Tricky density and bouyancy question

[jlin94]

Homework Statement

1. A piece of metal weighs 53.1 N in air, 36.6 N
in water, and 41.7 N in an unknown liquid.
Find the density of the metal.
Answer in units of kg/m3

2 Find the density of the unknown liquid.
Answer in units of kg/m3
2. Homework Equations [/b]

p= M/V

W= mg

The Attempt at a Solution

i have no clue how to do now?
how do i find the density of the metal and liquid w/out volume?

thanks a lot, really appreciate it!

 

[SteamKing]

Hint: You should know the density of water

 

[jlin94]

so is this what i should do:

W=mg
m= W/g
m = 36.6/9.8
m = 3.73 kg

then put this in

p= m/v
1000 = m/v
v = m/1000
v = 3.73/1000
v= 0.00373 meter cubed

then mass density of metal is

p = m/v
p = 3.73/0.00373
p = 1001.25 kg/mcubed

how should i find the density of unknown liquid

 

[sophiecentaur]

The upthrust is proportional to the weight of the liquid displaced. The block is completely submerged so the volume is the same for water and for the liquid.
You can calculate the upthrust in each case.
The upthrust in water is volume of water times density. That allows you to calculate the volume.

This volume produces the other value of upthrust so you can then work out the density because you know everything else you need. (weight of liquid displaced and volume)

You just need to be careful to use weight and mass where appropriate in order to come out with the right value for density.
Logical step by step and believe it will work.
Hint: As a quick reality check, the amount of upthrust from the unknown liquid is less but not a huge amount less so the density answer you get should be similar in proportion to that of water.