Energy is the measure of an object’s ability to do work (exert a force over a distance) on another system or object. Energy can never be created or destroyed; it can only be transformed into a different type of energy. When somebody says energy has been lost, the person really means that the energy was turned into some form that is unusable. The conservation of energy is one of the fundamental laws of our universe.
Potential Energy: The potential energy of an object/system is the energy that is stored and ready to be used in the object/ system. SI units: J
System: Any object or group of objects that we are studying. A system where energy is conserved is called a closed system.
Kinetic Energy: A measurement of the energy associated with an object in motion. Kinetic energy can also refer to energy associated with the vibration or motion of atoms or molecules. SI units: J
Work: If a force is exerted over a distance to move an object, the force is said to be doing work. SI unit: J
Conservative Forces: A force in which the work done to move a particle between two points is not affected by the path taken.
Non-Conservative Forces: A force in which the work done to move a particle between two points is affected by the path taken.
Power: The rate at which work is done by a system or object. SI units: J/s or W
There are many different types of potential energy that are differentiated by the way that the energy is stored.
All moving objects have kinetic energy. \(KE = \frac{1}{2}mv^2\)
Energy diagrams allow us to visualize how energy is being transferred.
Below is a diagram for a swinging pendulum that shows how energy changes forms from gravitational potential energy to kinetic energy.
In the work-energy theorem, the work done on an object is always equal to the change in kinetic energy of the object.
For example, gravity is a conservative force. When an object’s gravitational potential energy changes, only the object’s displacement determines the work done. The diagram on the right shows how the change in energy is the same whether the red ball takes the green path or the blue path. Gravity does work mgh along either paths.
Image Credit: CompuChip, Public Domain
\(E_i = E_f\)
\(E_i\) - initial energy
\(E_f\) - final energy
\(U_g = mgh\)
\(U_g\) - gravitational potential energy
m - mass
g - acceleration due to gravity
h - height
\(KE = \frac{1}{2}mv^2\)
KE - kinetic energy
v - velocity
\(W = Fd = \Delta KE\)
W - work
F - force
d - distance
\(p = \frac{\Delta W}{\Delta t}\)
P - power
t - time
The law of conservation of energy tells us that energy is not created or destroyed. Instead, energy is transformed from one form to another. We can use the conservation of energy to help us solve many types of physics problems.
Tip: When solving problems with gravitational potential energy, pick a reference point that will make calculations easier. The reference point does not have to be the ground.
An object of mass m begins at rest and starts falling through the air. After falling a distance h, how fast is the object going? Air resistance is negligible.
It is possible to solve this using the equations for linear motion, but it is easier to solve by using the conservation of energy. We can set the point where the potential energy PE = 0 at distance h below where the ball started.
\(PE_i + KE_i\)
=
\(PE_f + KE_f\)
begin with an equation showing energy is conserved
\(PE_i + 0\)
=
\(0 + KE_f\)
substitute 0 for the initial kinetic energy and the final potential energy
\(mgh\)
=
\(\frac{1}{2}mv^2\)
substitute in the known values
\(v\)
=
\(\sqrt{2gh}\)
solve for v