Density of Block Submerged into Swimming Pool

[sweetpete28]

A spring is mounted vertically at the bottom of an empty swimming pool. A block of mass M = 857 kg is attached to the spring, and it compresses the spring from its equilibrium position by distance xo. Now the swimming pool is filled with fresh water, and the block is submerged. You find the the spring is now extended distance x = 1.73xo from its equilibrium position. Find the density of the block.

I have zero clue how to start...can someone please help?

 

[ehild]

I have zero clue how to start...can someone please help?

Perhaps starting with a free body diagram of forces, including the buoyant force?

ehild

 

[sweetpete28]

ok..

mg down = 857 * 9.81 = 8407.17

buoyant force (when block is submerged) = density of fluid x volume submerged in fluid x gravity

 

[sweetpete28]

a little more help please...

 

[ehild]

The block is in equilibrium. What does it mean for the forces acting on it?

ehild

 

[sweetpete28]

Sum of the forces acting on block = 0. So: Mg = density of fluid x volume submerged x gravity...right?

 

[ehild]

And what about the spring?

ehild

 

[sweetpete28]

This is where I'm confused...for spring, Mg = 1/2kx^2...but how does this factor in?

 

[ehild]

This is where I'm confused...for spring, Mg = 1/2kx^2...but how does this factor in?

That is the energy. What is the force a spring exerts when it is stretched or compressed by x? Think of Hook's Law.

ehild

 

[sweetpete28]

It exerts a force equal to -kx

 

[ehild]

It exerts a force equal to -kx

See picture. What is the direction of this force when the tank is filled with water and the spring is extended?
What is the direction when there is no water in the tank?

ehild