Elastic ball , Inextensible string

AI Thread Summary
An elastic ball of mass 'm' is suspended by an inextensible string and is struck by a downward-moving particle of the same mass at a 37-degree angle with a velocity 'v'. The coefficient of restitution is given as 4/5, which is crucial for calculating the post-impact velocity of the ball. The discussion centers on determining the ball's velocity after the collision and the impulsive tension in the string at the moment of impact. The principles of elastic collisions and the relevant laws of motion are applied to solve these problems. Understanding these concepts is essential for addressing the questions posed.
Harshatalla
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Elastic ball , Inextensible string !

An elastic ball of mass 'm' is suspended from a fixed point by an inextenible string. A small particle of same mass 'm' moving downwards at an angle of 37 degrees with the vertical hits the ball directly with the velocity 'v'. If the coefficient of restitution is 4/5.

a)Find the velocity of the ball just after the impact.
b)Determine the impulsive tension (impulse) in the string at the instant of collision.
 
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Think of the equation of elastic collision. Which law is applied?
 
this question was given by my sir as he was not getting the problem
i don't know anything about elastic collisions
 
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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