# Debate! Which will fly further: Golfball, Baseball, Mouseball

Hello All,

I have a small Office Debate on which object would fly further when struck with a baseball bat.

The three objects that are being compared are:

Baseball
Golf Ball
Mouse-ball (The old computer mice had a rubber ball inside, but if you remove the rubber you get the solid steel ball that we are comparing)

My associates believe that the golf ball would fly the furthest, if all were struck with equal force by a baseball bat. They also believe that the baseball would fly further than the mouse-ball.

With what physics equations would we be able to prove which object would fly the furthest?

And, which object would indeed fly the furthest and in what order?

Thanks!

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rcgldr
Homework Helper
The amount impulse from equal average force depends on how compressable the ball is. The steel ball is very stiff, so the issue for the steel ball case is how elastic is the collision with the bat since the bat will compress more than the steel ball.

A better comparason might assume that all three balls start off with the same initial velocity. There's also the issue that within a range of speed, a rough or dimpled ball has lower total drag due to a transition into turbulent flow which reduces the size of the wake. At sufficiently higher speeds, the smooth ball has also transitioned into turbulent flow and ends up with a smaller wake than a rough ball.

jedishrfu
Mentor
First there was an old discussion on a similar topic:

My guess is the baseball is out because it transforms some of the energy imparted by the bat into internal heat as it deforms slightly.

The golf ball deforms less has some aerodynamic features (the dimples) and so will travel further than the baseball.

The steel mouse ball will probably travel the furthest given that it will deform the least has a smooth surface and is the lightest of the three.

I am assuming the bat provides the same momentum to each ball and so the steel mouse ball being the lightest will travel the furthest.

Conservation of momentum law

MY money is on golf ball - the other two were designed under different parameters, whereas the GB is continually re-engineered for maximum flight.

The golf ball and mouse ball have roughly the same mass. So that means they will be launched with similar initial velocities. But the mouse ball is about two times smaller in diameter, so its cross-section is four times less. According to the top diagram at http://www.grc.nasa.gov/WWW/k-12/airplane/dragsphere.html , the rough surface of the golf ball may help reduce the drag twofold maximum, which does not compensate for the 4-times difference in the cross-section. So I would say the mouse ball should be the winner.

jedishrfu
Mentor
The golf ball and mouse ball have roughly the same mass. So that means they will be launched with similar initial velocities. But the mouse ball is about two times smaller in diameter, so its cross-section is four times less. According to the top diagram at http://www.grc.nasa.gov/WWW/k-12/airplane/dragsphere.html , the rough surface of the golf ball may help reduce the drag twofold maximum, which does not compensate for the 4-times difference in the cross-section. So I would say the mouse ball should be the winner.
How is it affected using the steel center of the mouse ball with the rubber stripped away as described by the OP isn't that more like 3 to 4 times smaller and hence the steel mouse ball would go farther?

I would have to say the golf ball would travel the furthest. the baseball has to much mass and would travel the shortest distance due to air resistance. the question would be what type of bat is being used? aluminium or wood? because of the density of the mouse ball as well as the material there would be no rebound when hit, it would dent an aluminium bat, and could possibly break a wood bat. the golf ball would rebound off of either bat style the best so it would go furthest.

Well, I do not know exactly how much rubber/silicone padding the typical mouse ball really has.

Its a small layer of rubber/silicone, I would say 1/8th of an inch or so.

However,we are only talking about the steel core only in this scenario.

That sort of padding does not change the mass perceptibly, so the only two factors in flight are the roughness of the surface and the cross-section, the combination of which I think is superior to that of a golf ball. I am betting on the mouse ball.

IMO due to the golfballs has higher coefficient of restitution - being struck by a baseball bat, it will leave with greater initial velocity.

It is not the ball that has a coeff. of rest. It must be the system ball + bat. And are there any trustworthy coef. of rest. data on golfball + baseball bat systems? Or steel ball + baseball bat systems for that matter? I do not think so.

rcgldr
Homework Helper
According to the top diagram at http://www.grc.nasa.gov/WWW/k-12/airplane/dragsphere.html , the rough surface of the golf ball may help reduce the drag twofold maximum ...
That only happens in the speed range where Re (Reynold number) is around 10^5. For air Re ~= 70,000 (s/m^2) v l, where v is velocity in meters / second and l is length in meters. For a golf ball, l ~= .04267 meter, so if I've done my math correctly Re = 10^5 occurs about 33.48 m/s or 120 kph. At speeds much above or below this speed, the smooth ball has less drag (due to smaller wake).

As for the bat, you could consider an aluminum alloy bat that would be near elastic and not dent when striking the steel ball.

That only happens in the speed range where Re (Reynold number) is around 10^5. For air Re ~= 70,000 (s/m^2) v l, where v is velocity in meters / second and l is length in meters. For a golf ball, l ~= .04267 meter, so if I've done my math correctly Re = 10^5 occurs about 33.48 m/s or 120 kph. At speeds much above or below this speed, the smooth ball has less drag (due to smaller wake).
I do not disagree. I stated that roughness may help reduce drag, but even with that reduction the mouse ball fares better.

I do think we are talking about the regime where that happens, otherwise golfballs would not have dimples.