Diameter of football player's Piston

In summary, the problem involves a 54.0kg cheerleader using an oil-filled hydraulic lift to hold four 120kg football players at a height of 1.30m. The diameter of the cheerleader's piston is 19.0cm and the goal is to find the diameter of the football players' piston. The equation (F1/A1)=(F2/A2) is used, where F1 is the force of the cheerleader and players, and A1 is the area of the cheerleader's piston. However, the answer is incorrect and further clarification is needed on the setup and the relationship between the pistons.
  • #1
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Homework Statement



A 54.0kg cheerleader uses an oil-filled hydraulic lift to hold four 120kg football players at a height of 1.30m . If her piston is 19.0cm in diameter, what is the diameter of the football players' piston?

Homework Equations



I think the only equation needed is (F1/A1)=(F2/A2). I didn't think that density or the height being raised was relevant in this problem

The Attempt at a Solution



So first I rearranged the formula so that ((F2A1)/F1)= A2.

I know that the force is the weight of the cheerleaders(54 kg) and the four football players( 480). The value g cancels out, so I'm left with ...

(480pi(r1)^2)/54= pi(r2)^2

so by subbing in for r1 ( .095m) I get...

.252=pi(r2)^2

I then rearrange the formula to solve for r2

r2=sqrt(.252/pi)=r1=.283

then to get the diameter I multiply by two to get .566m or 56.6 cm

This however, is not the right answer. Can somebody please help?
 
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  • #2
Welcome to PF;
It depends on how she is holding who up with the lift ... and what the relationship is between her piston and the player's piston. You need to be explicit about the setup.

You seem to be saying that the pressure on the player's piston is the same as the pressure on the cheerleaders. Why?

Notice that the pi's cancel out in the first equation you have them in?
The ratio of the radii is also the ratio of the diameters too.

Lastly; how do you know your answer is incorrect?
 

1. What is the diameter of a football player's piston?

The diameter of a football player's piston refers to the size of the muscle in their leg that helps them generate power and speed. It can vary greatly depending on the individual player's body composition and fitness level, but on average, it is around 2-3 inches in diameter.

2. Why is the diameter of a football player's piston important?

The diameter of a football player's piston is important because it directly affects their performance on the field. A larger piston diameter can generate more power and speed, allowing the player to run faster and jump higher. It also contributes to their overall strength and agility.

3. How is the diameter of a football player's piston measured?

The diameter of a football player's piston is typically measured using a caliper or a measuring tape. The measurement is taken at the thickest part of the muscle, usually around the thigh area, while the player is flexing their leg muscles.

4. Can the diameter of a football player's piston be increased?

Yes, the diameter of a football player's piston can be increased through strength training and muscle building exercises. By consistently working out and targeting the leg muscles, players can increase the size and strength of their pistons, ultimately improving their performance on the field.

5. Are there any disadvantages to having a larger diameter piston?

While a larger diameter piston can provide certain advantages on the field, it can also make the player more prone to injuries such as muscle strains or tears. It also requires a lot of maintenance and proper training to avoid muscle imbalances and maintain proper alignment of the leg muscles.

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