Weight of a baseball...

[Externet]

Say a baseball weighs 150 grams. A pitcher can throw it about 80 metres away.
If it was made 50 g lighter, would the pitcher reach farther ?
If it was made 50 g heavier, would the pitcher reach farther ?

For sure if the baseball was a 2 g paper ball, the pitcher would reach perhaps only 8 metres away.
For sure if the baseball was a 5 Kg solid lead ball, the pitcher would reach perhaps only 8 metres away.

How could a baseball weight be 'tuned' to reach farther, getting the most kinetic energy from a pitcher arm ?

... Or is it already weight-tuned as designed ?

[Sensei]

Suppose so pitcher is accelerating 150 gram ball to 200 km/h (his max).

200 km/h = 200,000 m/h = 55.56 m/s

 

[math]E.K.=\frac{1}{2}*m_1*v_1^2 = \frac{1}{2}*0.15*55.56^2=231.5 J[/math]

That's energy he has to, at least, spend on acceleration.

 

Replace equation with different mass of ball:

[math]231.5 J = \frac{1}{2}*0.1*v_2^2[/math]

[math]v_2=68\frac{m}{s}[/math]

 

During flight ball will be decelerating due to air resistance, and gravitational attraction, and losing kinetic energy with time.

Area contacting with air will have influence how fast or slow it'll be happening. Solid metal has large density, so ball would have pretty small radius and small area (in comparison to non metal equivalent with the same mass).

But not if we throw ball in cosmic space. That's why astronauts must have their tools on wire, otherwise they would fly away.

Edited January 12, 2015 by Sensei

[Externet]

...Solid metal has large density, so ball would have pretty small radius and small area (in comparison to non metal equivalent with the same mass)....

 

Thanks.

Please do not introduce a change the diameter of the ball or aerodynamic characteristics. Keep the same as a standard baseball, 'tuning' only its weight. I did not specify thinking would be common sense related to the original post. Whatever a solid lead baseball weight be (if not ~5Kg.)

...Replace equation with different mass of ball:

[math]231.5 J = \frac{1}{2}*0.1*v_2^2[/math]

[math]v_2=68\frac{m}{s}[/math]

 

The equation tells me a 2 gram paper ball will be faster. But we know it will not reach farther. Am right or wrong?

[swansont]

There's more to it than simply the kinetic energy. The muscles in the body need to get the arm moving to a certain speed and there's a limit to that, even as the mass of the ball goes to zero.

[imatfaal]

I make it that if the arm can deliver 145 joules in increased KE (which is a 100mph pitch of a standard baseball) and there are no limits to arm speed (which of course there are) then the best mass would be around 85 grams. At less than 85 grams then the air resistance takes too high a toll and the ball loses horizontal velocity too quickly - at more than 85 grams the initial velocity is too low. This is basis a two metre high release point with a strictly horizontal trajectory

The initial velocity varies with the inverse root of the mass.

 

[latex]v_{initial}= \sqrt {\frac{2 \cdot E_{kinetic}}{m}}[/latex]

 

The deceleration due to air resistance varies with the inverse of the mass

 

[latex]a_{air}=- \frac {\rho \cdot A \cdot C \cdot v^2}{2m}[/latex]

rho is the density of air, A is the cross-sectional area, and C is a shape related dimensionless constant

[Externet]

Thanks. Those equations explain it.

 

 

I wonder how would a real world baseball game be like using a ~85 gram ball.

[imatfaal]

Thanks. Those equations explain it.

 

 

I wonder how would a real world baseball game be like using a ~85 gram ball.

 

I hope my numerical approximation were correct! I wonder if I should have increased the angle of trajectory to be more realistic

 

Not hugely different in the speed of pitches reaching the batter (I am a Brit so I hope those terms are correct) - the differences in speed were not immense at the important area. You would find the ball swirling in the wind on long catches, the pitcher would be able to use side winds/head winds more, and the added armspeed would cause many more injuries until a whole new generation with different techniques grew up.

[Externet]

 

... the added armspeed would cause many more injuries...

More injuries to the pitcher arm; but less injuries on unintended body impact; right ?

[swansont]

 

the added armspeed would cause many more injuries until a whole new generation with different techniques grew up.

 

But wouldn't be much added arm speed. Wiffle balls are about 20 grams, but they aren't being thrown at ~200 mph, which is what you get for sqrt(150/20) * 80, which should be attainable for a decent high-school pitcher.

 

100 mph, yes.

http://www.baseball-fever.com/showthread.php?114069-97mph-Wiffleball

 

And there's much less stress on the arm, throwing the very light ball.

[imatfaal]

 

But wouldn't be much added arm speed. Wiffle balls are about 20 grams, but they aren't being thrown at ~200 mph, which is what you get for sqrt(150/20) * 80, which should be attainable for a decent high-school pitcher.

 

100 mph, yes.

http://www.baseball-fever.com/showthread.php?114069-97mph-Wiffleball

 

And there's much less stress on the arm, throwing the very light ball.

 

Wiffle Ball? Gonna have to wiki that.

 

You're correct the speed increase is not that dramatic - but to be honest my comments were more personal. I remember when I had been playing tennis and picked up a cricket ball (about 160g) I would throw it with no trouble - but I often found that after I had been playing cricket and threw a tennis ball I would whip the arm and hurt both shoulder and elbow. Anecdotal, purely personal, and almost certainly unimportant.

[Delta1212]

 

Wiffle Ball? Gonna have to wiki that.

 

You're correct the speed increase is not that dramatic - but to be honest my comments were more personal. I remember when I had been playing tennis and picked up a cricket ball (about 160g) I would throw it with no trouble - but I often found that after I had been playing cricket and threw a tennis ball I would whip the arm and hurt both shoulder and elbow. Anecdotal, purely personal, and almost certainly unimportant.

Wiffle ball is baseball, except with a light plastic ball and bat. The ball has holes in it to cut down on the problem of air resistance encountered by the much lighter hollow plastic.

[Strange]

Talking of high-speed baseball: https://what-if.xkcd.com/1/