Find the diameter of the piston at certain heights

  • #1
sgk777
4
0
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
1698536610892.png

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?
 
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  • #2
Welcome, @sgk777 !

We need you to post your calculations, please.
 
  • #3
Lnewqban said:
Welcome, @sgk777 !

We need you to post your calculations, please.
A)

1698538424520.png


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:
1698538729776.png

when i plugged in the known values, i got an undefined number.
 
  • #4
redoing my calculations, i got this:

1698539414334.png

it doesnt seem reasonable though
 
  • #5
It might be useful to write down the units. Try again, please.
 
  • #6
1698540728097.png
 
  • #7
  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.
 
  • #8
sgk777 said:
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.)
 

FAQ: Find the diameter of the piston at certain heights

1. How do you calculate the diameter of a piston at a given height?

To calculate the diameter of a piston at a given height, you need to know the geometry of the piston and the cylinder. If the piston is part of a conical or tapered shape, you can use similar triangles or trigonometric relationships. For a cylindrical piston, the diameter remains constant regardless of height.

2. What measurements are required to determine the diameter of a piston at various heights?

You need the initial diameter of the piston at a known height, the total height of the piston, and the shape of the piston (whether it is cylindrical, conical, or another shape). For tapered pistons, additional measurements like the angle of taper or the base and top diameters are required.

3. Can the diameter of a piston change with height in a cylindrical piston?

No, in a cylindrical piston, the diameter remains constant at all heights. The diameter change with height typically applies to conical or tapered pistons.

4. How does the shape of the piston affect the calculation of its diameter at different heights?

The shape of the piston significantly affects the calculation. For cylindrical pistons, the diameter is constant. For conical or tapered pistons, the diameter varies with height, and you can calculate it using geometric relationships or trigonometric functions based on the taper angle or the dimensions of the base and top diameters.

5. Is there a formula for finding the diameter of a conical piston at a certain height?

Yes, for a conical piston, the diameter at a certain height can be found using the formula: \( D_h = D_b + \frac{(D_t - D_b) \cdot h}{H} \), where \( D_h \) is the diameter at height \( h \), \( D_b \) is the base diameter, \( D_t \) is the top diameter, and \( H \) is the total height of the piston.

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