Transforming Equations: How to Solve for 3-22a | Center of Pressure Homework

In summary, the student is struggling to solve for yc in the last term of the homework equation. They eventually figured out that the denominator in the last term of 3-22a reads ##(y_c+P_0/(\rho g \sin(\theta))A##, with which they agree. They then use the same method to solve for yc in the other factor.
  • #1
goldfish9776
310
1

Homework Statement


pls refer to photo 2 , (circled part) How to transform equation in 3-20 to become equation in 3-22a ?

Homework Equations

The Attempt at a Solution


i have tried in photo 3 , yet can get the same form as in 3-22a . In step 2 , i divided the y_p with Fr
 

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  • #2
I can see an error in your working. In the left hand term, you substituted FR=P0A (wrong), but in the right hand term you correctly used PcA.
I'll continue to study the text, but it is hard to read in places.

Edit:
I eventually figured out that the denominator in the last term of 3-22a reads ##(y_c+P_0/(\rho g \sin(\theta))A##, with which I agree.
Do you get that with the above correction?
 
Last edited:
  • #3
no , i still gt stucked here
 

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  • #4
goldfish9776 said:
no , i still gt stucked here
Put the denominator in the second term back into the form PcA for now.
Take the second term in the numerator (the one with yc2; you missed out the c subscript) and shift it into the first term after the equals sign. In the numerator there, you can extract a factor yc. The other factor is PcA, so cancels with the denominator.
 
  • #5
how to facrorise yc ? there are 3 terms there , but there are only 2 terms contain yc ... and i can't factorise PoA ...
 

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  • #6
goldfish9776 said:
how to facrorise yc ? there are 3 terms there , but there are only 2 terms contain yc ... and i can't factorise PoA ...
You have successfully factored out the yc. In the other factor, you have two terms each with a denominator PcA. So you can add together the numerators. I think you'll find those numerators add up to PcA.
 
  • #7
haruspex said:
You have successfully factored out the yc. In the other factor, you have two terms each with a denominator PcA. So you can add together the numerators. I think you'll find those numerators add up to PcA.
ok , i get my yc now , how to transform the ( (rho)g sin theta ( I xxc) / PcA )into the same form as 3-22a?
 
  • #8
goldfish9776 said:
ok , i get my yc now , how to transform the ( (rho)g sin theta ( I xxc) / PcA )into the same form as 3-22a?
In that term, expand the Pc in the denominator into P0+ etc. form, then divide through numerator and denominator by (rho)g sin theta.
 
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FAQ: Transforming Equations: How to Solve for 3-22a | Center of Pressure Homework

1. How do I solve for 3-22a in an equation?

The first step in solving for 3-22a in an equation is to isolate the variable by using inverse operations. This means that you should use the opposite operation on both sides of the equation to cancel out any constants or coefficients. Once the variable is isolated, you can solve for its value.

2. What is the significance of the center of pressure in an equation?

The center of pressure is the point where the total pressure acts on a body immersed in a fluid. It is an important concept in fluid mechanics because it helps determine the stability and equilibrium of a body in a fluid.

3. How do I calculate the center of pressure in an equation?

To calculate the center of pressure, you need to know the pressure distribution on the body and the area of each pressure distribution. The center of pressure can be found by taking the moment of each pressure distribution and dividing it by the total force. This will give you the distance from the reference point to the center of pressure.

4. What are some common applications of solving for 3-22a in equations?

Solving for 3-22a is commonly used in various fields such as engineering, physics, and mathematics. It can be used to determine the stability of structures, analyze fluid flow, and solve for unknown variables in mathematical equations.

5. How can I check if my solution for 3-22a is correct?

You can check your solution for 3-22a by plugging your answer back into the original equation and simplifying it. If your solution satisfies the equation, then it is correct. You can also use a graphing calculator to graph the equation and check if your solution is a point on the graph.

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