Download Kinetic Energy -Work-Kinetic Energy Theorem

-Kinetic Energy
-Work-Kinetic Energy
Theorem
-Energy Losses due to
Friction
-Power
AP Physics C
Mrs. Coyle
Energy and Work
• Energy is the ability to do work.
• Work is the energy transferred to
or from a system by a force that
acts on it.
Video Link: Kinetic Sculpture
• http://www.youtube.com/watch?v=
WcR7U2tuNoY&feature=related
Energy
• Symbol: E
• Scalar
• Units:
– J, Joule
– cal, calorie
– kcal, kilocalorie (Cal)
– erg
– eV
– pound -foot
Mechanical Energy
• Potential Energy
• Kinetic Energy
Kinetic Energy, K= 1 mv2
2
Energy of Motion
Question
• Can Kinetic Energy be Negative?
Derivation
of K
W 
xf
xi
 F dx  
xf
xi
vf
W   mv dv
vi
1 2 1 2
W  2mv f  2 mvi
ma dx
Work-Energy Theorem
W=KE
W=KEf-KEi
“In the case in which work is done on a
system and the only change in the
system is in its speed, the work done
by the net force equals the change in
kinetic energy of the system.”
• The Work-Kinetic Energy Theorem
can be applied to nonisolated
systems
• A nonisolated system is one that is
influenced by its environment
(external forces act on the system)
Potential Energy, U:
stored energy
• Examples:
– elastic potential energy –
stored in a spring
– gravitational potential energy
– electrical potential energy
• Compared to a Reference Point
(base level)
Conservation of Energy
• Energy can neither be created nor
destroyed. It can only change from
form to form.
• In a closed system energy is
conserved
• Conservation of Mechanical Energy
U1+ K1 = U2 + K2
Energy can be transferred
to and from the System by:
Work
Mechanical Waves
Heat transfer
Matter Transfer (across the
boundary of the system carrying
energy with it)
• Electrical Current Transmission
• Electromagnetic Radiation
•
•
•
•
Change in Energy of the
system equals total energy
transferred
• Esystem = ST
– T is the energy transferred across
the system boundary
– Twork = W
Theat = Q
• The Work-Kinetic Energy theorem is
a special case of Conservation of
Energy
What happens when kinetic
friction is present?
When friction is present, the work done
by the frictional force
W=f·r
is transferred to heat energy.
Internal Energy
• The energy associated with an
object’s temperature is called
its internal energy, Eint
Power
• Energy transfer per unit time
• Average power :
W
P
t
Instantaneous Power
dW
dr
P
 F   F v
dt
dt
dE
P
dt
Units of Power
• SI unit of power: Watt
1 watt = 1 J/s = 1 kg . m2 / s2
• US Customary unit: horsepower
– 1 hp = 746 W
kilo Watt · hour,
kWh
• kWh is a units of work or energy
• 1 kWh =(1000 W)(3600 s)=
=3.6 x106 J
Example 1 (#26)
A 3kg object has a velocity (6i-2j)m/s.
a) What is the kinetic energy at this
time?
b) Find the total work done on the
object if its velocity changes to
(8i+4j) m/s .(Note: v2 = v·v)
Ans: a)60J, b)60J
Pile Driver
Example 2 (#27)
• A 2,100kg pile driver is used to drive
a steel I-beam into the ground. The
pile driver falls 5m before coming
into contact with the top of the beam
and it drives the beam 12cm farther
into the ground before coming to
rest. Using energy considerations,
calculate the average force the beam
exerts on the pile driver while the
pile driver is brought to rest.
Ans: 8.78 x 105 upwards
Figure for Example 3
Example 3 (#32)
A 2kg block is attached to a spring of a
force constant 500N/m on a
horizontal table. The block is pulled
5.00cm to the right of equilibrium
and released from rest. Find the
speed of the block as it passes
through equilibrium if a)the
horizontal surface is frictionless and
b) the coefficient of friction between
block and surface is 0.350.
Ans:a)0.791m/s, b) 0.531m/s
Example 4 (#40)
A 650kg elevator starts from rest. It
moves upward for 3s with a constant
acceleration until it reaches its
cruising speed of 1.75 m/s.
a)What is the average power of the
elevator motor during this period?
b)How does this power compare with
the motor power when the elevator
moves at its cruising speed?
Ans: a)5.91x103 W= 7.92hp
b) 1.11x104 W= 14.9hp