Calculating Density Using Upthrust and Drag Force in Water

[jisbon]

Homework Statement

Ball of radius 3cm and mass 0.1kg released from rest in liquid. It eventually reaches terminal velocity at 2m/s. What is density of liquid? Give drag force as F=1.9v

Relevant Equations

Drag force + pgV = mg

So using FBD, I came out with:

since it reaches terminal velocity, I can assume F=0, thus mg = upthrust +drag
So my density = mg - drag force/g * volume
However the answer seems to be wrong from the answer key I was given. Any ideas why?
Thanks

 

[haruspex]

Homework Statement: Ball of radius 3cm and mass 0.1kg released from rest in liquid. It eventually reaches terminal velocity at 2m/s. What is density of liquid? Give drag force as F=1.9v
Homework Equations: Drag force + pgV = mg

So using FBD, I came out with:

View attachment 248071

since it reaches terminal velocity, I can assume F=0, thus mg = upthrust +drag
So my density = mg - drag force/g * volume
However the answer seems to be wrong from the answer key I was given. Any ideas why?
Thanks

Please post your working and answer.

 

[jisbon]

Please post your working and answer.

Volume= 4/3 pi r^3 = 1.13*10^-4
Density = 0.98-(1.9)(1.13*10^-4) / 9.8(1.13*10^-4) = 884.76

The correct answer provided was 850

 

[haruspex]

Volume= 4/3 pi r^3 = 1.13*10^-4
Density = 0.98-(1.9)(1.13*10^-4) / 9.8(1.13*10^-4) = 884.76

The correct answer provided was 850

You appear to have misinterpreted the v in F=1.9v. It refers to the velocity, not the volume.
The 1.9 needs units, e.g. kg/s to take a velocity in m/s and produce a force in N.

 

[jisbon]

You appear to have misinterpreted the v in F=1.9v. It refers to the velocity, not the volume.
The 1.9 needs units, e.g. kg/s to take a velocity in m/s and produce a force in N.

Ah alright, gotem! Thanks for your help :)