Calculating the Mass of a Steel Wrench in Water: A Density Dilemma

[bww]

A steel wrench feels 3N lighter in water.

a. what is the mass of the wrench?
b. how would your answer change if it took a more dense fluid to make the wrench feel 3N lighter?

a. ok so i know that density x volume=mass. The density of water is 1,000kg/m^3. That's about all I have. I don't really know where to go when i only have the weight of the steel and the density of water.

What are your thoughts?

 

[chroot]

The bouyancy force felt upwards on an object is equal to the weight of the fluid it displaces.

- Warren

 

[bww]

...i guess I'm still confused.

 

[chroot]

You know how much the displaced water weighs (it's given), and you know water's density, so you can calculate the volume of water that was displaced. The volume of displaced water is, of course, is the same as the wrench's volume.

You also know the density of the steel, so you're all set to find the wrench's mass.

- Warren

 

[bww]

how do i know the density of steel?

 

[chroot]

You said you know "the weight of the steel," by which I thought you mean density.

- Warren

 

[bww]

oh, no, I'm terribly sorry, my mistake. I meant that all i knew was that the weight of the wrench was 3N lighter in water. I do not have the density of the wrench. I only know that it weighs 3N less in water and that water's density is 1,000kg/m^3 and I need to find the mass of the wrench. sorry about that.

 

[chroot]

Well, I don't think there's any way to do this without another piece of information (like the density of steel).

Buoyancy isn't concerned with mass, just volume. If the wrench feels a buoyancy force of 3N, then you know its volume directly. But, as you know, you cannot relate mass and volume without knowing density.

The fact that the problem specifies that the wrench is made of steel leads me to believe you are supposed to look up the density of steel. It's probably given in a table in your book somewhere. Look up 'density' in the index.

- Warren

 

[bww]

...yeah you're right, you guys are a lot of help here. thanks. i figured it out.

 

[lvspink247]

I have the same question