Clay-stick inertia & energy problem

[MickeyBlue]

Homework Statement

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?

Homework Equations

1. L_f = L_i (conservation of angular momentum)
2. Is = ⅓ML²
3. Ic = mx²
4. K_rot = ½Iω²
5. K_l =½mVt²

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.

 

[haruspex]

Homework Statement

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?

Homework Equations

1. L_f = L_i (conservation of angular momentum)
2. Is = ⅓ML²
3. Ic = mx²
4. K_rot = ½Iω²
5. K_l =½mVt²

The Attempt at a Solution

View attachment 106431
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.

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?

 

[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.

 

[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.

 

[haruspex]

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.

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