How to Calculate Ultrasound Power from Float Displacement?

[bobred]

Homework Statement

There is a submerged float which is held in equilibrium by three hanging chains (see attached), a portion of the chain hangs below the float. Ultrasound directed onto the top face of the float (which is concave with angle α) and the float is displaced downward proportional to the ultrasound power. Find the power as a function of displacement.

Homework Equations

Power $W=\frac{Fc}{2\cos^2\alpha}$

Where F is the force and c is the speed of sound in water

The Attempt at a Solution

I need to relate the distance of the float displacement to the Force.
As it is displaced the weight of the chain decreases. Linear density is mass over length, I know the length of the chains and their masses, all the same.
How do I work out the loss of weight?

 

[haruspex]

Homework Statement

There is a submerged float which is held in equilibrium by three hanging chains (see attached), a portion of the chain hangs below the float. Ultrasound directed onto the top face of the float (which is concave with angle α) and the float is displaced downward proportional to the ultrasound power. Find the power as a function of displacement.

Homework Equations

Power $W=\frac{Fc}{2\cos^2\alpha}$

Where F is the force and c is the speed of sound in water

The Attempt at a Solution

I need to relate the distance of the float displacement to the Force.
As it is displaced the weight of the chain decreases. Linear density is mass over length, I know the length of the chains and their masses, all the same.
How do I work out the loss of weight?

The whole set up, and the quoted relevant equation, appear to relate to some relatively obscure branch of physics. Most people on this forum would, like me, have no idea about the application of that equation.

But maybe that's not what you are asking. Are you just asking how to relate the change in depth of the float to the change of force on it from the weight of the chains?
If so, I suggest you approximate each chain as two vertical sections joined by a U-shaped portion of constant size. Otherwise, you can look up 'catenary'.

 

[bobred]

Hi, yes I'm asking how to relate the change in depth of the float to the change of force on it from the weight of the chains.

 

[haruspex]

Hi, yes I'm asking how to relate the change in depth of the float to the change of force on it from the weight of the chains.

Did you understand my suggestion?

 

[bobred]

Looking into it now thanks.