PHYSICS 231 Lecture 10: Too much work

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PHYSICS 231Lecture 10 Too much work!

• Remco Zegers
• Walk-in hour Thursday 1130-1330
• Helproom

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WORK
Work Transfer of energy
Quantitatively The work W done by a constant
force on an object is the product of the force
along the direction of displacement and the
magnitude of displacement.
W(Fcos?)?x Units NmJoule
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An example
n
n
T
?45o
T
fk
?x
Fg
Fg
The work done by the person on the suitcase
W(Tcos45o)?x The work done by Fg on the
suitcase W(Fgcos270o)?x0 The work done by n on
the suitcase W(Fgcos90o)?x0 The work done by
friction on the suitcase W(fkcos180o)?x-ukn?x T
he work done by the suitcase on the person
W(Tcos225o)?x
opposite
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Non-constant force
W(Fcos?)?x what if Fcos? not constant while
covering ?x?
Example what if ? changes while dragging the
suitcase?
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Power The rate of energy transfer
Work (the amount of energy transfer) is
independent of time.
W(Fcos?)?x no time in here!
To measure how fast we transfer the energy we
define Power(P)W/?t (J/sWatt) (think about
horsepower etc). P (Fcos?)?x/?t(Fcos?)vaverage
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Example
A toy-rocket of 5.0 kg, after the initial
acceleration stage, travels 100 m in 2
seconds. What is the work done by the
engine? What is the power of the engine?
W(Fcos?)?hmrocketg ?h4905 J (Force by
engine must balance gravity!) PW/?t4905/22453
W (3.3 horsepower) or P(Fcos?)vmgv5.0 9.81
100/22453 W
h100m
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Potential Energy
Potential energy (PE) energy associated with the
position of an object within some
system. Gravitational potential energy Consider
the work done by the gravity in case of the
rocket WgravityFg cos(180o)?h-mg?h-(mghf-mghi
)mghi-mghf PEi-PEf The system is
the gravitational field of the earth.
PEmgh Since we are usually interested in
the change in gravitational potential energy, we
can choose the ground level (h0) in a convenient
way.
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Another rocket
A toy rocket (5kg) is launched from rest and
reaches a height of 100 m within 2 seconds. What
is the work done by the engine during
acceleration?
h100m
Change in potential energy PEf-PEimgh(2s)-mgh(0
)4905-04905 J Where did all the work
(29905-490525000 J)go?
Into the acceleration energy of motion (kinetic
energy)
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Kinetic energyConsider object that changes speed
only
V0
?t2s
a) WF?x(ma)?x used Newtons second law b)
vv0at so t(v-v0)/a c) xx0v0t0.5at2 so
x-x0?xv0t0.5at2 Combine b) c) d)
a?x(v2-v02)/2 Combine a) d) W½m(v2-v02) Ki
netic energy KE½mv2 When work is done on an
object and the only change is its speed The
work done is equal to the change in KE
WKEfinal-KEinitial
Rocket W½5(1002-02) 25000 J!! That was
missing!
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Conservation of mechanical energy
Mechanical energy potential energy kinetic
energy
In a closed system, mechanical energy is
conserved
MEmgh½mv2constant
V100
5 kg
What about the accelerating rocket?
At launch ME59.810½5020 At 100 m height
ME59.81100½5100229905
h100m
We did not consider a closed system! (Fuel
burning)
There is an additional condition, see slides
12,13,14
V0
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Example of closed system
A snowball is launched horizontally from the top
of a building at v12.7 m/s. The building is 35m
high. The mass is 0.2 kg. Is mechanical energy
conserved?
V012.7 m/s
At launch MEmgh½mv2 0.29.8135½0.21
2.7284.7 J
h35m
d34m
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Conservative forces
A force is conservative if the work done by the
force when Moving an object from A to B does not
depend on the path taken from A to B.
Example gravitational force
Using the stairs Wgmghf-mghimg(hf-hi) Using
the elevator Wgmghf-mghimg(hf-hi) The path
taken (longer or shorter) does not matter only
the displacement does!
h10m
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Non conservative forces
A force is non-conservative if the work done by
the force when moving an object from A to B
depends on the path taken from A to B.
Example Friction You have to perform more work
Against friction if you take the long path,
compared to the short path. The friction force
changes kinetic energy into heat.
Heat, chemical energy (e.g battery or fuel in an
engine) Are sources or sinks of internal energy.
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Conservation of mechanical energy only holds if
the system is closed AND all forces are
conservative
MEi-MEf(PEKE)i-(PEKE)f0 if all forces
are conservative Example throwing a snowball
from a building neglecting air resistance MEi-MEf
(PEKE)i-(PEKE)fWnc if some forces are
nonconservative. Wncwork done by
non-conservative forces. Example throwing a
snowball from a building taking into account air
resistance