How Much Volume Does an Iron Anchor Displace in Water?

[A_lilah]

Homework Statement

An iron anchor of density 7870 kg/m3 appears 290 N lighter in water than in air.
What is the volume of the anchor?

Homework Equations

Fnet = 0 (we are doing static fluids) = forces up - forces down

Fbuoyant = density of liquid*g*volume of object

density = mass/ volume, so mass = density*volume

Weight in the air = mg, so weight in the water = (mg - 290N)

density of water = 1000 kg/m^3

The Attempt at a Solution

Fnet = Fbuoyant - (mg - 290N)
0 = 1000 * g * volume - (7870* 9.8*volume - 290N)
-290N = 9800 * volume - 77126 * volume
factor out volume, and

-290/ -67326 = volume = .00431 m^3

(the units work out right, I just left them out here to try to make things clearer)
unfortunately this answer is wrong...
any help would be great!
thanks

 

[pandolph]

It's simpler than it looks.

All you need is the Fbouyant equation, with 290 N on the left hand side and the values for g and the density of water on the right. Then solve for V. (This assumes that you can neglect the density of air (=1.29 kg/m**3) in comparison to the density of water, and, since the buoyant force is only given to 3 figures, this seems to be the case.)