energy, impulse and momentum
TRANSCRIPT
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Assoc. Prof. Raafat Ibrahim
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ENERGY (joules)
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Conservation of ENERGY
IF,
In a mass system where internal friction forces are sufficiently
small to be neglected
AND
No work is done on the system during an interval of motionby external force (other than gravitational force)
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That is,
THEN The net energy of the system remains constant
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Conservation of ENERGY
That is,
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The net energy of the system remains constant
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EXAMPLE 1
The 3kg slider is released from rest at position 1 and slides withnegligible friction in a vertical plane along the circular rod. The
attached spring has a stiffness of 350 N/m and has an unstretchedlength of 0.6m. Determine the velocity of the slider as it passesposition 2.
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EXAMPLE 1
The 3kg slider is released from rest at position 1 and slides withnegligible friction in a vertical plane along the circular rod. The
attached spring has a stiffness of 350 N/m and has an unstretchedlength of 0.6m. Determine the velocity of the slider as it passesposition 2.
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The 3kg slider is released from rest at position 1 and slides with
negligible friction in a vertical plane along the circular rod. The
attached spring has a stiffness of 350 N/m and has an unstretched
length of 0.6m. Determine the velocity of the slider as it passes
position 2.
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EXAMPLE 1
Substituting in conservation of energy equation
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Linear momentum of the system
is the vector sum of the linear
momenta of all its particles
Linear momentum of a system of particles
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Linear momentum (G) = mv
For a particle of mass of the
system
(1)
m
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Linear momentum of a system of particles
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Substituting in Eq. (1)
From the definition of center of mass
Therefore,
m
Velocity of mass w.r.t O
velocity of center of mass
velocity of w.r.t translating
reference frame moving with Cm
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Linear Impulse-Momentum principle
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Product of force and time Linear Impulse
Total external linear impulse (impact force) on the particle equals the
corresponding change in the linear momentum
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EXAMPLE 2
z
y
F
mg
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Angular momentum of a system of particles
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m
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Angular momentum of a system of particles
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m
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Angular momentum of a system of particles
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m
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Angular Impulse-Momentum
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EXAMPLE 3
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Conservation of Momentum
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In the absence of an external impulse, the momentum of a system
remains unchanged
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EXAMPLE 4
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The 25Mg flatcar supports a 7.5Mg vehicle on a 5o ramp built on
the flatcar. If the vehicle is released from rest with the flat caralso at rest, determine the velocity v of the flatcar when the
vehicle has rolled s =12m down the ramp just before hitting the
stop at B. Neglect all friction and treat the flatcar as particles.
s
x
y
v
o
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EXAMPLE 4
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s
x
y
v
o
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EXAMPLE 4
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s
x
y
v
o
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EXAMPLE 4
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s
x
y
v
o
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What You Learned!
Work and Energy
Conservation of Energy
Impulse and Momentum
Linear Impulse and Momentum
Angular Impulse and Momentum
Conservation of Momentum