Download d - Aurora City Schools

Work and Energy
Work…
…is the product of the magnitude of
displacement times the component of
force parallel to the displacement.
W = F‖ d
Units: N·m or Joules (J)
Consider a crate pulled across a surface.
Where…
 F is the applied force
 d is the displacement
 θ is the angle between the force and
the direction
F

F‖ = Fcosθ
d
Work = Fd cos 
Consider the same crate being pulled up an
incline…
Work = Fd cos 
θ = ZERO in this situation!!! The
force and the displacement are in the
same direction
F
d
Work
Net work in moving an object is
independent of the path to get there.
Same amount of work done
More force needed
Shorter distance traveled
Less force needed
Greater distance traveled
Energy – What is it?
The ability to do work
Types of Energy
Kinetic
Gravitational Potential
Elastic Potential
Heat
Light
Sound
Electrical
Chemical
Nuclear
Mechanical
Energy – energy
associated with an
object’s position or
motion
Consider a cart with an initial velocity vi and a
net force acting on it through a distance d…
vi
vf
Fnet
Fnet
d
Wnet = Fnet d
Remember F = ma = m(vf2 – vi2/2d)
So…
Wnet = m(vf2 – vi2/2d)d
Wnet = m(vf2 – vi2/2)
Wnet = ½ mvf2 – ½ mvi2
Energy - Kinetic
Kinetic Energy is the energy that an
object possesses due to its motion

If the mass of a body is m and its speed is
v then its kinetic energy is given by
KE = ½ mv2
Work-Energy Theorem
W=½
W = ΔKE
2
mvf
–½
2
mvi
The net work done on an object
(by a net force) is equal to a
change in kinetic energy of the
object
Example problem
-A 10.0 kg sled is initially moving across a
frozen pond at a speed of 4.2 m/s. How
far will it travel if the coefficient of
friction between the sled and ice is 0.10?
Energy - Potential
• Potential Energy – the energy of an
object due to its position, shape, or
condition
• An system acquires potential energy
when work is done against another
force
Energy - Potential
Gravitational Potential Energy

This is the energy of an object associated
with its position in a gravitational field
(work done against the force of gravity to
put it there)
GPE = mgh



m = mass of the object
h = height of object above some fixed
position (the position is arbitrary)
g = the acceleration due to gravity
Energy - Potential
Elastic Potential Energy




This is the energy that an object possesses
due to its position of being stretched or
deformed (work done against the elastic
restoring force)
FOR A SPRING (or similar)…
EPE= ½ k x2
x = amount of stretch
k = the spring constant (a characteristic of
the object being stretched)
The Principle of Conservation
of Energy
Energy can be transformed from
one form to another, but it cannot
be created nor destroyed, i.e. the
total energy of a system is constant
Energy transformations occur when
work is done
Conservation of Energy
Since energy is conserved for a system,
when we compare the total at two
different points…
Total E1 = Total E2
KE1 + GPE1 + EPE1 = KE2 + GPE2 + EPE2
Power
Power is the rate of doing work or the
rate at which energy is transferred.
P = W/t
Units: J/s = Watt
Alternate: P = W/t = Fd/t = Fv