WORK, ENERGY, POWER, AND MOMENTUM

A. WORK
Work is defined as the product of force applied to an object and the distance through which the force is applied. Another way of saying this is work is the amount of force applied to an object times the distance the object moves in the direction of the force.
Equation:
W = F•d
Where W = work (joule)
F = force (Newton)
D = distance (meter)
Two conditions must be met in order to work to be done are:
1. Force must be applied
2. The force must make an object move in the direction as the force. If the direction of movement is not the same as the direction of the applied force, no work is done.
1. Work done by constant force
The work done by a constant force in moving an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to the displacement.


2. Work done by variable force
An example of variable force doing work is in stretching a spring. As a spring is stretched (or compressed) farther and father, the restoring force of the spring gets greater and increasing applied force is required. It is found that the applied force F is directly proportional to the displacement or the change in length of the spring. In equation form, this is expressed:
F = kx
B. ENERGY
Energy is the ability to do work. And work involves a change in movement. Energy in its various forms is necessary for all sorts of change. So another way of defining energy is the ability to cause change. One unit in which energy is measured is the joule (J)
Forms of Energy
• Mechanical: energy relating to moving objects
• Heat: energy related to the vibration of the particles that make up an object
• Chemical: energy related to the bonds that hold particles together
• Electromagnetic: energy related to moving electrical charges
• Nuclear: energy related to the decay of the nucleus of atoms
Energy can be classified into:
a. Kinetic Energy
Kinetic energy is the energy of a moving object. An object that moves has kinetic energy. Light and heat from the sun are examples of kinetic energy.


KE = ½mv2
Where KE = kinetic energy
m = mass
v = speed.
• The more mass an object has, the more kinetic energy it has
• The faster an object is going, the more kinetic energy it has
• The more potential energy an object starts with, the more kinetic energy it can release
b. Potential Energy
Potential energy (PE) is the energy of position.
PE = mgh
Where m = mass (gram)
g = gravitation force (m/s2)
h = height (meter)
• The energy stored in an object because of its position
• The work done to move an object to a new position is stored in the object as potential energy
• Potential energy stored in an object that will move because of gravity is called gravitational potential energy
Gravitational Potential Energy
This is energy, which is stored in the gravitational field of the Earth. If work is done in separating an object from a zero point (lifting it up) the energy stored in the gravitational field is equal to the work done in lifting the object.
Equation:
PEgrav = mgh (measured in Joules).
Elastic Potential Energy
This is energy, which is stored by distorting the shape of an elastic object such as a spring or a bow. The distorted state of the object is that aspect of the object, which contains the energy. The work done in distorting the object is equal to the energy stored in it. Equations:
PEelastic = ½ks2 (measured in Joules)
where k is the elastic constant of the object and s is the amount of distortion or stretch.
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed, although it can be changed from one form to another.
Matter can be considered as a form of energy; matter can be transformed into energy and energy into matter according to the law of conservation of energy.
E = mc2
where E = rest energy,
m = rest mass
c = speed of light (3x108m/s)
C. POWER
Power is the rate at which work is being done, or the amount of work done per unit time. Power is equal to the work done divided by the time it takes to do it.
P = W/t
SI unit of power is the watt.
1 watt (W) = 1 joule/second (J/s)
Power tells us how fast work is being done or how fast energy is transferred.

D. MOMENTUM
Momentum is the product of the mass and velocity of an object
p = mv

a. Linear Momentum
Linear Momentum is a measure of the tendency of a moving object to continue in motion along a straight line.
p = mv
The law of conservation of momentum states: In the absence of outside forces, the total momentum of a set of objects remains the same no matter how the objects interact with one another.
b. Angular Momentum
Angular momentum is a measure of the tendency of a rotating object to continue spinning about a fixed axis
Defining angular momentum is complicated, depends on:
• How fast the object is turning
• Mass of the object
• How the mass is distributed (the further the mass is from the center of the object, the greater the angular momentum)


Collisions
1. Elastic collisions
a. Head-on collision (1 dimensional)
In the case of two objects colliding head on we find that the final velocity





Special case: m1>>m2

b. Multi-dimensional collisions
In the case of objects colliding in more than one dimension, as in oblique collisions, the velocity is resolved into orthogonal components with one component perpendicular to the plane of collision and the other component or components in the plane of collision.

2. Inelastic collisions
A common example of a perfectly inelastic collision is when two snowballs collide and then stick together afterwards. This equation describes the conservation of momentum:







References

Hurd, Dean. 1993. Physical Science. New Jersey: Prentice Hall
Shipman and Wilson. 1990. An Introduction To Physical Science 6th Edition. Toronto: DC. Health and Company
Wilson, Jerry D. 1994. College Physics. USA: Prentice Hall
http://homepage.mac.com/dtrapp/ePhysics.f/WWorkPowerEnergy.html
http://www.mathsrevision.net/alevel/pages.php?page=93
http://physics.ucsd.edu/students/courses/winter2005/physics1a/documents/4.3NewtonsThirdLaw.pdf
http://www.physicsforums.com/showthread.php?t=8895
http://en.wikipedia.org/wiki/Momentum