The distance from the top of a block floating in the water to water

[PoPrOcKsRoCk]

Homework Statement

A 8 cm × 8 cm × 8 cm wood block with a density of 653.49 kg/m3 floats in water.
What is the distance from the top of the block to the water if the water is fresh?

Homework Equations

The Attempt at a Solution

weight= density*volume*g
weight=653.49*(512)*9.8
weight=3278951.424 Newton

weight=densitywater*g* 8 cm* 8 cm*depth
3278951.424=1000*9.81*8*8*d
3278951.424=627200*d
d=5.22792 cm...which is wrong

I have also tried subtracting 8 from 5.22792 and I got 2.77208 cm. I tried to submit it into my homework website and it is telling me I am wrong. I just don't understand what I am doing wrong.

 

[cepheid]

Yeah well, your units of length are not consistent throughout the calculation. In some quantities, you use centimetres and in other quantities you use metres.

 

[cepheid]

Also, the "d" you are calculating is the height of the immersed part. You want the height of the un-immersed part.

 

[PoPrOcKsRoCk]

So I would need to change the 8 cm to 0.08 m, right?

If I do that, then my answer would be;

weight= density*volume*g
weight=653.49*(5.14*10^-4)*9.8
weight= 3.2788 Newton

weight=densitywater*g* 8 cm* 8 cm*depth
3.2788=1000*9.8*0.08*0.08*d
3.2788=62.72*d
d=0.0522768 m?

And the height of the un-immersed part is 7.9477 m?

 

[cepheid]

The last part is def. wrong. Remember, the height of the box is 8 cm, not 8 m. So you need to subtract your final answer from 0.08, not from 8. Assuming you did the calculations right (which I haven't checked), this means that more than half the box is immersed.

 

[PoPrOcKsRoCk]

The last part is def. wrong. Remember, the height of the box is 8 cm, not 8 m. So you need to subtract your final answer from 0.08, not from 8. Assuming you did the calculations right (which I haven't checked), this means that more than half the box is immersed.

I tried the answer 7.9477 m and it told me I was right. I don't understand how though because the 8 is in cm and the 0.0522768 is in m. I will have to talk to my professor about that. Thank you for your help.