energy work and linear momentum
TRANSCRIPT
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Energy Work and
Linear Momentum
Chamila Sumathiratna-FIVT
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Energy and Work Energy is the
ability to dowork
Work is beingdone wheneversome physicalforce is being
used to movean object somedistance
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Forms of EnergyO Forms of Mechanical Energy
O Potential energy
O Kinetic energy
O Strain energy/elastic potential energy
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Calculating Kinetic EnergyO Calculating kinetic energy.
If we know the mass of an object and its
velocity we can determine the amount of kineticenergy possessed by using the following
formula:
O kinetic energy = 1/2 (mass of
object)(velocity of object) 2
O or KE = 1/2 mV 2
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Potential EnergyO The amount of
energy contained in
an object at rest dueto its height.
O Potential Energy =
(mass)(gravity)(heigh
t)
O PE= mgh
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Elastic Potential Energy
O Force exerted ona spring
F=kx
O Where k is springconstant
O Work done orenergy stored inthe spring is the
area under thecurve in graph
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Conservation of EnergyO When a closed
system is considered
energy cannot becreated or destroyed
O Can only be
transferred from one
form to the other.
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Application
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Work Done
O Definition of work
When an object undergoes a displacement with
magnitude along a straight line, while a constantforce with magnitude F, making an angle with s
acts on the object, the work done by the force on the
object is (F cos ) s
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ApplicationO A person pushes a car 19 m.
If he pushes with a constantforce with magnitude 210 N,
how much work does he doon the car
O (a) if he pushes in thedirection the car is heading
andO (b) if he pushes at 30 to
that direction?
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Momentum
Momentum= Mass x Velocity
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Momentum
Momentum is a vector quantity
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Change of MomentumO In order to stop
the vehicle, need
to bring themomentum to
zero.
O Time taken to
stop the vehiclemay differ
Take a long time to stop.
How about the force required??
Take a short time to stop
How about the force required??
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ImpulseO Impulse is force
applied into time
that the force isapplied
O Impulse = change in
momentum
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Application
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Same Impulse
O Impulse for all three situations are same.
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Conservation of momentum
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The law of conservation of
linear momentum
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Elastic and Inelastic Collisions
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Elastic and Inelastic collisionsKinetic
energy isconserved
Kinetic
energy is
NOTconserved
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Application-perfectly elastic
There are two elastic balls green and red.The Green
ball come at 3m/s and hit on red ball which is initiallyat rest. After collision green ball comes to rest and
red ball travels at v m/s. find v.
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Application-perfectly inelastic
Find the velocity of the two balls
sticked together
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Angular MomentumO Linear momentum=
mass x velocity
O Angular momentum=Linear momentum x radius
of rotation
P=mv kgm/s
L=rmv kgm 2/s
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ApplicationO What is the angular
momentum of a
100 g mass tied tothe end of a 0.75 m
long string and
spun overhead
once per second?
O L=rmv
O Can be applied for a
point mass
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Rotational Inertia/moment of
inertia
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Moment of Inertia
O Which has more
rotational inertia?O If the mass is
distributed further
from axis of
rotation, moment ofinertia will be larger
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Conservation of Angular
Momentum vs conservation oflinear momentum
O In the absence of
any net externaltorque, the totalangularmomentumof a closed system is
conserved..
O In the absence of
any net external
force, the total linearmomentum of a
closed system is
conserved..
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Contd,
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Equation for Angular
MomentumO Linear momentum P=mv kgm/s
O Angular momentum L=rmv kgm 2/s
O
v=rO Again L=rm(r)
L= mr L= I
I=moment of inertiaAngular momentum=moment of inertia x angularvelocity
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ApplicationO What is the moment of
inertia of the followingpoint masses arranged
in a square?
O a) about the x-axis?
O b) about the y-axis?
O c) about the z-axis?
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ApplicationO I door= Ms
2/3.
O Find the angular
velocity of thecompound unit
O Find kinetic energy in
two situations
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ApplicationAn acrobat stands at the center of a turntable,
holding his arms extended horizontally, with a
5.0 kg dumbbell in each hand in figure . He is
set rotating about a vertical axis, making one
revolution in 2.0 s. His moment of inertia
(without the dumbbells) is 3.0 kg m2 when his
arms are outstretched, and drops to 2.2 kg m2when his arms are pulled in close to his chest.
The dumbells are 1.0 m from the axis initially
and 0.20 m from it at the end.
O Find the acrobats new angular velocity if he
pulls the dumbbells close to his chest, and
O Compare the final total kinetic energy withthe initial value.