Energy, Impulse and Momentum

7/21/2019 Energy, Impulse and Momentum

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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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m


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15

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

Documents

Energy, Impulse and Momentum