Question about Elastic force and Buoyancy force

[MatinSAR]

Homework Statement

Elastic force and Buoyancy force

Relevant Equations

Archimedes' principle

Suppose a wooden cube with a side of 10 cm is connected to the bottom of a water container by a spring. If the density of wood is 0.6g/cm^3 and the density of water is 1g/cm^3 , what is the elastic force of the spring? Is it 4N or 6N ?

I think the answer is 4N … But the book says it is 6N , Could you please guide me which one is correct ?!

My answer : Spring force = Buoyancy force - Weight of the cube = 10N - 6N = 4N

 

[Doc Al]

My answer : Spring force = Buoyancy force - Weight of the cube = 10N - 6N = 4N

Your thinking looks good to me. (Did the book provide a solution or just the answer?)

 

[MatinSAR]

Your thinking looks good to me. (Did the book provide a solution or just the answer?)

Thank you for your answer.
It said the Spring force is equal to the Buoyancy force that acts on wooden cube and this Buoyancy force is equal to the weight of the cube due to complete submersion in water …

 

[Lnewqban]

... this Buoyancy force is equal to the weight of the cube due to complete submersion in water …

Something is not correct about this last statement.
The weight of what cube?

 

[MatinSAR]

Something is not correct about this last statement.
The weight of what cube?

We have only one wooden cube in the question and the weight of the cube is 6N.

 

[Doc Al]

It said the Spring force is equal to the Buoyancy force that acts on wooden cube

That's not right. (It ignores the weight of the cube.)

and this Buoyancy force is equal to the weight of the cube due to complete submersion in water

That's also not quite right (as @Lnewqban points out).

What book are you using?

 

[Lnewqban]

We have only one wooden cube in the question and the weight of the cube is 6N.

There was a heavier cube originally ocupying the volume of our unique and now submerged wooden cube.

 

[MatinSAR]

That's not right. (It ignores the weight of the cube.)

Thank you …

What book are you using?

It's not a reference book like Fundamentals of Physics or …
It was a kind of school book for being ready for the tests and exams …

There was a cube originally ocupying the volume of our unique and now submerged wooden cube.

I'm sorry but I don't understand … Do you mean 6N is false ?!

 

[Lnewqban]

... I'm sorry but I don't understand … Do you mean 6N is false ?!

Please, see:
https://en.m.wikipedia.org/wiki/Buoyancy

The buoyancy effect is generated by the weight of the fluid that has been displaced by the volume of the fully submerged wooden cube.
The fluid surrounding the solid is puting pressure on it, trying to regain that volume.

Think of the cube as a piston of wood pushing down and a piston of water pushing up, only that harder, in the same ratio in which the densities of water and wood differ.

It is only about the statement of post # 3 above, your answer is good.

 

[MatinSAR]

It is only about the statement of post # 3 above, your answer is good.

Thank you.