Watching the Indians play the Yankees on Friday night I was reminded of our discussion of momentum and impulse. The game was tied and was going into a 13th inning so tensions were high. At some point in the 13th inning, the umpire was hit in the head by a pitch that the batter had not swung at. Both the batter and catcher turned around and were visible concerned when this happened. When he was hit, the umpire stumbled backwards and braced his hands on his knees. He removed his helmet and collected himself for a few moments, then nodded that he was okay, put his helmet back on and resumed his position. There were many slow-motion replays of the impact during this time.
These replays made me think of the equations for momentum and impulse we talked about before fall break and the importance of wearing a helmet, especially in sports like baseball. If the baseball was around 142.5 grams (the average weight for a baseball) which is equal to 0.1425 kg, and Dellin Betances of the Yankees was pitching at approximately 82.4 mph (his average pitch velocity) which is equal to 36.8 m/s, then the momentum of the baseball was 5.244 kgm/s. I found this according to the equation p = mv.
If the umpire was not wearing a helmet, then the baseball would have hit him directly in the forehead and would have taken less time to stop. According to the equation, FΔt = Δp, the sum of the forces multiplied by the change in time will be equal to 5.244 kgm/s (the overall change in momentum). Thus, a shorter time for the ball to stop would correspond to a greater force. Because the umpire was wearing a helmet as is required, the time for the baseball to stop was greater. In this way, the force was distributed over a larger time so the overall force was smaller. Luckily, the umpire seemed to be okay after the incident. This is a good example of why helmets are so important!