Answer :
The average recoil force exerted on the baseball pitching machine, calculated using the concept of impulse and change in momentum, is approximately 58.95 N.
To calculate the average recoil force exerted on the pitching machine by a baseball that it pitches, we first need to understand the concept of impulse. Impulse is the product of force and the time over which the force is exerted and it equals the change in momentum of the object.
The momentum p of an object is given by the product of its mass m and its velocity v. So, if a baseball of mass 0.15 kg is pitched with a speed of 39.3 m/s, its initial momentum pi is 0 kg sup>m/s (before being pitched), and its final momentum pf is m v = 0.15 kg 39.3 m/s after being pitched.
The change in momentum pf - pi is thus 0.15 kg 39.3 m/s. Since the balls are pitched at a rate of one every 0.1 seconds, the time interval t over which each impulse occurs is 0.1 seconds. So the average force F experienced by the pitching machine due to one ball is the change in momentum divided by the time interval.
F = (pf - pi) / t
Substituting the values we have:
F = (0.15 kg 39.3 m/s) / 0.1 s = 58.95 N
The average recoil force experienced by the machine for each pitch is thus approximately 58.95 N, directed opposite to the pitching direction.