Download Work, Power, and Energy

Work, Power, and
Energy
Momentum Review
Momentum = mass x velocity
=mv
If the boulder and the boy
have the same momentum,
will the boulder crush the
boy?
Hint: Which would have
the
larger speed?
Review Videos
Momentum and Projectile Motion in action:
Jumping a Football Field
Conservation of Momentum - Recoil:
Dorm Chair Hit
Work
 Work
is the amount of force applied for a
certain distance
W=F*d
The unit for Work can be found from force (N) and
distance (m) or N*m
But a N*m is also equivalent to a Joule (J)
So the unit we use for Work is the Joule
(J)
 When
calculating work, we only use forces
and distances that are in the same
direction or orientation.
BAD
GOOD
Force
Force
Displacement
Displacement
Work = Force x Distance
F = 500 pounds (2000 N)
D = 8 feet (2.5 meters)
----------------------------------W = 2000 N x 2.5 m
= 5000 N-m
----------------------------------Alternative unit: Joule
1 N-m = 1 joule (J)
Work =
Force x Distance
If the wall doesn't
move,
the prisoner does no
work.
Try this problem
 What
is the work done by pushing a
dumpster with 60N of force a distance of
3m?
Try this Problem
 What
is the work done by accelerating a
50kg block at 2m/s2 a distance of 6
meters?
Power
 Power
is the amount of work done over a
specific period of time
P=W/t
The unit for power is the J/s or Watt (W)
Power = Work/ Time
1 joule / second = 1
watt
Try this Problem
 What
is the power generated by moving a
bucket of water 7m with an applied force
of 4N for a total amount of time of 4s?
 Power
can also be calculated using
• P = F*v
• You can see that this equation is
equal to (F*d)/t with the following
proof
P = F * v = (F * d) / t
F * d/t = F * d/t
Graphing Work
 To
find the amount of work done
graphically you need to draw a Force vs.
Distance graph
 Once you plot your points, find the line of
best fit
 To determine the amount of work done for
a particular range, take the area under the
curve

The area under the curve of a Force vs.
Distance graph is = to the amount of WORK
done
The graph below shows the force applied to
move a block 6m. Find
 the work done for the first 3m.
 the work done moving the block 6m.
Energy

Work can be found by not just F*d but also by
finding the change in energy in the system.
W  E
W  KE
1
W   ( mv 2 )
2
1
W 
m( v ) 2
2
1
1
2
W 
mv f  mvi2
2
2
Types of Energy
Energy – energy involved with
moving objects
 Kinetic
• KE = ½ mv2
• Units are in Joules (J)
Potential Energy – stored
energy involved with the height of the
object
 Gravitational
• PEg = mgh
• The height to which the object has risen is
determined by using a reference level


The position where PE is defined to be zero
Units are in Joules (J)
Potential Energy – stored energy of
a spring
 Spring

This is the amount of energy that compressed
or stretched springs carry


• PEsp = ½ kx2
Where ‘k’ is the spring constant in units of N/m
• Spring constants vary and depend entirely
upon the construction of the spring
and ‘x’ is the distance that the spring is
stretched or compressed from it’s equilibrium
position
• Units are in Joules (J)
Gravitational Potential Energy
Energy store by lifting.
Energy = Work = F x d
PEg = mgh
m = mass
g = acceleration of Gravity
h = height
What P.E. is gained when a 100 kg object is
raised 4m straight up?
ΔP.E. = mgΔh
= (100 kg)(9.8 m/s2)4 m
= 3920 J
Calculate the work
An object weighing 15 N is lifted from the ground
to a height of 0.22 m. Find object's change in PE
ΔP.E.= mgΔh
mg = 15 N
ΔP.E. = 15 N(.22m)
ΔP.E. = 3.3 Nm = 3.3 J
h = .22 m
Conservation of Energy
 The
Law of Conservation of Energy states
that in a closed, isolated system, energy
can neither be created nor destroyed
• Energy is conserved

The sum of kinetic energy and gravitational
potential energy of a system is called
mechanical energy.
 Total


Energy:
E = KE + PEg + PEsp
Where there is no spring in the system, the
mechanical energy of that sytem is:
E = KE + PEg
 This
means that since the energy in a
system never changes,
• If you increase KE  you decrease PE
• If you increase PE  you decrease KE
Important Note

Any extra energy that may be lost is transferred
to heat energy (Q) by any friction in the system

The reference tables include this when it is
written:

E = KE + PE + Q
• Ignore the  on the reference table for this equation
because internally, the total energy will never change
Gravity supplies the energy to move objects
like a roller coaster
Watch what happens to the KE and PE over
time….
 Skiing
is another example of conservation
of energy



If you ski down a steep slope and start at the
top, your total mechanical energy starts as
gravitational potential energy
As you start skiing downhill, that potential
energy is converted to kinetic energy
As you ski down the slope, your speed
increases as more of your potential energy is
converted to kinetic energy
Pendulums


The simple oscillation of a pendulum also
demonstrates conservation of momentum
At the highest point where the pendulum is
initially released, all the energy is in the form of
potential energy
 But as the pendulum bob is swinging, its energy
is in the form of kinetic energy
 This is the energy that gives the pendulum
bob its velocity
 At the lowest point on the pendulum’s swing, the
PE = 0 and the KE is maximized
Three types of Energy
Gravitational potential changes to kinetic
and then work.
Conservation of Energy
 Conservation
of Mechanical Energy
KEbefore + PEbefore = KEafter + PEafter
Conservation of Energy
 Pendulums

Brainiac
 Pendulums

and Conservation of Energy
and Conservation of Energy
Science World
Try this Problem
 A bike
rider approaches a hill at a speed of
8.5m/s. The combined mass of the bike
and rider is 85.0kg. Find the initial kinetic
energy of the system.
 The
rider coasts up the hill. Assuming
there is no friction, at what height will the
bike come to rest?
Collisions
 Previously
we has a conservation of
momentum in collision situations
pbefore = pafter
 Now,
we also have a conservation of
energy within collisions
KEbefore = KEafter
Collisions and KE
KEAi + KEBi = KEAf + KEBf
½ mv2Ai + ½ mv2Bi = ½ mv2Af + ½ mv2Bf
Spring Potential Energy

As previously mentioned, the spring potential
energy can be found by the equation:
PEsp = ½ kx2

According to Hooke’s Law: The force exerted
by a spring is equal to the spring constant times
the distance the spring is compressed or
stretched from its equilibrium position
F = -kx
Spring Constant and Energy in a Spring

A spring stretches by 18cm when a bag of potatoes
weighing 56N is suspended from its end. What is the PE
stored in the spring?
F = 56N
x = 18cm = 0.18m k = ?
F = -kx
K=F/x
K = 56N / 0.18m
K = 310 N/m
PEsp = ½ kx2
PEsp = ½ (310N/m)(0.18m)2
PEsp = 5.0 J