Angular momentum problem (ball sticking to one end of a see saw)

AI Thread Summary
The problem involves a 4.80 kg ball dropped from 15.0 m onto a uniform bar that pivots at its center, with a 5.40 kg ball on the opposite end. The approach to solving it involves conserving angular momentum, using the initial velocity derived from equating kinetic and potential energy. The challenge lies in determining the moment of inertia (I) of the system after the collision. Once I is calculated, angular velocity (ω) can be found, and the height the ball rises can be determined through energy conservation. Clarification on units and the specific question being asked is also needed.
Storm Butler
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Homework Statement



A 4.80 ball is dropped from a height of 15.0 above one end of a uniform bar that pivots at its center. The bar has mass 7.00 and is 8.60 in length. At the other end of the bar sits another 5.40 ball, unattached to the bar. The dropped ball sticks to the bar after the collision.

Homework Equations





The Attempt at a Solution


my attempt at doing this was to conserve angular momentum. so it is initially mvr where r is half of the length of the rod and v is the velocity found by equating kinetic energy with potential energy. then i set this equal to Iw of the final system but i don't know how to find I of this. I figured once i had I i could find w and set v of ball to wr and then use conservation of energy again to find the hight the ball rose.
 
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Two issues: 1. what are your units? and 2. what is the question?

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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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