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Impulse and Momentum

1) Momentum is defined as the product of mass and velocity. It is a vector quantity. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse of the net force acting on the object. 2) In a system where no external forces act, the total momentum of the system is conserved. If the interactions are also conservative, then the total kinetic energy of the system is conserved. 3) In an elastic collision, both momentum and kinetic energy are conserved. The relative velocity of the objects before and after collision is the same magnitude but opposite direction.

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99 views21 pages

Impulse and Momentum

1) Momentum is defined as the product of mass and velocity. It is a vector quantity. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse of the net force acting on the object. 2) In a system where no external forces act, the total momentum of the system is conserved. If the interactions are also conservative, then the total kinetic energy of the system is conserved. 3) In an elastic collision, both momentum and kinetic energy are conserved. The relative velocity of the objects before and after collision is the same magnitude but opposite direction.

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Ayla
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IMPULSE MOMENTUM

ENGR. NIKKO JOHN LEO S. LOBOS, ECE, ECT


MOMENTUM AND IMPULSE
• Thus Newton’s second law says that the net force ΣF
acting on a particle equals the time rate of change
of the combination “mv” the product of the
particle’s mass and velocity
• P = mv
• The greater the mass m and speed v of a particle,
the greater is its magnitude of momentum mv.
• Vector Quantity
MOMENTUM AND IMPULSE
• We often express the momentum of a particle in
terms of its components:
IMPULSE AND MOMENTUM THEOREM
• The impulse of the net force, denoted by J is
defined to be the product of the net force and the
time interval.

• Impulse is a vector quantity; its direction is the same


as the net force ΣF
• Its magnitude is the product of the magnitude of
the net force and the length of time that the net
force acts.
IMPULSE AND MOMENTUM THEOREM
• If the net force F is constant, then dp/dt is also
constant.

• end up with a result called the impulse–momentum


theorem:

• The change in momentum of a particle during a


time interval equals the impulse of the net force
that acts on the particle during that interval
EXAMPLE

b) 0.525, baseball c) 0.641, woman


EXAMPLE
CONSERVATION OF MOMENTUM
• Let’s consider:

We now define the total momentum P of the


system of two particles as the vector sum of
the momenta of the individual particles; that is,

If external forces are also present, they must


be included on the left side of along with the
internal forces
CONSERVATION OF MOMENTUM

This is the simplest form of the principle


of conservation of momentum.
EXAMPLE

V_a2 = -0.40 m/s


Change in Pa = -1.2 kg *m/s
Change in Pb =1.2 kg *m/s
Va2 – Va1 = -2.4 m/s
Vb2 – Vb1 = +4.0 m/s
EXAMPLE

Vbx = 1.89 m/s


Vby = -0.83 m/s
Vb = 2.1 m/s
Beta = -24°
MOMENTUM CONSERVATION AND
COLLISION
• include any strong
interaction between bodies
that lasts a relatively short
time.
• Then momentum is
conserved and the total
momentum of the system
has the same value before
and after the collision.
MOMENTUM CONSERVATION AND
COLLISION
• If the forces between the bodies are also
conservative, so that no mechanical energy is lost
or gained in the collision, the total kinetic energy of
the system is the same after the collision as before.
Such a collision is called an elastic collision
• A collision in which the total kinetic energy after
the collision is less than before the collision is called
an inelastic collision.
COMPLETELY INELASTIC COLLISION
• An inelastic collision in
which the colliding
bodies stick together
and move as one body
after the collision is
often called a
completely inelastic
collision
EXAMPLE
EXAMPLE

V = 8.3 m/s
ELASTIC COLLISION
• elastic collision in an isolated system is one in which
kinetic energy (as well as momentum) is conserved.
• Elastic collisions occur when the forces between the
colliding bodies are conservative
• From conservation of kinetic energy we have:

• conservation of momentum
ELASTIC COLLISIONS, ONE BODY
INITIALLY AT REST
ELASTIC COLLISION AND RELATIVE
VELOCITY
• In a straight-line elastic collision of two bodies, the
relative velocities before and after the collision
have the same magnitude but opposite sign.

• In an elastic collision, the relative velocity of the two


bodies has the same magnitude before and after
the collision.
EXAMPLE

V2a = -1.0 m/s


vB2 = 3.0 m/s
EXAMPLE

vB2 = 4.47 m/s


a = 36.9°
b = 26.6°

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