How Do You Calculate the Tension in a Wire for a Submerged Iron Cube?

[Bcisewski]

I could use some help on what formula or combination of formulas I am missing.
An iron (p = 7860 kg/m3) cube measuring 15.4 cm on a side is suspended from a wire. Find the tension in the wire when the block is completely submerged in water (p = 1000 kg/m3). The answer is 246 N

1) I have tried first to find the volume, v=m/p or v*p=m 3652*7860=28706795.04 , (3652=v, 15.4 cubed)
2) I tried then to find F of the block with, Fb=(3562)(1000)(9.81)=35789600
3) I then used both numbers in a final eq. FT=mg-Fb (28706795)(9.81)-(35789600)= to big of number

Thanks for the help.

 

[Astronuc]

Note that the density is given in $$kg/m^3$$, but the side length is given in $$cm$$. So be careful not to mix units.

The volume of a cube 15.4 cm on a side is of course 15.4^3 or 3652.264 $$cm^3$$. 1 m = 100 cm, so the volume, $$V$$, = 0.0036523 m^3.

The tension,T, in the wire, which is simply the gravitational force exerted on the block, is given by,

T = (m(block) - m(water))g.

$$m\,=\,\rho\,V$$

Note that the block is completely submerged so it displaces an equal volume of water.

 

[wais]

It seems like you are on the right track with your calculations. However, there are a few things that need to be corrected in order to get the correct answer of 246 N for the tension in the wire.

First, when calculating the volume of the iron cube, you need to convert the side length from centimeters to meters. So, the volume should be 0.0154^3 = 3.8796 x 10^-5 m^3.

Next, when calculating the buoyant force (Fb), you need to use the volume of the displaced water, not the volume of the iron cube. This is because the buoyant force is equal to the weight of the water that is displaced by the object. So, the correct equation would be Fb = (3.8796 x 10^-5 m^3)(1000 kg/m^3)(9.81 m/s^2) = 0.3801 N.

Finally, when calculating the tension in the wire, you need to use the correct formula which is FT = mg - Fb. So, the final equation would be FT = (0.3652 kg)(9.81 m/s^2) - 0.3801 N = 2.46 N. This is the same as 246 N, but the units are in Newtons instead of kilograms.

In summary, the formula you were missing was the volume of the displaced water when calculating the buoyant force. Also, make sure to use the correct units for each variable in the equations. I hope this helps clarify any confusion. Good luck!