Find the diameter of the piston at certain heights

[sgk777]

Homework Statement

A 56.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 130 kg football players at a height of 0.900 m. The diameter of the cheerleader's piston is 18.0 cm.

A) What is the diameter of the football players' piston if the cheerleader and football players are at the same height?

B) What is the diameter of the football players' piston if the football players are held to a height 0.900 m above the cheerleader?

Relevant Equations

F1/A1 = F2/A2 + pgh

I solved for part A by using the equation r2 = sqrt(m2/m1) * r1

im having trouble solving for part B, I know that you would use the equation F1/A1 = F2/A2 + pgh and solve for r2, but when I solved for r2, I got an undefined number. Can someone run me through this question?

 

[Lnewqban]

Welcome, @sgk777 !

We need you to post your calculations, please.

 

[sgk777]

Welcome, @sgk777 !

We need you to post your calculations, please.

A)

B)

F1/A1 = F2/A2 + pgh
(F1/A1 = F2/A2 + pgh)(A1 * A2) multiply both sides by A1 and A2 to cancel out the denominator
that gives:
A2F1 = A1F2 +A1A2(pgh)
subtract A1A2(pgh) from both sides:
A2F1 - A1A2(pgh) = A1F2
factor out A2:
A2(F1 - A1(pgh)) = A1F2
divide both sides by (F1 - A1(pgh)):
A2 = A1F2 / (F1 - A1(pgh))
solve for r2, where A1 = pi(r1)^2 and A2 = pi(r2)^2 and F1 = m1g and F2 = m2g.
that gave me:

when i plugged in the known values, i got an undefined number.

 

[sgk777]

redoing my calculations, i got this:

it doesnt seem reasonable though

 

[hutchphd]

It might be useful to write down the units. Try again, please.

 

[sgk777]

 

[hutchphd]

1. What units on 900 are required so that the equation makes sense?
2. Where did you get that number?
3. Are you using /mixing cm and m in tha same equation? Care is required.

 

[haruspex]

A2 = A1F2 / (F1 - A1(pgh))
solve for r2, where A1 = pi(r1)^2 and A2 = pi(r2)^2 and F1 = m1g and F2 = m2g.
that gave me:
View attachment 334444

How did $F1 - A1(pgh)$ become $1-A1(pgh)$? (I assume p is 900 kgm^-3.)