Softball Bat Speed vs Bat Weight

[arsenal1021]

Ok So I have been wondering this for awhile.

Could someone help me find an equation to figure this out.

I play slowpitch softball and was curious about swing speed and the weight of the bat.
If we keep the mass of the ball constant (.198 kg), and the pitch speed constant (8.94 m/s), and have 4 different bats (a22oz-b24oz-c26oz-d28oz):(a=.624kg b=.680kg c= .737kg d=.794kg) that correspond with swing speeds (fastest swing speed for the lightest bat) let's call them 40-50-60-70mph so(17.88m/s-22.35m/s-26.82m/s-31.29m/s). so...
.624kg@31.29m/s - .680kg@26.82m/s - .737kg@22.35m/s - .794kg@17.88m/s.

So I guess I am trying to find the velocity of the ball after the collision with the bat.

at some point with different swing speeds does the lighter massed bat become infective vs the higher massed bat??

Could I put all of this into a graph?

Does anyone have an equation for this??
(m1v1b + m2v2b = m1v1a + m2v2a) ? if it is this I don't know how to find the velocity of the bat after collision.

m1:mass of ball (.198kg)
v1b: Velocity Of ball before collision (8.94)
m2: mass of bat before collision
v2b: velocity of bat before collision
v1a: velocity ball after collision
v2a: velocity bat after collision ((??)another equation??)

please help me, thanks

 

[Andrew Mason]

Ok So I have been wondering this for awhile.

Could someone help me find an equation to figure this out.

I play slowpitch softball and was curious about swing speed and the weight of the bat.
If we keep the mass of the ball constant (.198 kg), and the pitch speed constant (8.94 m/s), and have 4 different bats (a22oz-b24oz-c26oz-d28oz):(a=.624kg b=.680kg c= .737kg d=.794kg) that correspond with swing speeds (fastest swing speed for the lightest bat) let's call them 40-50-60-70mph so(17.88m/s-22.35m/s-26.82m/s-31.29m/s). so...
.624kg@31.29m/s - .680kg@26.82m/s - .737kg@22.35m/s - .794kg@17.88m/s.

So I guess I am trying to find the velocity of the ball after the collision with the bat.

at some point with different swing speeds does the lighter massed bat become infective vs the higher massed bat??

Could I put all of this into a graph?

Does anyone have an equation for this??
(m1v1b + m2v2b = m1v1a + m2v2a) ? if it is this I don't know how to find the velocity of the bat after collision.

m1:mass of ball (.198kg)
v1b: Velocity Of ball before collision (8.94)
m2: mass of bat before collision
v2b: velocity of bat before collision
v1a: velocity ball after collision
v2a: velocity bat after collision ((??)another equation??)

please help me, thanks

The equation you want to use is:

m_{ball}v_{ball} = F_{avg}t_{contact}

The force on the bat is determined by the hardness of the bat, compression of the ball and by the force of the batter's arms/hands on the bat as the bat is striking the ball. The mass of the bat should not make that much difference. The time of contact is determined by the speed of the bat - the longer the bat remains in contact with the ball, the greater the ball speed. The faster the ball speed and bat speed, the greater the compression of the ball and the longer the bat remains in contact with the ball.

AM