Transcript Work & Energy

Chapter 5
Work, Energy, Power
Work
The work done by force is defined
as the product of that force times
the parallel distance over which it
acts.
W  Fs cos
The unit of work is the newtonmeter, called a joule (J)
Energy
The amount of energy transferred
to the object is equal to the work
done.
Types of Energy
• Kinetic Energy = “Motion Energy”
• Potential Energy = “Stored Energy”
Kinetic Energy
Kinetic Energy is the energy
possessed by an object
because it is in motion.
KE  mv
1
2
2
Work-Kinetic Energy Theorem
 When work is done by a net force on an
object and the only change in the object
is its speed, the work done is equal to the
change in the object’s kinetic energy

– Speed will increase if work is positive
– Speed will decrease if work is negative
Wnet  KEf  KEi  KE
Ex: Work and Kinetic Energy
 The hammer head
has a mass of 0.4 kg
and speed of 40 m/s
when it drives the
nail. If the nail is
driven 3.0 cm into the
wood and all of the
kinetic energy is
transferred to the
work one on the nail,
What is the average
force exerted on the
nail.
Example: Block w/ friction
 A block is sliding on a surface with an initial
speed of 5 m/s. If the coefficient of kinetic
friction between the block and table is 0.4, how
far does the block travel before stopping?
y
x
5 m/s
Gravitational
Potential Energy
Gravitational Potential Energy is
the energy possessed by an
object because of a gravitational
interaction.
PEg  mgh
Work and Gravitational Potential
Energy
 PE = mgy
 Wgrav ity  PEi  PEf
 Units of Potential
Energy are the
same as those of
Work and Kinetic
Energy
Potential Energy in a Spring
Elastic Potential Energy
– related to the work required to
compress a spring from its equilibrium
position to some final, arbitrary,
position x
–
1 2
PEs  kx
2
Force
Distance
Power
Power is the time rate of
doing work or how fast you
get work done.
work done by a force
AveragePower 
time taken to do this work
W Fd
P

 Fv  Force  Speed
t
t
Power
 The unit of power is a joule per
second, called a Watt (W).
ft lb
1 hp  550
 746 W
s
Power - Examples
 Watt is the work output if you
perform 100 J of work in 1 s?
 Run upstairs! If you raise
your body (70 kg or 700 N)
3 m in 3 seconds, how
powerful are you?
 Shuttle puts out a few GW
(gigawatts, or 109 W) of
power!
Conservation of Energy
Energy can neither be
created nor destroyed, but
only transformed from one
kind to another.
(KE  PE)inital  W  (KE  PE)final
Energy is Conserved
Energy is “Conserved” meaning it
can not be created nor destroyed
– Can change form
– Can be transferred
– PE into KE, KE into PE, KE into HEAT
Total Mechanical Energy does not
change with time.
– ΔPE + ΔKE = 0
– PE + KE = constant
Energy Conservation Example
 Drop 1 kg ball dropped from 10 m.
10 m
8m
P.E. = 98 J
K.E. = 0 J
– starts out with mgh = (1 kg)(9.8 m/s2)(10
m) = 98 J of gravitational potential energy
P.E. = 73.5 J
K.E. = 24.5 J – halfway down (5 m from floor), has given
up half its potential energy (49 J) to kinetic
energy
6m
P.E. = 49 J
K.E. = 49 J
• ½mv2 = 49 J  v2 = 98 m2/s2  v  10 m/s
4m
2m
P.E. = 24.5 J – at floor (0 m), all potential energy is given
K.E. = 73.5 J
up to kinetic energy
• ½mv2 = 98 J  v2 = 196 m2/s2  v = 14 m/s
0m
P.E. = 0 J
K.E. = 98 J
Roller Coasters
Since
PE + KE = Etotal ,
The shape of a
potential energy
curve is exactly
the same as the
shape of the
track!
Roller Coasters - Example
If the height of the
coaster at A is 60
m from the
ground, how fast
will you be moving
at B, C, D?
Assume no friction
and the height of
B is 10 m and C is
20 m
On to problems...
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