gravitational potential energy

kinetic energy

electromagnetic energy

Electrical energy

Electric potential energy

chemical potential energy

sound energy

elastic potential energy

thermal energy

nuclear potential energy





Closed system is an isolated system from the outside systems.  It does neither gains nor losses energy to the other systems.


In an Open system, system either gains or losses energy to an outside system.


Total amount of energy in a closed system stays constant.  The law of conservation of energy states that energy cannot be created or destroyed in a closed system..  It can only be changed from one form to another.


If all other forms of energy do not change, the total mechanical energy (gravitational potential energy + kinetic energy) will be constant in a closed system.





General Equation of gravitational potential energy is given below.  The following formulas are valid anywhere in the universe.


EG: Gravitational potential energy of the body with respect to central body (J)
G:  universal gravitation constant (G = 6.67 x 10-11 N.m2/kg2)
m:  Mass of a body influenced by the gravitational field of the central body (kg)
MMass of the central body (kg)
rDistance between the centres of the two bodies (m)

g:  Gravitational field strength (g = 9.80 N/kg)


Gravitational potential energy is the energy possessed by an object due to its elevation above Earth's surface.  If the change in the vertical displacement is not much, the following formula can be used since gravitational field intensity does not vary much over the small vertical displacement.  Gravitational potential energy is always stated relative to a reference level, and is a scalar quantity.


The strength of a gravitational field varies with the location.  Near the surface of the Earth, it is around:

g = 9.80 N/kg



ΔEG:  Gravitational potential energy (J) (positive for upward, negative for downward displacement)

m:  Mass of the object (kg)

g:  Gravitational field intensity (N/kg)

Δh:  Magnitude of the vertical displacement (m) (positive for upward, negative for downward displacement)




Kinetic Energy:  Energy of motion.  It is a scalar quantity 



Ek:  Kinetic energy (J)

m:  Mass of the object (kg)

v:  Speed of the object (m/s)





Total mechanical energy is the sum of the gravitational potential energy and the kinetic energy.

Total mechanical energy =  Gravitational potential energy + Kinetic energy


Conservation of mechanical energy:

If all the other forms of energy does not change in a closed system, total mechanical energy will be constant in this system.





Hooke's law states that the deformation of an elastic object is proportional to the force applied to deform it.  If a force is applied to an object, it will stretch. An object also can be compressed if the compression force is applied.  If the force is removed, the object will return to the original shape.  If the force applied is too great, the object can be permanently deformed.  In this case, the elasticity is destroyed and object becomes inelastic.


Not all the springs obey Hooke's law.  An ideal spring obeys Hooke's law.  It means that the magnitude of the force applied to the spring is directly proportional to the distance the spring has moved form the equilibrium.



F = k.x


k:  Spring constant of the elastic object (proportionality constant, force constant) (N/m)

x:  Amount of deformation (m).  It is positive for the stretch, negative for the compression
Fapp:  Force applied to spring to stretch or compress an elastic object (N)
Fspring:  Force applied by the spring to stretch or compress an elastic object (N)

The force will be positive if the force and the displacement are in the same directions.  The force will be negative if the force and the displacement are in the opposite directions.


Force applied to spring and the force applied by the spring are always in the opposite directions:  Fspring = - Fapp


Elastic Potential Energy:


The energy stored in objects that are stretched, compressed, bent, or twisted is called elastic potential energy.  Elastic potential energy equals to the work done to deform the spring or energy stored in the spring.  It is the area under the F -versus x graph.  Since the area is a triangular in shape, the following formula has been created.


                     Ee:  Elastic potential energy stored in the elastic object (J)

For the horizontal surface:


Simple Harmonic Motion


Simple harmonic motion (SHM) is defined as a periodic vibratory motion in which the force and acceleration directly proportional to the displacement.



k:  Spring constant of the elastic object (N/m) (proportionality constant, force constant)
x:  Amount of deformation (m)
m:  Mass of the object (kg)
v:  Speed of the object (m/s)
ET:  Energy in simple harmonic motion (J)

Acceleration in simple harmonic motion:

a:  Acceleration (m/s2)
is constant, therefore acceleration depends on the displacement from the equilibrium position.


