Tonight's mythbuster

[bsfins]

Well, I wasn't sure where to put this...I was watching Mythbusters on the Discvery channel.They were doing a myth of a football filled with Helium would fly farther than one filled with air.

They cut a few scenes of a football team playing,and a kicker kicking a couple of field goals.I thought,hmm those look familiar,but they are based out of San Fran California. They showed them again,they are from a football game at the Local College,Missouri State,back when it was Southwest Missouri State.

I thought it pretty cool..

P.S. A helium filed ball doesn't fly as far,less mass. Force=Mass times Acceleration
If the force applied is equal,the one with the heavier mass tends to fly longer.Inertia is conserved.

I'm no engineer,something close to that,it's been over ten years since my physics classes

[Frimp]

I watched it. I was more impressed with catching the bullet with the teeth.

Kari is SO hot.

[Brian Fein]

I AM an engineer - so I'll say that "THEORETICALLY" the ball should fly farther.  Mostly because the WEIGHT of the ball is less, thanks to the buoyancy of the helium.  However, due to the buoyancy of the helium in comparison to the weight of the ball itself, the difference is negligible and the distance wouldn't be much more (i'm thinking fractions of an inch).  Its that whole Newton's law of gravity being that all object fall at the same rate.

I could work out the kinematics for you, if you want, but its all theoretical values.  Real world behaves much different than theory.

As for your F=ma - if F is held the same, and mass decreases, accelleration would have to increase.  But, even if accelleration increases, that just means more time in flight, no necessarily more distance.

[Dave Gray]

I AM an engineer - so I'll say that "THEORETICALLY" the ball should fly farther. Mostly because the WEIGHT of the ball is less, thanks to the buoyancy of the helium. However, due to the buoyancy of the helium in comparison to the weight of the ball itself, the difference is negligible and the distance wouldn't be much more (i'm thinking fractions of an inch). Its that whole Newton's law of gravity being that all object fall at the same rate.

I could work out the kinematics for you, if you want, but its all theoretical values. Real world behaves much different than theory.

As for your F=ma - if F is held the same, and mass decreases, accelleration would have to increase. But, even if accelleration increases, that just means more time in flight, no necessarily more distance.

I can't help but think that your reasoning is flawed. 

F=ma

F= Force given to the ball upon launch.
m= mass of the ball
a= acceleration of the launcher/ball (QB's arm)

The whole point of this would be how to find the difference in F between helium and air-filled.  Why would you assume that F stays constant?

We have 2 variables - m, because the mass of the ball changes with helium, as opposed to air, and possibly a, if the QB would be able to accelerate an object faster that had less mass.

[JVides]

I was watching Mythbusters on the Discvery channel.They were doing a myth of a football filled with Helium would fly farther than one filled with air.

Love that show

[Brian Fein]

I can't help but think that your reasoning is flawed.

F=ma

F= Force given to the ball upon launch.
m= mass of the ball
a= acceleration of the launcher/ball (QB's arm)

The whole point of this would be how to find the difference in F between helium and air-filled. Why would you assume that F stays constant?

We have 2 variables - m, because the mass of the ball changes with helium, as opposed to air, and possibly a, if the QB would be able to accelerate an object faster that had less mass.

No, you're backwards...

F is the force put onto the ball by the propellant (QB's arm, or i'd guess in this case a throwing machine).  The acceleration in the equation is the accelleration of the object as a result of the force.

The force would have to be the same.  If i put a 20 pound force on a block, its going to accellerate faster than if i put a 10 pound force on it.  Thus, if you vary the mass, you keep force constant and see what the accelleration is.  But regardless, they're not looking for accelleration, they're looking for distance.

I'm going to run the numbers out and see what the theories of kinematics and projectile motion have to say about this issue.

Trust me, I have a degree in this stuff.

[BeefStewert]

I agrre with Brian.  F would stay constant as long as the kicker hit the both balls the same.  Therefore acceleration on the ball is the same.  The other part of the formula, though, is that wind resistance on the football would be the same as well since the shape of the ball didn't change.  Therefore using F=ma again, constant wind resistance would equate to a quicker deceleration of the football.  So, the question is, is the increased deceleration greater than the icreased acceleration.  If it is, the ball won't fly as far.  Am I right, Brian?

[Dave Gray]

Looking at this again, I don't even think that F=ma is the correct equation to use in this scenerio.

It seems to me that the helium ball would be in the air longer (increasing t) but may not be moving as quickly on a horizontal path. 
I guess you're playing with two variables working against each other.

[BeefStewert]

Acceleration has the time (t) part of the equation you are talking about.  Remember the units for acceleration is distance/time^2.

There is no question that F=ma is the start of the problem.  The ball would not enter the air without the force of the kicker's foot hitting it and the distance that it goes in the air has a direct relationship with how hard he hits it. 

The other factor that needs to be held constant is the angle at which the kicking force is applied.  It sounds like the mythbusters were trying to test the helium theory so that should be the only variable in the test.

[BeefStewert]

It wouldn't be so confusing if we were talking about a football shaped ping pong ball, right?  I think it is the same idea - the wind resistance kills the flight. 

[Dave Gray]

The fact that it's a throw and not a kick, might make a difference...but I guess not.

The way I remember it, the equation for distance = 1/2 at^2.  Is that right?

[Brian Fein]

Here's what I came up with...

I made certain assumptions:
the force pushing the ball is 100 N = 22.5 lb
the ball is fired at a 45 degree trajectory angle
the time of throwing the ball is 0.1 seconds

The air-filled ball is about 0.12 kg more massive than the He ball.  Thus the accelleration under the 100 N force is higher, and the initial velocity coming off the throwing machine is higher.  Makes sense so far.

Plugging numbers into the equations of Kinematics -

The air ball should travel 454 m in 2.3 seconds (damn, this guy's got a gun)
The He ball should travel 870 m in 2.88 seconds (jesus!)

Of course alot of it has to do with the assumptions.  100 N is a decent force..  The numbers don't really make sense how they came out but I can't find a math error.

I'm gonna try doing it another way, here, in a few....

[Brian Fein]

The fact that it's a throw and not a kick, might make a difference...but I guess not.

The way I remember it, the equation for distance = 1/2 at^2. Is that right?

distance is 1/2 a t^2 + Vo t

Finding Vo, a and t is most of the problem.  All three are different for each ball.

And, since you don't know the initial velocity, but you know a force, you have to use conservation of energy and impulse and momentum to get there.  You use F dt / m to get Vo.

[Dave Gray]

Brian, I see how you're using force...that makes sense to me now.
So that's a constant -- okay.

But what is the time assumption you're using....the time it takes to actually throw the ball?

[Brian Fein]

yeah, that's the big jump.  The time over which the force is applied. 

If anyone else can give me another way to translate that 100N force into an initial velocity, I'm all ears.  I used the equation for impulse and momentum to do it

F*dt=m*Vo