Find the Force and centre of pressure using double integrals

[coolusername]

Homework Statement

https://www.physicsforums.com/attachment.php?attachmentid=66269&stc=1&d=1391481187

The questions are on the link above.

Homework Equations

P = (y + 60)/10
depth (D) = y + 60

The Attempt at a Solution

a) I set up the double integral:
Force (F) = ∫(0 -> 2∏)∫(0 -> 1) [(y+60)/10]dA
I then rearrange the double integral into polar coordinate format.
∫(0 -> 2∏)∫(0 -> 1) [(rsinθ+60)/10]rdrdθ
F = 6∏

I don't know if this is correct or if I'm approaching this problem correctly.
I pictured this as x being the surface of the sea and anything below the x is positive y.
So I was wondering if I did this correctly.

b) I don't know how to approach this question as usually the mass equation, in this case the force equation, contributes to finding the centre of force. They are asking for center of pressure. How can I come up with an equation for each x and y component of pressure when I only have force?

Any feedback is appreciated! Thanks

 

[Dick]

Homework Statement

https://www.physicsforums.com/attachment.php?attachmentid=66269&stc=1&d=1391481187

The questions are on the link above.

Homework Equations

P = (y + 60)/10
depth (D) = y + 60

The Attempt at a Solution

a) I set up the double integral:
Force (F) = ∫(0 -> 2∏)∫(0 -> 1) [(y+60)/10]dA
I then rearrange the double integral into polar coordinate format.
∫(0 -> 2∏)∫(0 -> 1) [(rsinθ+60)/10]rdrdθ
F = 6∏

I don't know if this is correct or if I'm approaching this problem correctly.
I pictured this as x being the surface of the sea and anything below the x is positive y.
So I was wondering if I did this correctly.

b) I don't know how to approach this question as usually the mass equation, in this case the force equation, contributes to finding the centre of force. They are asking for center of pressure. How can I come up with an equation for each x and y component of pressure when I only have force?

Any feedback is appreciated! Thanks

The integral for total force looks ok. I think you would do 'center of pressure' just like 'center of mass'. Just treat P=(y + 60)/10 as though it were the mass in a center of mass question.