TBR Elastic Collisions - how to measure velocity?

[dartmed]

---

Members don't see this ad.

I understand that in elastic collisions, momentum is always conserved (unless there is an external force on the system of course). How do I measure the resultant velocities when two balls collide in an elastic collision? TBR doesn't address this.

I know the velocities swap each other when the masses are equal, but what if the masses were not equal? Then, how I measure the measure the velocity?

 

[sciencebooks]

I understand that in elastic collisions, momentum is always conserved (unless there is an external force on the system of course). How do I measure the resultant velocities when two balls collide in an elastic collision? TBR doesn't address this.

I know the velocities swap each other when the masses are equal, but what if the masses were not equal? Then, how I measure the measure the velocity?

Momentum is conserved in elastic and inelastic collisions.

momentum (initial) = momentum (final)

Let's consider ball A and B, using i for initial and f for final. To solve for any missing velocity, use the equation below (it's just conservation!):

(mass A)(velocity Ai) + (mass b)(velocity Bi) = (mass A)(velocity Af) + (mass b)(velocity Bf)

Which just says:

momentum Ai + momentum Bi = momentum Af + momentum Bf

or

momentum i = momentum f

 

[MossyFiber]

(mass A)(velocity Ai) + (mass b)(velocity Bi) = (mass A)(velocity Af) + (mass b)(velocity Bf)

To answer your question...
(velocity Af) = ( (mass A)(velocity Ai) + (mass b)(velocity Bi) ) / (mass b)(velocity Bf)
(velocity Bf) = ( (mass A)(velocity Ai) + (mass b)(velocity Bi) ) / (mass a)(velocity Af)

 

[dartmed]

Momentum is conserved in elastic and inelastic collisions.

momentum (initial) = momentum (final)

Let's consider ball A and B, using i for initial and f for final. To solve for any missing velocity, use the equation below (it's just conservation!):

(mass A)(velocity Ai) + (mass b)(velocity Bi) = (mass A)(velocity Af) + (mass b)(velocity Bf)

Which just says:

momentum Ai + momentum Bi = momentum Af + momentum Bf

or

momentum i = momentum f

Thank you. I understand the formula, but that's where I was getting at.

For example, if mass 1 = 10 kg, mass 2 = 20 kg. v1i = 10m/s and v2i = -20m/s

What are the final velocities for v1f and v2f going to be?

How do we apply the momentum equation if this was an elastic collision?

If I did this...

m1v1i + m2v2i = m1v1f + m2v2f

(10)(10) + (20)(-20) = (10)(v1f) + (20)(v2f)

How do I figure out v1f and v2f?

 

[dartmed]

To answer your question...
(velocity Af) = ( (mass A)(velocity Ai) + (mass b)(velocity Bi) ) / (mass b)(velocity Bf)
(velocity Bf) = ( (mass A)(velocity Ai) + (mass b)(velocity Bi) ) / (mass a)(velocity Af)

What if neither bf nor af are given? Thanks!

 

[MossyFiber]

Two equations, two unknowns, you can still solve for it.

 

[MossyFiber]

substitute...
(Vaf) = ( (ma)(Vai) + (mb)(Vbi) ) / (mb)(Vbf)
(Vbf) = ( (ma)(Vai) + (mb)(Vbi) ) / (ma)(Vaf)

(Vbf) = ( (ma)(Vai) + (mb)(Vbi) ) / (ma)( ( (ma)(Vai) + (mb)(Vbi) ) / (mb)(Vbf) )
and solve for Vbf...