Homework Help: Clay-stick inertia & energy problem

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1. Sep 24, 2016

MickeyBlue

1. The problem statement, all variables and given/known data
A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it.

Q2: What is the ratio of the final mechanical energy to the initial mechanical energy?
2. Relevant equations
1. Lf = Li (conservation of angular momentum)
2. Is = ⅓ML2
3. Ic = mx2
4. Krot = ½Iω2
5. Kl =½mVt2

3. The attempt at a solution

I can't find the problem with my working in part 2; wondering if someone can point me in the right direction please. I calculated the angular velocity as 0.53 rad/s.

2. Sep 24, 2016

haruspex

I get almost the same, but you might have some rounding error. Keep another digit of precision all the way through. I get .325.
I note that it asks for the ratio, so technically the answer should be of the form 0.32:1. Do you know what the official answer is?

3. Sep 24, 2016

MickeyBlue

No, I don't have an official answer yet. I thought the same about the ratio, but my online submission doesn't recognise colons.

4. Oct 7, 2016

MickeyBlue

I'd like to follow up from my previous answer: if the clay and the stick are taken as one system, and we assume no friction about the pivot, is the case not that mechanical energy is conserved? That would make the ratio 1:1 (or just 1).

I'm not 100% sure on this.

5. Oct 7, 2016

haruspex

The initial mechanical energy must be that before the collision. Since the bodies coalesce, it cannot be conserved.