Download Lecture 12

Work and Energy
Energy Conservation
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Clicker Question #5
Rocket Science!!! The major principle of
rocket propulsion is:
a)
b)
c)
d)
e)
Conservation
Conservation
Conservation
Conservation
Conservation
of
of
of
of
of
energy
force
velocity
momentum
volume
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New term: Work
• Work carries a special meaning in physics
– Simple form: work = force  distance
W=F·d
– Note: force and distance are vectors, but W is a scalar
• Means: (magnitude of F component along d )  (magnitude of d)
• Work can be done by you, as well as on you
– Are you the pusher or the pushed?
• Work is a measure of expended energy
– Work makes you tired
– But sometimes doing no work (physics-wise) makes you tired!
• Examples
– Push a box across the floor: work by you against friction force
– Get accelerated in your car: work on you by car's engine
– Hold a barbell over your head for 30 minutes
• Oops: no work, physics-wise ! (F yes, but d=0)
• Why are you tired? Ans: your muscles are flexing just to stay still
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Work = Energy
• Energy is "the ability to do work"
– Raised brick can do work: let it fall on nail
• How did it get raised? I did work on brick
• Where does energy go? Force on nail × distance driven
– Work = F d = energy
• So, unit of work = newton-meter = joule (J)
• Different kinds of energy
James Joule,
1818-89
– Energy due to motion: kinetic energy (KE)
• example: falling brick
– Due to position near earth: gravitational energy (GE)
• example: brick before it is dropped (compare to brick on ground)
• GE is one kind of potential energy = energy due to location
– Energy due to random motion of molecules: thermal energy (heat)
• more on heat soon...
– Energy released by breaking up molecules (chemical) or nuclei (nuclear)
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Gravitational Energy (GE)
• Gravitational (Potential) Energy near the surface of
the Earth:
Work = Force  Distance
W = mg  h
m
h
m
Lift the mass = spend energy
(do work on mass).
Drop the mass = get energy
(mass can do work for me!)
Recover work done by whoever lifted it!
GE = 'stored work'.
BUT there is no universal zero-point for the h used in the GE formula !
Lift 10kg mass 1 m above floor: W=mgh=100N·1m=100 J of GE relative to floor.
Floor might be 10 m above ground! GE =1000 J relative to ground.
Building might be on edge of Grand Canyon... etc
Only differences in vertical position matter: always must specify relative to what.
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Only vertical displacements affect GE
Ramp = tool to lift heavy weights
Exert a smaller vertical force over a larger distance to achieve the
same change in gravitational potential energy (height raised)
Total work done may be larger (if friction along ramp!)
Larger Force
Short Distance
Smaller Force
Long Distance
Fup`
Normal
component
•
•
•
mg
Push 100 kg mass up a ramp 10 m long and 1 m high
M N (220 lb) of force to lift directly: task for strong person!
mg = 980
Work done = (980 N)(1 m) = 980 N·m (J) for direct lift
Extend over 10 m, and only 98 N (22 lb) is needed: anyone can do it
– Work done is still 980 J - neglecting frictional forces/losses along ramp
parallel
component
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Work is Exchange of Energy
• Energy is the capacity to do work
• Two main categories of energy
– Kinetic Energy: Energy of motion
• A moving baseball can do work
• A falling anvil can do work
• Thermal energy = KE of molecules
– Potential Energy: Stored (latent) capacity to do work
• Gravitational potential energy (perched on cliff)
• Mechanical potential energy (as in a compressed spring)
• Chemical potential energy (stored in molecular bonds)
• Nuclear potential energy (in bonds between nucleons)
• Energy can be converted between types
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Everyday Energy Conversion
• Falling object converts gravitational potential energy into kinetic
energy
• Friction converts kinetic energy into thermal energy
– makes things hot (rub your hands together)
– irretrievable energy: dispersed among molecules!
• Truck's motor converts chemical energy (gasoline) into KE
• Toaster converts electrical energy (KE of electrons in wires) into
thermal energy
• Generator converts mechanical energy into electrical energy
– Doing work on something increases that object’s energy by
amount of work done, transferring energy from the agent
doing the work
– Work done by something decreases object's energy by
transferring energy from that object
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Energy is "Conserved" !
•
The total energy (in all forms) in an “closed” system remains constant
– the whole Universe is a "system" too
– Energy cannot be created or destroyed, but can go from one form to another
•
This is one of Nature’s “conservation laws”
– Conservation laws apply to:
• Energy (includes mass via E = mc 2)
• Momentum
• Angular Momentum
and, as we'll see:
• Electric Charge
• Properties relating to nuclear forces (with no macro-world examples)
•
Conservation laws are fundamental in physics, and stem from symmetries
of nature
– Conservation of energy relates to time-reversal symmetry
– Conservation of momentum relates to spatial (or rotational) symmetries
– Other physical quantities are also conserved at subatomic level:
• always related to some symmetry property of forces involved
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Energy Conservation Demonstrated
•
•
•
•
Roller coaster car lifted to initial height (put energy in)
Converts gravitational potential energy to motion
Fastest at bottom of track
Re-converts kinetic energy back into potential as it
climbs the next hill "under its own momentum"
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Quantifying Kinetic Energy: KE = ½mv
2
• The kinetic energy for a mass in motion is
KE = ½ mv
2
notice: depends on (speed)2
• Example: 1 kg object moving at 10 m/s
(1/2)(1kg  10m/s)2 = 50 (kg-m/s2)m = 50 N-m = 50 J of kinetic energy
• Ball dropped from rest at a height h (GE = mgh) hits the ground
with speed v : compare its original GE with its final KE
–
–
–
–
x=h
t=0
KE=0
GE=mgh
x=0
t=2gh
KE=½mv 2
GE=0
We expect conservation of E so should have ½mv 2 = mgh
h = (½)gt 2 (distance travelled in free fall from rest: x = (½)at 2)
v = gt  (v) 2 = (gt) 2 = g 2t 2 (v after free-falling for time = t)
GE = mgh = mg (½gt 2) = (½)mg 2t 2 = ½mv 2 = KE - check!
• Ball has converted its gravitational potential energy into kinetic
energy: the energy of motion
• This gives us a simpler way to find v of falling object: energy
GEinitial =mgh =KEfinal = ½ mv 2
Notice m cancels out: doesn't matter, v2 = 2gh for any mass
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