Hydrostatics: pressure and forces and density

[Patricia Reid]

A 5.0 kg cube of metal has a density of 3000 kg m³ and is held by a vertical string while immersed in water which has a density of 1000 kg m³ . Assume that the cube is oriented so that all the faces are either vertical or horizontal.

1. What is the difference in pressure between the top of the cube and the bottom?
2. What are the vertical components of force due to water pressure on the top and bottom of the cube?
3. Assuming that the cube is in equilibrium, what is the tension in the string?

p=p_°-pgz

I was wondering how you get the pressure when you are only given density. Also, you do not know how deep the metal is... does that not matter?

Thanks in advance! Any hints would be helpful.

 

[jbriggs444]

It is a cube. You know its mass and its density. Can you compute its volume? If you know its volume, what does that tell you about its height?

 

[Patricia Reid]

So 5 kg * m³/3000 kg = 0.001667 m³ Therefore the height must be 0.119 m but what does this tell you about pressure?

 

[jbriggs444]

You know the density of the water and the acceleration of gravity. How does pressure vary with depth?

 

[Patricia Reid]

Pressure would increase with depth.
So p=g*h*density
=9.81*1000*0.119=
1163 PaThen for the next part the the force is equal to pressure times area which would equal 1163 Pa * (0.119m)²=16.4 N

Then for finding the tension in the rope... The correct answer is 32.8 N what do you double the answer from the second part?

 

[jbriggs444]

Rule 1 in many, many physics problems: Draw a free body diagram.

What forces are acting on the metal cube?

 

[Patricia Reid]

Ok thanks! Got it