Help elastic collistion, cons of momentum problem

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In a perfectly elastic collision problem, block 1 with a speed of 10 m/s collides with block 2, which has twice its mass and a speed of 5 m/s. The equation for conservation of momentum is applied, leading to the relationship v1 + 2v2 = 20. The reason for multiplying v2 by two is due to block 2's greater mass, which affects the momentum calculation. The mass terms cancel out in the equation because they are proportional, simplifying the analysis. Understanding these steps is crucial for solving elastic collision problems effectively.
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Block 1 moves with speed of 10m/s to right. It hits block 2 which has twice the mass of block 1 and speed of 5m/s to right. compute the magnitude and direction of block 1 for a perfectly elastic collision.

solution:

u1 = 10m/s
u2 = 5m/s

m1v1 + m2v2 = m1u1 + m2u2 ---->
v1 + 2v2 = u1 + 2u2
...= 10 + 2(5) = 20

(1) v1 + 2v2 = 20

why did u2 and v2 get multiplied by two and why did the m cross out?
 
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nchin said:
why did u2 and v2 get multiplied by two and why did the m cross out?
Are you saying you've just copied these steps from somewhere else and don't know the logic behind them? If those steps were your own work, surely you know why you made them.
 
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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