Kinetic and Potential Energy
Conservation of Energy
Kinetic Energy
kinetic energy - the energy objects have
because they are in motion
m –mass of object (kg)
v – velocity of object (m/s)
 Like work, the unit of energy is the
joule (J)
Example
A 1400 kg car is travelling at 30 m/s. What
is its kinetic energy?
Work-Energy Theorem
An important relationship can be found
between work and kinetic energy. It is
known as the work-energy theorem,
“the change in an object's kinetic energy is
equal to the net work done on the object.”
Example
pool cue strikes a ball of mass 0.25 kg and
gives it a speed of 1.5 m/s. If the force
exerted by the cue is 20 N, over what
distance did this force act?
Example 2
A soccer player kicks a soccer ball initially
at rest. She exerts a force of 500 N on the
ball over a distance of 10 cm. If the ball
has a mass of 450 kg, with what speed
does it leave her foot?
Potential Energy
 Potential energy - energy an object has because of its
position or state. (stored work)
 Use the symbol U to represent potential energy.
 A battery contains chemical potential energy and when
that energy is released, it can do work to power your
walkman, etc.
Gravitational Potential Energy
The potential energy used most often in
physics is gravitational potential energy.
When you lift a bowling ball, you must do
work against gravity. That work is
transformed into gravitational potential
energy which can be released as kinetic
energy if you drop the ball.
Formula for PE
 To eliminate the
choosing of a
reference point we
talk about change in
potential energy
Example
What is the increase in the gravitational
energy of a 5 kg book that is lifted from the
floor to a table 1.5 m high?
Example 2
A falling ball of mass 250 g losses 25 J of
gravitational potential energy. What
distance has the ball fallen?
Potential Energy of a Spring
You can also store potential energy in a
spring. The formula for this is:
Us = ½kx2
Notice that it's the same formula as the
work done by a spring. Also notice that
spring potential energy is always positive.
Example
A spring has a spring constant of 800 N/m.
How much must this string be stretched to
store 75 J of potential energy?
Displacement and PE
Energy and Conservation
 One of the most fundamental and powerful ideas
in physics is the one of energy conservation.
 the total mechanical energy of a system is
conserved. That is, the energy it initially has
must be equal to its final energy.
 mechanical energy-the sum of its kinetic and
potential energies.
Energy Conservation
You can write the conservation of energy
statement in many different mathematical
forms. Here are some of them:
KEi + PEi = KEf + PEf
Example
A biologist uses a spring-loaded gun to
shoot tranquilizer darts into a wild African
hamster. The spring in the gun has a
spring constant of 940 N/m. A 38 g dart is
loaded into the gun and the spring is
compressed a distance of 25 cm. With
what speed will the dart leave the gun?