in http://www.straightdope.com/mailbag/mbat.html, Ken misses the point of the question, i think. the question was, basically, can you hit a ball farther with a heavy bat or a light bat. Ken talks about how the force that you impart to the bat doesn’t depend on its weight. i’ll buy that to some approximation (*).
but the real question, i believe, revolves around how much force can be transferred from the bat to the ball. doing a quick thought experiment, if my bat weighs 2 tons, and i manage to accelerate it to go an inch per second, then when the ball contacts it, it’s not going to fly off at 100 miles per hour.
on the other hand, if my bat weighs just more than nothing, and i impart the same force to it, and it’s travelling several thousand miles an hour when it hits the ball, that ball’s going to fly.
i’m sure there are more factors to consider, but it seems like Ken just dropped, um, the ball.
(*) this assumes that the biomechanics don’t differ too much for different bat weights, that people are perfect machines, etc. as a thought experiment, how much could you accelerate that 2-ton bat in the real world?
Actually, dannyv is saying the opposite, that a lightweight bat will send the ball further. But I don’t think he’s right. If we have a multi-ton bat, and the collision between bat and ball is perfectly elastic (probably a good approximation for real baseball bats), and the bat is not moving at all, then the ball will bounce off the bat at the same speed it hit it at, i.e., nearly 100 MPH.
i think we’re all pretty wrong, actually, although samclem’s link helps out some.
let’s start with me. i missed ken’s line that samclem points out. i think the reason that i missed it is because everything leading up to that seems to say that bat mass doesn’t matter. but even his argument is bogus. F = ma. sure. but “We can affect the amount of force generated by either changing the mass (weight) of the bat, or the acceleration of the bat (bat speed).”? no way. acceleration ain’t speed. And what does this have to do with how much energy is transferred to the ball?
so i think ken may have gotten it right, but with incorrect supporting arguments.
my post makes some “frictionless plane” arguments that i think are invalid. but i’m not quite sure. reading samclem’s link has gotten me all befuddled…
so that takes care of ken being incomplete, and me being wrong. now on to chronos chronos makes another “frictionless plane” assumption in the perfectly elastic ball. which the link pretty handily discounts. the collision is hardly inelastic. and if the bat isn’t moving at all, then we’re not talking about batting, we’re talking about bunting (or something close).
back to the line of thought that i hope ken was trying to use. F=ma, v=at, K=1/2mv-squared. so Kinetic energy,
3 2
m t
K = ----
2
2F
assuming all fonts equal…
(where’s .eq when you need it?)
assuming that t is constant (when we start swinging the bat doesn’t depend on how heavy it is), and that F is constant (the person/machine has a flat torque curve - a big assumption!) we end up with K being proportional to mass cubed. so the amount of energy available to be transferred to the ball is much more with a heavier bat. i’m no good at non-elastic collision mechanics, but unless anyone wants to step up to the plate, i’ll assume that the difference in bat mass/speed doesn’t contribute as much to the energy transfer as the amount of energy to transfer.
so i’m back to ken was right, but didn’t support it very well. and i’ll crawl back in my hole and lurk.
I had a (very) minor in physics, but you’re making my head hurt.
Let me put it into words that seem logical to me. And If I’m mirroring Ken, so be it.
The most important thing in the equation of how far that ball is gonna go is bat speed. Period.
If you had a 36 oz. bat and a machine swung it at a certain fixed rate of speed ( x ), and a machine pitched a ball at a certain fixed rate of speed, then the ball (assumimng it hit the bat in the exact same spot) would go a certain fixed distance.
If you substituted a 46 oz. bat, but the machine was still swinging at the fixed rate of speed of x, and the pitching machine was still throwing the ball at x speed, the ball would go very slightly farther. I don’t think it would be significant.
Unless I’m wrong, Mark McGuire hit 500 ft. homeruns because he had muscles and size which allowed him to whip the bat around faster than most of his fellow players. Significantly faster than the average player. He had more bat speed.
m[sup]3[/sup]t[sup]2[/sup]
K = -------
2 F[sup]2[/sup]
Hint: use the code tag.
But I think your algebra is off.
a = F/m = v/t, v = Ft/m
K = 1/2 m v[sup]2[/sup] = 1/2 m (Ft/m)[sup]2[/sup] = m F[sup]2[/sup]t[sup]2[/sup]/2 m[sup]2[/sup]
K = F[sup]2[/sup]t[sup]2[/sup]/2m
Chronos, the link says a baseball has a coefficient of restitution of 0.5, so inelastic collision is not a safe assumption.
dannyv, Chronos was approximating the baseball hitting a wall (a multi-ton bat with zero velocity). Also, you are correct that speed does not equal acceleration. What I think Ken was trying to say is that the speed of the bat upon impact depends upon the acceleration of the bat, because the batter is basically accelerating the bat through the whole swing. He just didn’t say it explicitly.
I think when dealing with impacts, what’s important is not F=ma or KE, but rather momentum. That’s what I remember from my dynamics classes.
from personal playing experience, and not physics…I tried using heavier and lighter bats…what I’ve found is that I hit a ball farthest using the heaviest bat that I could swing at my maximum swing velocity.
to explain—there is a maximum rotational velocity that I can generate with my arms…depending on my strength, I can generate that speed with no bat…a 10oz bat…a20ozbat…etc…
I have to find the HEAVIEST bat that I can still generate my maximum (or nearly maximum) velocity. Obviously, swinging a 20oz bat at 100mph vs a 32oz bat at 100mph will give a greater distance with the heavier bat.
chronos makes another “frictionless plane” assumption in the perfectly elastic ball. which the link pretty handily discounts. the collision is hardly inelastic. and if the bat isn’t moving at all, then we’re not talking about batting, we’re talking about bunting (or something close).