Density of Block Submerged into Swimming Pool

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.

ehild
Homework Helper

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

ehild

ok..

mg down = 857 * 9.81 = 8407.17

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

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

ehild

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

ehild
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ehild

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

ehild
Homework Helper
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

Last edited:
It exerts a force equal to -kx

ehild
Homework Helper
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

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• springwater.JPG
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