Question

In: Physics

A 6.0 kilogram mass is to be suspended from a cylindrical cord made of rubber with...

A 6.0 kilogram mass is to be suspended from a cylindrical cord made of rubber with equilibrium length 1.5 meters. If an oscillation frequency of 5 Hertz is desired when the mass is pulled so the cord stretches, what diameter should the cord have? Assume the Young’s modulus of the rubber is 2*10^6 N/m^2 , the yield stress is 3*10^6 N/m^2, and the shear modulus is 0.5*10^6 N/m^2.

Expert Solution

Hi,

Hope you are doing well.

We know that,

Frequency of a SHM (Simple harmonic motion),

Where,

'' is the Force constant of rubber.(N/m)

'' is the Mass suspended.(kg)

Given that,

Frequency of a SHM,

Mass suspended,

Also we know that,Force constant of rubber, '' is given by

Where,

'' is the Young's modulus of rubber.(N/m²)

'' is the Area of cylindrical cord.(m²)

'' is the Length of cylindrical cord.(m)

From equation (1),

Given that,

Force constant of rubber,

Length of cylindrical cord,

Young's modulus of rubber,

Area of cylindrical cord,

Hope this helped for your studies. Keep learning. Have a good day.

Feel free to clear any doubts at the comment section.

Please don't forget to give a thumps up.

Thank you. :)

genius_generous answered 2 years ago

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