Calculating upthrust on a solid object

[azsx11]

Calculating upthrust on an object

Homework Statement

An object made entirely of one material has a volume of 30m³. It floats in a liquid of density 30 g/cm³ with only half it's mass below the liquids surface. The object is then placed in a liquid of the same volume but with a density of 1 g/cm³. If the final upthrust that will act on the object is expressed in the form a*10^bN give the values of a and b. Assume g to be 10 ms²

Homework Equations

d=m/v

The Attempt at a Solution

1st liquid

3000=m/30
=90000
90000/2 = 45000 Kg displaced

45000 * 10 = 450000 N upthrust (archimedes)
45000/3 = 15000 N upthrust in 2nd liquid

a=1.5, b=4

I honestly have no idea really.

 

[rl.bhat]

Hi azsx11, welcome to pF.
How did you get
3000 = m/30?

 

[azsx11]

Hi azsx11, welcome to pF.
How did you get
3000 = m/30?

Sorry, I got my order wrong.

d = 30 g/cm³ = 30000 Kg/m³

30000 = m/30

m= 900000 Kg

etc...

Is this the right way to approach the question?

 

[rl.bhat]

When the body is floating, weight of the body is equal to the weight of the displaced liquid.
So what is the weight of the object?
In the second liquid whether the object sinks or floats?
If it sinks, what is the weight of the displaced liquid?

 

[azsx11]

When the body is floating, weight of the body is equal to the weight of the displaced liquid.
So what is the weight of the object?
In the second liquid whether the object sinks or floats?
If it sinks, what is the weight of the displaced liquid?

This is what I've tried to do.

900000/2 - half of the object is submerged.

= 450000 Kg displaced

450000*10 = 4500000 N upthrust.

(I'm not sure if that's correct)

If it sinks the weight of the displaced liquid is equal to the objects weight.

= 900000 Kg

900000*10 = 9000000 N

Am I on the right track?

 

[rl.bhat]

If it sinks the weight of the displaced liquid is equal to the objects weight.
It is no true.

If it sinks the weight of the displaced liquid is equal to the loss of objects weight.

 

[azsx11]

If it sinks the weight of the displaced liquid is equal to the objects weight.
It is no true.

If it sinks the weight of the displaced liquid is equal to the loss of objects weight.

Sorry, I'm none the wiser.

Was my calculation up to that point correct?

 

[rl.bhat]

In the second case, volume of the displaced liquid is...?
What is the density of the water?
What is the mass of the water and its weight?
Hence what is the upthrust?