Energy Energy is Conserved ∆KE = W.
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Transcript of Energy Energy is Conserved ∆KE = W.
Part 2, A: THERMODYNAMICS
WORK
156
Definition (Young): Energy is the capacityto do work.
Part 2, A: THERMODYNAMICS
WORK
1656
Definition (Young): Energy is the capacityto do work.
W = Fd
W is the work done (Joules)F is the applied force (Newtons)d is the distance moved as a
result of the applied force (meters)
Part 2, A: THERMODYNAMICS
KINETIC ENERGY
Quantity of Motion
KE = ½ m v 2
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Part 2, A: THERMODYNAMICS
KINETIC ENERGY
An object of mass 10 kg has a speed of10 m/sec. What is the kinetic energy?
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Part 2, A: THERMODYNAMICS
KINETIC ENERGY
An object of mass 10 kg has a speed of10 m/sec. What is the kinetic energy?
KE = ½ (10 kg) (10 m/sec) (10 m/sec)500 Joules
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Part 2, A: THERMODYNAMICS
KINETIC ENERGY
An object of mass 10 kg has a speed of10 m/sec. By how much will the kineticenergy increase if the speed is doubled?
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Part 2, A: THERMODYNAMICS
KINETIC ENERGY
An object of mass 10 kg has a speed of10 m/sec. By how much will the kineticenergy increase if the speed is doubled?
KE = ½ m (2v) = 2 (½ m v ) = 4 (½ m v )
The kinetic energy is 4 times greater.
2 2 2 2
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Energy
Energy is Conserved
∆KE = W
Energy
Energy is Conserved
∆KE = W
Work-Energy Theorem
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Motion – Newton’s Laws
Special Case: Friction
Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.
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Motion – Newton’s Laws
Special Case: Friction
Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.
NOTE: We already solved this problem in our discussions about Newton’s second Law.
John E. Erdei, SCI190 Lecture Slides – Newton’s Second Law, Slide 18, University of Dayton (Unpublished) .
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Motion – Newton’s Laws
Special Case: Friction
Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.
ΔKE = W = F d = µk m g d
½ m v2 = µk m g d
v2 = 2 µk g d
d = v2 / ( 2 µk g) = 0.25 m
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Motion – Newton’s Laws
Special Case: Friction
Example: A force is applied to an object, causing the object to slide on a table (with friction) at a constant velocity. The speed is 2 m/sec. If the force is removed, how far will the block slide before it stops? The coefficient of kinetic friction is 0.8 and g = 10 m/s2.
Note: This is the same result that we got using the constant acceleration equations
d = ½ a t2
Δv = a t
Energy
Potential Energy
Potential energy comes in a variety of forms.
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Motion – Newton’s Laws
gsurface = G Mearth / R2 earth
Earth
MEarth
REarth m
r
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Motion – Newton’s Laws
g = G Mearth / r2
Earth
MEarth
REarth m
r
Energy
Potential Energy
Gravitational Potential Energy of a mass m at a distance r from the Center of the
Earth
PEGRAV = mgr
= G Mearth m / r
Energy
Potential Energy
More commonly written
Gravitational Potential Energy of a mass m at a distance h from the Surface of the
Earth
PEGRAV = mg ( REarth + h)
Energy
Potential Energy
Change in Gravitational Potential Energy of a mass m at a distance h from the Surface of the Earth
h << Rearth
∆PEGRAV = mgh
Earth
h
Energy
Potential Energy
Gravitational Potential Energy
often written as
PEGRAV = mgh
Where h is measured from the surface of the earth
Part 2, A: THERMODYNAMICS
Power
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Power is defined to be the rate at whichenergy is used.
P = Energy/Time
Part 2, A: THERMODYNAMICS
Power
37
P = Energy/Time
Energy measured in JoulesTime measured in SecondsPower measured in Joules/sec = Watt
Energy
Potential Energy
Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.
Energy
Potential Energy
Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the statium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.
There is actually not enough information to determine the work from first principles. However, since the change in kinetic energy is 0, the work done by the player must be used to increase his potential energy (Conservation of Energy). The amount of potential energy (PE = mgh) is the same, independent of running or walking, and therefore the amount of work done by the player is the same if he runs or walks!
Energy
Potential Energy
Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.
If this is true, why do they make you run as punishment, ie, why not punish the player by making him walk at a leisurely pace to the top of the stadium????
Energy
Potential Energy
Football coach Jones becomes angry with a player, and in order to get the players attention, coach Jones makes the player go from playing field level up to the top row of seats in the stadium. Will the player do more work if he walks to the top row or runs to the top row? Assume the player starts from rest and stops when he reaches the top.
The punishment is related to Power, and not directly to work. Since
P = W / t
Walking will result in the work to be expended over a longer time period, therefore requiring less power. Running expends the work over a shorter time period, therefore requiring more power.
