Calculating upthrust on a solid object

In summary, when the object is floating, the weight of the object is equal to the weight of the displaced liquid. When the object is submerged in liquid, the weight of the object is less because it is submerged in liquid.
  • #1
azsx11
4
0
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*10bN 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.
 
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  • #2
Hi azsx11, welcome to pF.
How did you get
3000 = m/30?
 
  • #3
rl.bhat said:
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?
 
  • #4
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?
 
  • #5
rl.bhat said:
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?
 
  • #6
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.
 
  • #7
rl.bhat said:
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?
 
  • #8
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?
 

FAQ: Calculating upthrust on a solid object

What is upthrust?

Upthrust, also known as buoyancy force, is the upward force exerted by a fluid (such as water) on an object immersed in it.

How is upthrust calculated on a solid object?

Upthrust on a solid object can be calculated using the formula: upthrust = volume of the object * density of the fluid * acceleration due to gravity.

What factors affect the upthrust on a solid object?

The upthrust on a solid object is affected by the volume of the object, the density of the fluid it is immersed in, and the acceleration due to gravity.

Can a solid object have zero upthrust?

No, a solid object will always experience some amount of upthrust when immersed in a fluid. The only exception is if the object has the same density as the fluid, in which case it will experience neutral buoyancy.

How does the shape of a solid object affect the upthrust?

The shape of a solid object does not directly affect the upthrust, but it can indirectly affect it by changing the volume of the object and thus changing the amount of upthrust it experiences.

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