Finding the normal force of a block under water, under pressure

[JoeyBob]

Homework Statement

See attached

Relevant Equations

dP/dz = -density*gravity

So since the block is at the bottom there's no pressure pushing it up. To calculate the mass and force of gravity, I multiplied the density of the block by its height and cross sectional area and got 564 kg. Multiplying this by 9.8 I got the force of gravity of 5527.2 N.

Now to find the force of pressure from the water acting on the block I multiplied the waters density by the cross sectional area and height (1.2-0.2) and gravity. This gave 14700.

Adding the two forces I get 20227.2 which ends up being 2.02272 when the answer is suppose to be 8.08.

 

[haruspex]

since the block is at the bottom there's no pressure pushing it up

I don't think you should suppose a watertight seal between the block and the bottom of the tank.

 

[Chestermiller]

What is the depth of the water at the top of the block?

 

[haruspex]

What is the depth of the water at the top of the block?

@JoeyBob's working has the term (1.2-0.2).

 

[Chestermiller]

@JoeyBob's working has the term (1.2-0.2).

Does this mean it is 1.0 m below the surface?

 

[haruspex]

Does this mean it is 1.0 m below the surface?

The top is, I believe.

 

[Frabjous]

What about the air pressure?

 

[Chestermiller]

What about the air pressure?

Yes. When you include the air pressure, you get the desired answer.

 

[haruspex]

What about the air pressure?

The question is a bit deceptive. It is natural to think we are being asked for the normal force from the tank, but in fact it wants the total force acting on the base of the block. Even assuming it is not a watertight seal, that includes the force due to the pressure in the water there, which in turn includes a component from the air pressure acting on top of the water.

 

[JoeyBob]

What about the air pressure?

The question is a bit deceptive. It is natural to think we are being asked for the normal force from the tank, but in fact it wants the total force acting on the base of the block. Even assuming it is not a watertight seal, that includes the force due to the pressure in the water there, which in turn includes a component from the air pressure acting on top of the water.

Thanks for the help, I had to multiply the air pressure from the cross sectional area and then add it to the other forces I got. This gave the right answer.

Why don't I multiply this one by gravity like I did the others?

 

[Frabjous]

Pressure already includes the effects of gravity. It is caused by the weight of the atmosphere.