Conservation of Momentum in a Two-Pendulum Collision

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The discussion focuses on solving a physics problem involving two pendulums colliding and sticking together. The initial setup includes one pendulum with mass m and another with mass 3m, with the first pendulum released from a 45° angle. To determine the maximum angle after the collision, the conservation of momentum is applied to find the velocity of the combined mass post-collision. The proposed solution involves calculating the maximum angle using the formula arccos[(30 + sqrt(2))/32], resulting in approximately 79.0 degrees. The key to solving the problem lies in correctly applying the conservation of momentum principle.
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I have to solve this problem but every answer I've come up with so far has been wrong. If anyone knows how to solve it, I'd greatly appreciate some enlightenment. Thanks.
Here's the question:
Two pendulums are hung adjacent to each other as shown in Fig. 7.20. Bob 1 has a mass m, and bob 2 has a mass 3m. Bob 1 is pulled aside until the support string makes an angle of 45° with the vertical direction and then is released. When the bobs collide, they stick together. What is the maximum angle made by the support strings with respect to the vertical after the collision?
 
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is the answer

arccos [ [30 + sqrt(2)] / 32 ]
= arccos [ 0.9817 ]
= 79.0 degrees?
 
In order to find the maximum angle that the two balls rise to, you need to know the velcoity of the two balls after the collision. This is easy to find using conservation of momentum
m1v1+m2v2=(m1+m2)v'
One of the balls is initially at rest, so the problem is even easier.
m1v1=(m1+m2)v'
 
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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