M2 energy and momentum

If Kinetic energy is lost during a collision how can total momentum be conserved?


Posted from TSR Mobile

they are different quantities

If Kinetic energy is lost during a collision how can total momentum be conserved?


Posted from TSR Mobile

Can you explain how they are different?


Posted from TSR Mobile

write down the definition of momentum and the definition of kinetic energy

they are different quantities

Yes but velocity is a component of momentum and if kinetic energy is lost then velocity will decrease so surely momentum will also decrease


Posted from TSR Mobile

definitely not

in the system some velocities decrease some may increase,

The momentum in the absence of external forces stays the same.
The kinetic energy will decrease unless the collision is elastic, ie the coefficinet of restitution is 1

I think what I've being missing is that the momentum will be the same the instant before collision and the instant after but anytime after this, friction could act on the individual particles and reduce the momentum in the system? Is this true?


Posted from TSR Mobile

this is a different matter altogether.
Now momentum is not even conserved as there is an external force (and neither is energy)

What happens after is a different question

Ok so it is in the instant of collision conservation of momentum would be true then


Posted from TSR Mobile

At the instant of collision,
the momentum of the system is conserved
the kinetic energy of the system is reduced, unless the collision is perfectly elastic (restitution coefficient is 1/never in real life)

Ok then I really still don't get this. Isn't it true that:
a) velocity is a component of kinetic energy (1/2mv^2 + 1/2nx^2 where n and x are the mass and velocity of the second object in the collision)
b) therefore if kinetic energy has fallen, given that mass stays the same, velocity must have fallen in magnitude
c) momentum is the sum of the mv and nx (mass X velocity of both objects)
d) if kinetic energy has fallen and therefore totally velocity has fallen in magnitude then the sum of mv and nx must be smaller than the initial sum (therefore momentum of the two objects added together is not conserved as kinetic energy has fallen).

I just don't see how what I say isn't true? Can you tell me where I'm going wrong? Is it only the 2 objects that are involved in the collision that are considered in the system?


Posted from TSR Mobile