Silent Ringing Bell

anubis01

1. The problem statement, all variables and given/known data
A large bell is hung from a wooden beam so it can swing back and forth with negligible friction. The center of mass of the bell is 0.65m below the pivot, the bell has mass 37.0 Kg, and the moment of inertia of the bell about an axis at the pivot is 19.0 kg*m^2. The clapper is a small, 1.8 kg mass attached to one end of a slender rod that has length L and negligible mass. The other end of the rod is attached to the inside of the bell so it can swing freely about the same axis as the bell.

a)What should be the length of the clapper rod for the bell to ring silently-that is, for the period of oscillation for the bell to equal that for the clapper?


2. Relevant equations
T_bell=2pisqrt(I/mgd)

3. The attempt at a solution
okay so we have to have T_bell=T_Clapper
T_bell=2pisqrt(I/mgd)=2pisqrt(19/37*9.8*0.65)=1.784 s
1.784=T_Clapper=2pisqrt(I/mgd)
(1.748^2*g)/2pi=L=4.96m

Now I still have the wrong answer with this method, could someone please help me determine waht I'm doing wrong, as always any help is appreciated.

Doc Al

Shouldn't that 2∏ be squared?

anubis01

yes it should, sigh I really need to improve my arithmitic skills. Thanks for the help.

swifty

What about the 1.8kg ?

swifty

A large bell is hung from a wooden beam so it can swing back and forth with negligible friction. The center of mass of the bell is 0.45 below the pivot, the bell has mass 40.0 , and the moment of inertia of the bell about an axis at the pivot is 20.0 . The clapper is a small, 1.8 mass attached to one end of a slender rod that has length and negligible mass. The other end of the rod is attached to the inside of the bell so it can swing freely about the same axis as the bell.
What should be the length of the clapper rod for the bell to ring silently-that is, for the period of oscillation for the bell to equal that for the clapper?

Im getting 2.2 meters !? Can someone solve!!

Antiphon

It's a trick question. You are solving for the bell to "swing" silently not "ring" silently. The answer (to the actual question) is that you have to mismatch the clapper and bell frequencies to ensure a hit (or it can't ring) and then it has to be in vacuum so it can ring silently.

anubis01

using the above work I got 1.1m, You should also remember to have (2pi)² instead of just 2pi in the final part of the equation. It would also be helpful if you were to post your work.

swifty

Sight at me.. Cheers man.