Constrained motion question (using moments of inertia/energy)

Mutant_Fruit
Messages
3
Reaction score
0
I've attached a screenshot of the question. This is what I've tried so far:

I've calculated the initial energy of the system (which is all potential energy):
Energy of disc:
0.5*I*w^2 + 0.5 *m*v^2 + m*g*h
= 0 + 0 + 0

Energy of arm:
0.5*m*v^2 + m*g*h
= 0 + 4*9.81*1.5Cos(45)
= 41.62 joules

Energy of collar:
0.5*m*v^2 + m*g*h
= 0 + 1*9.81*3Cos(45)
= 20.81 joules

Then i moved time on until the supporting arm BC was horizontal and calculated the energy at that stage (which would be all kinetic). When i do that, i end up calculating that the speed of the collar is 1.04 m/s. However, the answer is supposed to be 7.315 m/s.

I'm doing something wrong, but i can't figure out what it is. Any hints on how this is supposed to be solved would be great.

Thanks.

http://img127.imageshack.us/img127/3230/question8wo.th.jpg
 
Last edited by a moderator:
Physics news on Phys.org
In all probability, your flaw lies in determining the kinetic energy term of the arm. Specify what you did.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top