Download Lesson 29: Kinetic Energy

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Work and Mechanics
Lesson 29: Kinetic Energy
Lesson 29: Kinetic Energy
The Energy of Motion
We have already discussed a few different forms of energy, and we have said that energy
cannot be created or destroyed (short of nuclear reactions). With this in mind, let’s think
about the falling object experiment. As the object falls, its potential energy is decreasing
because its height is decreasing. No nuclear reaction is happening, thus we are not
destroying energy, so where is the energy going?
There is energy associated with the motion of objects, called kinetic energy. The potential
energy that is lost as the object falls is mostly transformed into kinetic energy. (A small
quantity of energy is transferred into disturbing the
atmosphere through which it falls.)
Think about pitching a baseball. The faster you want
the ball to cross the plate, the more work it is for you
to pitch it. So in some way, velocity is related to
kinetic energy. Now, think about trying to pitch a
“shot” [the 8-16lb. metal ball used in the shot put
event] the same speed. You probably couldn’t do it,
but if you could, it would be a lot more work!
Kinetic Energy
 Is the form of energy associated
with motion
 Increases with increasing
velocity
 Increases with increasing mass
 Transforms easily to and from
potential energy
So, we can guess that kinetic energy of an object depends on its velocity and mass, but are
there other factors? Well, let’s do some work the way Newton did, and try to figure it out
mathematically.
Imagine a body at rest (i.e. zero velocity) in a vacuum (no atmosphere) with a constant
mass m that is suddenly subjected to a constant force of F. (We will assume that this body is
not under the influence of gravity.) By Newton’s second law (F = m  a), the body will
accelerate at a constant rate that we will call a. Since the body started from rest and has
now begun to accelerate in the direction of the force, this means that over a period of time,
the position and velocity will change. Let’s say that after a time t, the body has moved a
distance of d and attained a velocity of v. The diagram below is intended to illustrate this
situation.
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Work and Mechanics
If we recall the definition of work, we could write
a mathematical statement that describes how
much energy is imparted to the body due to the
force F. With the assumptions we have made, there
is no other place for this imparted energy to go
besides to become kinetic energy. Therefore, we
can say that the work imparted to this body is the
kinetic energy of the body.
The work done on the object becomes kinetic
energy. Work is force times distance, and force is
mass times acceleration.
We also recall that acceleration is a change in
velocity per change in time. Since we started at zero
velocity and zero time, a = v/t.
The distance traveled is just the average velocity of
the body during its move multiplied by the time it
was in motion.
Since the body started at rest and gained velocity
uniformly, the average velocity during its move is
just half of the final velocity.
So kinetic energy is purely a function of mass and
velocity, but is not simply the product of the two.
The velocity term is squared and there is a factor
of one-half included. Let’s check the units – this is a
great way to check ourselves for errors.
Lesson 29: Kinetic Energy
NASA-Threads
Work and Mechanics
Lesson 29: Kinetic Energy
It should be noted that the relationship developed here gives us a method of calculating
kinetic energy due to the translation of a body, but does not account of kinetic energy due
to the rotation of a body. To find the total kinetic energy both have to be considered.
Class Problem: The Barringer Meteorite Crater in Arizona is 570 feet deep and nearly a
mile wide. Scientists believe the crater was crated approximately 50,000 years ago when
a meteorite struck the earth. Key estimates on the characteristics of the meteorite
include . . .
mass of meteorite = 270,000,000 kg
diameter of meteorite = 46 m (150 ft)
velocity at impact = 12 km/s (28,600 mph)
Estimate the kinetic energy of the meteorite when it impacted the earth.
Some comparisons:
 Energy used in one year per capita in US = 1012 J
 Energy used to put shuttle into orbit = 1013 J
 Energy to burn a million tons of coal = 1016 J
