Qns On The Equations Of Momentum

[Delzac]

hi, i read in a textbook that one equation for momentum is :

where U = intial velocity, V = Final velocity

U_1 + V_1 = V_2 + U_2 ----------- (1)

Equation (1) is derieve from Equation of " conservation of momentum " and " conservation of kinetic energy". and that they assume that

V_2 is not equal is U_2 and ,

V_1 is not equal to U_1.

why did they take this assumption? ( the book did not offer further explanation)

And what does it mean physically when u take

V_2 = U_2 and ,

V_1 = U_1. ??

+ Collision is Elastic +

 

[NEWO]

think about what u and v actually mean first, u is the initial velocity like you said and v is the final velcity.

i thought that the conservation of momentum is given by;

$$mu_{1}+mu_{2}=mv_{1}+mv_{2}$$

where $$u_{1}$$ is the initial velocity of object 1 and $$u_{2}$$ is the initial velocity of object 2, and likewise for the final velocity. this is conservation of momentum for inelastic collisons.

when v=u it means that no kinetic energy is lost during the collision.

 

[Doc Al]

That equation says that the relative velocity of approach before the collision equals the relative velocity of separation after the collision. It is derived by combining conservation of momentum and conservation of energy. (Thus it is only valid for elastic collisions.) In the derivation, one divides by terms equivalent to "V_2 - U_2" and "V_1 - U_1", so if V_2 = U_2 or V_1 = U_1, you'd be dividing by zero, which is a no-no.

But that's not very restrictive, since if V_2 = U_2 & V_1 = U_1 there would be no collision anyway.

 

[NEWO]

That equation says that the relative velocity of approach before the collision equals the relative velocity of separation after the collision. It is derived by combining conservation of momentum and conservation of energy. (Thus it is only valid for elastic collisions.) In the derivation, one divides by terms equivalent to "V_2 - U_2" and "V_1 - U_1", so if V_2 = U_2 or V_1 = U_1, you'd be dividing by zero, which is a no-no.

But that's not very restrictive, since if V_2 = U_2 & V_1 = U_1 there would be no collision anyway.

lol I meant that I am a bit tired so not thinking straight