Is there a formula I can apply in this case?

[abe]

ok, I'v never been on a physics site before but thought I'd look for one for help on this question... also forgive me but I probably won't be using proper physics terms... object A at a constant mass & speed is struck by object B which has a mass 5x that of object A and a speed 2x that of A. the result I can measure, my question is something like this, on paper how can I calculate what increase in speed of B will be required to overcome a decreese in mass of B? now applied to the real world... 70mph fast ball (5oz) 28oz bat swung at 140mph (end of bat) how much faster do you need the bat to travel with a 24oz bat to achieve the same result assuming all other variables remain the same. thanks Abe

 

[TVP45]

A good place to find out a little more about formulating your question would be Robert Adair's Physics of Baseball. Large libraries should have it.

 

[ogb p]

I can provide a formula that can be applied in this case. The formula is known as the conservation of momentum, which states that the total momentum of a system before and after a collision remains constant. In this case, the formula would be:

m1v1 + m2v2 = m1v1' + m2v2'

Where m1 is the mass of object A, m2 is the mass of object B, v1 is the initial velocity of object A, v2 is the initial velocity of object B, v1' is the final velocity of object A, and v2' is the final velocity of object B.

To solve for the final velocity of object B, we can rearrange the formula to:

v2' = (m1v1 + m2v2 - m1v1') / m2

In the case of the 70mph fast ball (5oz) and 28oz bat swung at 140mph, we can plug in the values and solve for v2':

v2' = (5oz * 70mph + 28oz * 140mph - 5oz * v1') / 28oz

Assuming all other variables remain the same, we can rearrange the formula again to solve for v1':

v1' = (5oz * 70mph + 28oz * 140mph - 28oz * v2') / 5oz

Using this formula, we can calculate the required increase in the bat's speed to achieve the same result with a 24oz bat. However, it is important to note that this formula is based on ideal conditions and may not account for all real-world factors. Other variables such as air resistance, friction, and the elasticity of the objects involved may also affect the outcome. Therefore, it is always important to conduct experiments and gather data in the real world to confirm the results of any formula.