Since the speed is increasing when the spring is moving into equilibrium point, acceleration is positive.  But the speed is decreasing when the spring is moving away equilibrium point, then acceleration will be negative.



In a horizontal frictionless surface, the total energy of the system is the sum of the elastic potential energy in the spring and the kinetic energy of the mass:


A:  Amplitude




A simple pendulum also undergoes simple harmonic motion (SHM).



T:  Period of the pendulums (s)
g:  Gravitational acceleration (m/s2)

L:  Length of the pendulum (m)

Rest mass energy:

Rest mass energy is the total energy that an object had because of its mass


E = mc2

E:  Rest mass energy (J)

m: Mass (kg)

c: Speed of light (3x108 m/s)


[Mass defect: m (kg)] = [Total mass of reactants (kg)] – [total mass of product of nuclear fusion reaction (kg)]


Mass defect is converted to energy according to the Einstein’s Theory of relativity (E = mc2)


1 kJ (kilojoule) = 103 J

1 MJ (megajoule) = 106 J

1 GJ (gigajoule) = 109 J






Work is the energy transferred to an object.  When a force is applied to the abject if the object moves, work will be created.  Work, like energy, is a scalar quantity, and does not have direction.


Work Created by a Constant Force:


W = F cos q Dd


F:  Force (N)

q: Angle between the force and displacement

Dd: Displacement (m)

W: Work (Joules, J)

1 Joule (1 J) = 1 N.m


Work Created by a Varying Force:


Total work done by a varying force is equal to the area under the force-displacement curve.


W = Σ Fx Dx


Work Done by Kinetic Energy (Work-energy theorem):

Total work equals the change in the object's kinetic energy, provided that there is no change in any other form of energy (for example gravitational potential energy).  The theorem is valid even for a force is not constant.


Work = Final kinetic energy - Initial kinetic energy


According to the work-energy theorem if an external force acts upon an object, causing its kinetic energy to change from Ek1 to Ek2, then the mechanical work (W) is given by:

W = \Delta E_k = E_{k2} - E_{k1} = \frac{1}{2}m \Delta (v^2) \,\!

m:  the mass of the object

v:  the object's speed.


Negative Work (Created by all Non-conservative Forces, Frictions)


Negative work will be created if the force and displacement in the opposite directions.  If you try to stop a moving object or decrease the speed of the object, you will take energy from the system.  You will create a negative work.  Friction also creates a negative work.  Work created by friction is converted into thermal and sound energy.


Work created by all non-conservative forces, such as frictions, equals the change in total mechanical energy.


Work = Final mechanical energy - Initial mechanical energy


Work created by constant kinetic friction force over a horizontal surface is as follows:


W = - FK . Δd


W:  Work created by kinetic friction (J)


FK:  Magnitude of the kinetic friction force (N)


Δd:  Displacement (m)


Positive Work:


Positive work will be created if the force and displacement in the same directions.


Zero Work:


 If you push a box and box does not move and displacement is zero, there will be no work.


If the force applied and the displacement are perpendicular each other, there will be no work.  Component of the force over the distance will be zero.


If a spaceship travels in the space with a negligible net force, there will be no work.  Net force is zero.






AMA: Actual mechanical advantage in the inclined plane (ratio)



Load force:  FG: Force required lifting the load vertically (N)

Applied force: FA:  Force required moving the object up the inclined plane (N)





t = F ℓ

t:  Magnitude of the torque (N.m) (since torque is not work, J is not used as an unit)

F:  Force applied (N)

ℓ:  The length of the lever arm (m)





Power is the energy or work per unit of time.





W:  Work (J)

E:  Energy (J)

Δt:  Elapsed time (s)

P:  Power (W or J/s)


watt:  1 W = 1 J/s = 1 N.m / s


1 Horse power = 746 W


P = F. Vav


P:  Power (W)

F:  Force (N)

Vav:  Average speed (m/s)