Billiards Ball Collision Analysis

AI Thread Summary
The discussion focuses on analyzing the collision between two identical billiard balls after a glancing impact. The key point is the application of the momentum conservation principle, where the total momentum before the collision equals the total momentum after. The participant questions whether the standard momentum formula suffices or if additional considerations are needed for angled collisions. It is noted that since the balls are identical, their mass can be eliminated from the equations. The conversation emphasizes that even in non-linear collisions, momentum conservation applies, requiring vector components for velocity and momentum.
JonathanSnow
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Homework Statement



2 identical biliards balls collde after a glancing collision determine the speed of the other ball,
2333351843_353551cc01.jpg

Homework Equations



MaVa + MbVb = MaVa' + MbVb' ?

The Attempt at a Solution



is this just as simple as the momentum formula before and after, or am I forgetting somthing obvious, because 5cm/s in the other direction dosent make any sense
 
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also is there a different formula to use for this when its on an angle, i know momentum before has to equal momentum after as does kinetic energy, mind you its not asking for kinetic, only speed, the balls are the same size so in the momentum formula we can get rid of the mass?, and its obvious its perfectly elastic anyways.
 
If the collision isn't on a straight line you can use the same momentum equation, only now the velocity and momentum are vectors with 2 components.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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