Download KINETIC AND POTENTIAL ENERGY

FIRST- LET’S DEFINE OUR TERMS
Energy- The Ability to Cause Change
Change is any kind of change, whether in shape, speed, heat, pressure, or light
Kinetic Energy- The energy an object gains when it is in motion
An object in motion has more energy (can cause more change) then an object at
rest.
Potential Energy- Stored energy
An object at a high point, under strain (like a stretched spring), or able to react
chemically has potential energy.
CONSERVATION OF ENERGY
The total energy of the universe is constant. Energy cannot be created or destroyed, it
can only be TRANSFORMED.
This means that the total energy (the kinetic energy plus the potential energy) in a
system is constant.
POTENTIAL ENERGY FROM GRAVITY
The potential energy an object gains from being lifted against the force of gravity is
called GRAVITATIONAL POTENTIAL ENERGY. More height equals more energy.
For any object it can be calculated by multiplying the height off the ground (in meters)
by the mass (in kilograms) and the acceleration due to gravity (Remember: F=ma)
𝑷𝑬 = 𝒎 × 𝒉 × 𝟗. 𝟖 𝐦 𝐬 𝟐
OTHER TYPES OF POTENTIAL ENERGY
Food has chemical potential energy that your
body uses to do things like move, think, and
stay warm
Gasoline has chemical potential energy that
engines turn into heat energy in order to do
work
A spring, a catapult, or a stretched rubber band
have mechanical potential energy, energy
stored in an object because it is under
stress.
KINETIC ENERGY
As we’ve seen in our lab activity, the kinetic energy of an object depends on its mass
and it’s velocity. It can be calculated using the equation 𝑲𝑬
𝟏
𝟐
= × 𝒎 × 𝒗𝟐
The equation shows that as the mass increases, the kinetic energy increases by the
same amount. Try adding numbers to see why.
𝟏
𝟐
𝟏
𝟐
𝑴𝒂𝒔𝒔 𝒐𝒇 𝒇𝒊𝒗𝒆 𝒌𝒊𝒍𝒐𝒈𝒓𝒂𝒎𝒔
𝟏
𝟐
𝟏
𝟐
𝑴𝒂𝒔𝒔 𝒐𝒇 𝒕𝒆𝒏 𝒌𝒊𝒍𝒐𝒈𝒓𝒂𝒎𝒔
𝑲𝑬 = 𝒎𝒗𝟐 = × 𝟓 × 𝟐𝟐 = 𝟏𝟎𝑱
𝑲𝑬 = 𝒎𝒗𝟐 = × 𝟏𝟎 × 𝟐𝟐 = 𝟐𝟎𝑱
SO- Doubling the mass doubles the kinetic energy if the velocity is the same.
KINETIC ENERGY AND VELOCITY
𝟏
From the equation 𝑲𝑬 = 𝒎𝒗𝟐 , we showed that
𝟐
doubling the mass doubles the kinetic energy. Any
change in mass causes an identical change in
kinetic energy.
Velocity is different. A change in velocity causes a
much greater change in kinetic energy. This is
because the velocity is squared to find the kinetic
energy. If you double the velocity, you quadruple
the kinetic energy.
PUTTING THE EQUATIONS TOGETHER
The total energy of the ball is CONSTANT. So while at the
top of the hill it only has potential energy, at the
bottom it only has kinetic energy. AND THE TWO ARE
EQUAL.
Total Energy = PE + KE
𝒎 × 𝒉 × 𝟗. 𝟖 𝐦 𝐬𝟐 =
𝟏
𝒎 × 𝒗𝟐
𝟐
PE at the top = KE at the bottom
This means that if we know how high the hill is, we can
find out how much kinetic energy it will have at the
bottom.
FINDING VELOCITY FROM KINETIC ENERGY
With the kinetic energy of an object we can also determine its velocity.
𝟏
𝑲𝑬 = 𝒎 × 𝒗𝟐
𝟐
Divide both sides of the equation by the mass
𝑲𝑬 𝟏 𝟐
= 𝒗
𝒎
𝟐
Multiply both sides of the equation by two
𝟐 × 𝑲𝑬
= 𝒗𝟐
𝒎
Then take the square root of both sides to go from the square of the velocity to the
velocity alone.
𝟐 × 𝑲𝑬
=𝒗
𝒎
HERE’S ALL FOUR EQUATIONS
Gravitational Potential Energy:
𝑷𝑬 = 𝒎 × 𝒉 × 𝟗. 𝟖
Kinetic Energy:
𝑲𝑬 = × 𝒎 × 𝒗𝟐
Velocity from Kinetic Energy:
𝒗=
Mass from Kinetic Energy:
𝒎=
𝟏
𝟐
𝟐×𝑲𝑬
𝒎
𝟐×𝑲𝑬
𝒗𝟐
SUMMARY
-The total energy in a system does not change
-The potential energy of an object is the stored energy
-Gravitational potential energy is dependent on height and mass and is directly
proportional to both.
-Kinetic Energy is the energy an object gains from moving
-Kinetic energy is dependent on mass and velocity. It is directly proportional to mass
and directly proportional to the square of the velocity (the velocity multiplied by
itself).
-If you know the gravitational or mechanical potential energy of an object, you also
know its maximum possible kinetic energy.