Calculating Density of a Liquid with Archimedes' Principle

[bpw91284]

Homework Statement

It is found that a 3.70-kg aluminum ball has an apparent mass of 2.20 kg when submerged in a particular liquid.
Calculate the density of this liquid in kg/m3.

Homework Equations

Bouyancy force=density*volume*gravity
Volume=mass/density

The Attempt at a Solution

1. Look-up density of Al: density=2.7*10^3 kg/m^3

2. Volume of ball=(mall ball)/(density of ball)=0.00137m^3

3. Bouyancy force on ball=2.2*9.81=21.582N=weight of fluid displaced (Archimede's principle)

4. So the mass of 0.00137m^3 of the fluid can be solved by...
weight of fluid=(mass of fluid)g
mass of fluid=2.2kg

5. density of fluid=(mass fluid)/(volume of fluid)=1606 kg/m^3...

Did I use the apparent mass correctly in step 3?

 

[Nacer]

Bouyancy force on ball=(3.70-2.20)*9.81.

Regards,

Nacer.

 

[bpw91284]

Bouyancy force on ball=(3.70-2.20)*9.81.

Regards,

Nacer.

Can you explain why and did I do the rest of problem correctly?

 

[denverdoc]

try a free body diagram where the ball is suspended in the fluid from a spring scale. Ordinarily the weight measured would be g*3.7, only in this case the scale measures 2.2*g kg. the difference is the upwards directed buoyancy force. (which as you have noted is density*volume*g.)

in this case, the problem is a bit of a curve ball as normally the x being sought is the density or volume of the object and not the medium, which is what I think got you a little tangled up above. that help at all?

 

[bpw91284]

This look correct?

1. Look-up density of Al: density=2.7*10^3 kg/m^3

2. Volume of ball=(mass ball)/(density of ball)=0.00137m^3

3. Buoyancy force on ball=(3.7-2.2)g=14.715N=weight of fluid displaced (Archimedes's principle)

4. So the mass of 0.00137m^3 of the fluid can be solved by...
weight of fluid=(mass of fluid)g
mass of fluid=1.5 kg

5. density of fluid=(mass fluid)/(volume of fluid)=1095 kg/m^3

 

[denverdoc]

i didn't run the numbers but I think you nailed it. Didn't need to multiply and then divide by g, but that's a small nitpick.