Finding Temperature with Speed?

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To prove that a soccer ball cannot catch fire, the discussion centers on determining the speed required to reach the ignition temperature of leather, which is 212 degrees Celsius. The fastest recorded kick is 221 km/h, but there is no straightforward equation linking speed and temperature due to the complexities of frictional heating and wave drag. The conversation suggests calculating the viscous drag on the ball and the work done to overcome it, followed by using the specific heat of the ball's material to find the temperature rise. Ultimately, achieving the necessary speed to ignite the ball may require an impractically powerful kick that could deform it. The conclusion emphasizes that while theoretical calculations can be approached, practical application remains challenging.
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I'm trying to prove that a soccer ball cannot catch on fire. I'm trying to prove that by determining how fast a ball needs to go to reach that temperature, then comparing it with the fastest kick and its temperature. Right now I know that leather ignites at 212 degrees Celsius and that the fastest kick was measured at 221 km/h. How exactly would I determine the speed of an object with the temperature and vice versa. An equation should be all I need, I've tried looking for one but to no avail. Thanks.
 
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alucrid said:
How exactly would I determine the speed of an object with the temperature and vice versa. An equation should be all I need, I've tried looking for one but to no avail.

Why do you think there is a one-to-one relationship between temperature and speed? If you heat a soccer ball, it doesn't start moving.
 
Vanadium 50 said:
Why do you think there is a one-to-one relationship between temperature and speed? If you heat a soccer ball, it doesn't start moving.

Oh, I wasn't thinking that. I was just saying an equation that had both speed and temperature in it so I can solve for the missing variable. If it includes other information I could easily find that out, i.e. mass of a soccer ball, etc. So with the temperature I could solve for the speed and with the speed I could solve for the temperature.
 
Supersonic aircraft start getting noticeably hot at about 1500 mph. Actually catching fire might require 2000mph or so. But there is no simple equation for this. It's a matter of frictional heating and wave drag. http://en.wikipedia.org/wiki/Wave_drag
 
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On a very high level you would need a few things. But as others said - there is no "easy" equaton. And I doubt you will get a good answer because the velocity might require an extremely powerful kick that may deform the fotball for good. However academically thinking I would approach the problem like this:

1. Calculate the viscous drag by the air on the football. Calculate the work done by the foot ball to overcome this drag (force x distance). Assume a straight path with uniform velocity or a projectile motion depending on how simple or how realistic treatment you are looking for.

2. Use the specific heat of the football material to calculate the temperature rise. And bingo this equation is what you may be looking for.

-SNB
 

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