bill and Ted (masses 50 and 70 kg, respectively)
climb into the cars at the start of the ride.
After they are strapped in,
the cars shoot forward at speed
**v** towards the first hill.
As the cars roll up the hill, gravity pulls them
straight down and the tracks push them
up and to the left,
in a constantly changing direction.
It would be very difficult to account for the forces
on the cars as they coast up the hill ....
but energy makes the situation easy to analyze.

Q: If the hill isH = 100 feet tall,how fast must the cars be moving to make it up and over the hill? Express your answer in miles per hour.

Well, no, not in general. The roller coaster was an example of the
way that KE can be exchanged for gravitational potential energy
and vice-versa.
Although the **total energy ** of a system of objects
is always conserved throughout their interactions,
the KE, by itself, is not.

However, there are occasional situations in which
KE IS conserved.
For example, when hard, solid balls -- like billiard balls --
collide, the kinetic energy before the collision
may be the same as the kinetic energy afterwards.
We call collisions in which KE is conserved **elastic collisions.**
When high-energy physicists smash particles together
in giant accelerators,
they often see elastic collisions
between sub-atomic particles.

Here's a less exotic example of an elastic collision:
a baseball (**m1 = 0.145 kg**) thrown horizontally at
**v = 40 m/s**
strikes a stationary bowling ball (**M2 = 6 kg**) head-on.

You will learn in University Physics I how to figure out the relationship between the initial and final velocities of balls in an elastic collision. It turns out that, in this particular situation, the result is pretty simple:

Q: What is the final speed of the baseball? What is the final speed of the bowling ball? What is the initial KE? What is the final KE?

An **invariant quantity** is one that
has the same value, no matter which observer is making measurements.
The space-time interval

is an example of an invariant quantity.

Is kinetic energy an invariant quantity? Let's find out.

The Blue Man throws a ball (**m = 0.2 kg **)
at a speed of **v = 20 m/s** to the right.

Q: What is the kinetic energy of the ball, according to the Blue Man?

But the Blue Man and the ball are all travelling across
the landscape at a speed of **w = 50 m/s**,
as measured by the Red Men.

Q: What is the kinetic energy of the ball, as measured by the Red Men?

- You might look at the notes to one of the other courses I teach, University Physics I for more details about kinetic energy and momentum in the non-relativistic regime.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.