# Hydrostatics: pressure and forces and density

• Patricia Reid
In summary, a 5.0 kg cube of metal with a density of 3000 kg m3 is held by a string in water with a density of 1000 kg m3. The pressure at the top of the cube is equal to the pressure at the bottom, which is 1163 Pa. The vertical components of force due to water pressure on the top and bottom of the cube are equal to 16.4 N. The tension in the string is equal to 32.8 N.
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?

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?

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?

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

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?

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

What forces are acting on the metal cube?

Ok thanks! Got it

## 1. What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that deals with the study of fluids at rest, specifically focusing on the pressure and forces within a fluid.

## 2. What is pressure in hydrostatics?

Pressure in hydrostatics is the force per unit area that is exerted by a fluid on its container or any surface that it comes into contact with. It is measured in units of force per unit area, such as pascals (Pa) or pounds per square inch (psi).

## 3. What factors affect pressure in hydrostatics?

Pressure in hydrostatics is affected by the density and depth of the fluid, as well as the acceleration due to gravity. The greater the depth and density of the fluid, the higher the pressure will be. The acceleration due to gravity also plays a role in determining the pressure, with higher gravity resulting in higher pressure.

## 4. How is density related to pressure in hydrostatics?

Density is directly related to pressure in hydrostatics. As the density of a fluid increases, so does the pressure. This is because more particles in a given volume means more collisions and therefore a higher force per unit area, resulting in higher pressure.

## 5. Why is hydrostatics important?

Hydrostatics is important in various fields such as engineering, meteorology, and oceanography. It helps in understanding the behavior of fluids at rest, which is crucial in designing structures that will be in contact with fluids, predicting weather patterns and ocean currents, and studying the movement of water in different bodies of water.

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