Momentum & Impulse : Conservation Mtm

[ conservation law][ energy considerations ]





The Principle of Conservation of Momentum

The total linear momentum of a system of colliding bodies, with no external forces acting, remains constant.

for two perfectly elastic colliding bodies note:

i) By Newton's 3rd. Law, the force on X due to Y , (Fx) is the same as the force on Y due to X , (Fy) .

Fx = Fy

ii) By Newton's 2nd. Law, the rate of change of momentum is the same, since F = (rate of change of momentum)

iii)Because the directions of the momentum of the objects are opposite, (and therefore of different sign) the net change in momentum is zero.


Example #1

A 5 kg mass moves at a speed of 3 ms-1 when it collides head on, with a 3 kg mass travelling at 4 ms-1, travelling along the same line.
After the collision, the two masses move off together with a common speed.

What is the common speed of the combined masses?

momentum & impulse problem #1


Example #2

An artillery shell of mass 10 kg is fired from a field gun of mass 2000 kg.
If the speed of the shell on leaving the muzzle of the gun is 250 ms-1 , what is the recoil speed of the gun?

conservation of momentum problem #2


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Energy changes during collisions

Consider the kinetic energy change involved during a collision. Remember that no energy is actually lost, it is just converted into other forms. Energy can be transformed into heat, sound and permanent material distortion. The later causes the internal potential energy of bodies to increase.

If no kinetice energy is lost (K.E.= ½ mv2 ) then the collision is said to be perfectly elastic. However if kinetic energy is lost, the collision is described as inelastic. In the special case when all the kinetic energy is lost, the collision is described as completely inelastic. This is when to two colliding bodies stick to one another on impact and have zero combined velocity.

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linear motion
average velocity
instantaneous velocity
circular motion 1
projectile motion
parabolic motion
relative motion
Newton's 2nd Law
connected particles
KE & PE changes
elastic strings
conservation momtm.
coefft. restitution




EdxlM1 Mechanics spec.
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EdxlM2 Mechanics spec.
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uniform acceleration
non-uniform accln.
simple harmonic motion
circular motion
relative motion
Newton's Laws
connected particles
work & energy
power & efficiency
more circular motion
elastic strings
conservation momtm
coeff. restitution
part. forces in equilib.
rigid bodies