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Regents Physics
Work and Energy
Energy and Work
Energy is the ability to Work Work is the transfer of energy to an object
when the object moves due to an application of a force
W = Fd unit is Joules (J) Energy is also measured in Joules
When is Work Done?
Work is only done when the direction of motion is in the direction of the force
So we can rewrite the equation to:
W = Fcos dF
The F is important!
F = Fg = force due to gravity on an object In this case, you are doing work against or
with the force of gravity F = applied force = pushing or pulling
something F = force of friction doing work against
friction
The direction is important
The force must be in the direction of motion For example: A person holds a book and
walks 2 m across the room. Is work being done against the force of gravity? No!
Force on book
Your motion
Forces are at90 degrees.No work is done!
Power The Rate at Which Work is Done
Work is done when a force moves an object in the direction of the force Work = Force x distance
Power is the rate at which work is done Power = work (J) / time (s) Unit of Power is a Watt (W) = J/s P = Work / time = Fd/t = Fv
Forms of Energy
Energy has many different forms. Here we discuss the various forms of energy! Forms of Energy Stored Energy and Energy of Motion
Forms of Energy
Energy has many forms, including: Thermal Energy – heat, is the total kinetic energy
possessed by the individual particles of an object Internal Energy – is the total of the potential and
kinetic energies of an object Nuclear Energy – is the energy released by nuclear
fission or fusion Electromagnetic Energy – is the energy associated
with electric or magnetic fields
Stored Energy - Potential Energy
The energy possessed by an object due to its position or condition
If there is no energy loss due to friction, the work done to bring an object from its original position is equal to the object’s change in potential energy
We can see this in observing changes in gravitational potential energy
PE = mgh
Gravitational Potential Energy Objects gravitational potential energy as
they are lifted to a distance above the Earth’s surface
Work is done against gravity to lift the object
As long as there is no loss due to friction, the change in potential energy is due only to change in height!
PE = mgh
Work and Energy Relationship
If there is no friction, all the work done in lifting an object to a new height is equal to the object’s increase in potential energy
The change in potential energy depends only on the height, not on the path taken
For example
10 Kg
W = 98 JVs. 10 Kg
Work also = 98 J
Conservative Forces
When work done against a force is independent of the path taken, the force is said to be a conservative force
Gravitation is an example of this type of a force
Notice no friction is involved
Nonconservative Forces
Air resistance and friction are examples of nonconservative forces
The work done against a nonconservative force is dependent upon the path taken Path A requires more work than Path B
1.0m10 KgA
B
Nonconservative example
W = 98 JJust to lift it
Wf = Ffd
Ff = ukFN
FN gets larger as the angle gets smaller, so…A requires more work against friction than B
Energy of Motion - Kinetic Energy Energy associated with
motion Kinetic energy is
gained as potential energy is lost
KE = 1/2mv2
M = mass in kilogramsV = velocity in m/sKE = energy in joules
Conservation of Energy
Just like momentum, energy is also conserved Energy cannot be created or destroyed, it can only be transferred! The sum of the changes in a closed system must be equal to zero We must consider energy conservation under “perfect” and reality
like situations
KE gained = potential energy lost!
Click picture for demo!
Ideal Mechanical Systems
The sum of the kinetic and potential energies in a system is called the total mechanical energy
Ideal Mechanical System – is a closed system in which no friction or other nonconservative force acts The sum of the kinetic and potential energy changes is equal to zero Example: the pendulum
Click above for demo!
Nonideal Mechanical Systems
When a system is acted upon by a nonconservative force, such as friction, it is called a nonideal mechanical system
The friction opposes the motion of two objects in contact with each other and moving relative to each other
The frictional energy is converted into internal energy..an increase in temperature
Ideal vs. Nonideal
Ideal NonIdeal
KE = -PE
1/2mv2 = mgh
ET = PE + KE + Q
ET = mgh + 1/2mv2 + Q
Regents Physics
Springs!!
Elastic Potential Energy
Energy is stored in a spring when work is done stretching or compressing it
This energy is called elastic potential energy
Compression / Elongation
The compression or elongation of a spring is the change in spring length from it’s equilibrium position when a force is applied to it
The compression (elongation) of the spring is directly proportional to the applied force…provided the elastic limit of the spring is not exceeded
This gives us an equation!
Hooke’s Law
Fs = kx
The applied force on a spring is proportional to the distance the spring is displaced (x) and the spring constant (k)
k is the spring constant and is the constant of proportionality between the applied force and the compression/elongation of the springUnit is the Newton - meter
Springs Store Energy
Work done to compress/stretch a spring is equal to the stored potential energy..just like in gravitation!
Thus…
W = Fsx = ½ kx • x = ½ kx2
PEs = ½ kx2
Click for demo
#1
#2
#3
#4
#5
#6
End: Ask Mr. O for the HW
Use the following diagram to answer questions #5 - #7. Neglect the effect of friction and air resistance.
5. As the object moves from point A to point D across the frictionless surface, the sum of its gravitational potential and kinetic energies
a. decreases, only.
b. decreases and then increases.
c. increases and then decreases.
d. remains the same.
6. The object will have a minimum gravitational potential energy at point a. A.
b. B.
c. C.
d. D.
e. E.
7. The object's kinetic energy at point C is less than its kinetic energy at point a. A only.
b. A, D, and E.
c. B only.
d. D and E.
