Velocity of each ball at the moment of impact: V = u + Ft/m

AI Thread Summary
The discussion focuses on calculating the velocity of two heavy balls attached to a light metallic rod at the moment of impact with the ground. Key concepts include the conservation of linear momentum and energy, while neglecting friction and the rod's mass. The equations presented, particularly V = u + Ft/m, are derived from Newton's second law and relate the force acting on the balls to their acceleration and final velocity. A question is raised about the reaction force from the ground and its lack of work on the system. Understanding these principles is crucial for solving the problem effectively.
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Homework Statement


Two heavy balls of equal mass M are attached to the long but light metallic rod standing
on the floor. The rod with the balls falls to the floor. Find the velocity of each ball at the moment
when the rod hits the ground. Neglect mass of the rod and the friction between the balls and the
floor.



Homework Equations





The Attempt at a Solution

 
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Conservation of linear momentum may help. Friction is negligible, conservation of energy may also be of help.

A question: Can you explain why reaction force (by the ground) on the ball, touching ground at all moments, does no work on the two-ball system!
 
Last edited:
Equations for Velocity:

1)F=Ma ->
f(a) => V=u+at
2)F=M(v-U)/t

ft=m(V-u)
ft/m+u=V
V=u+ Ft/m
 
Last edited:
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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