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Momentum in a Collision Between Two Exercise Balls

Nikki Nappi
Period E

For my snow day blog, I decided to test the momentum of a collision between two exercise balls. I have always wanted to run at someone with an exercise ball, and this seemed like the perfect excuse to do it. So, I went to Walmart, bought two exercise balls, both of the same diameter, both weighing about 2 pounds, or 0.91 kg. I found this, since the box had no information about the weight of the ball, by first weighing myself without the ball, then weighing myself with the ball, and subtracting the difference, which was two pounds. Google converter then told me this was about 0.91 kg. However, I know that the weight of the ball is not the same as the mass of the ball. So I did some calculations.



Then, my mom and I ran at each other. I set up a tripod and took a video of the collision on my phone, and used logger pro to find the velocity of our balls before and after the collision. (Since the balls went flying out of our hands after the collision, I decided to exclude our masses from the mass in the momentum calculations, just to show that the mass of the ball stayed the same throughout the entire collision. Also, my mom refused to tell me her weight.) In logger pro, I measured the width of my walkway outside and marked one meter from one spot to the other. I then put this into logger pro and began plotting points from the center of the ball.



My mom's ball before the collision -
Velocity : 0.4028 m/s
Momentum : 0.037 kg m/s
p = mv
p = 0.0929 kg * 0.4028 m/s
p = 0.037 kg m/s




My ball before the collision -
Velocity : -0.688 m/s (since I was running to the left, it is actually positive )
Momentum : 0.0639 kg m/s
p = mv
p = 0.0929 * -(-0.688)
p = 0.0639 kg m/s


My mom's ball after the collision -
Velocity : -0.5565 m/s (since it went to left, it will actually be positive)
Momentum :  0.51699 kg m/s
p = mv
p = 0.0929 kg * -(-0.5565 m/s)
p = 0.51699 kg m/s


My ball after the collision -
Velocity : 0.596 m/s
Momentum : 0.055 kg m/s
p = mv
p = 0.0929 kg * 0.596 m/s
p = 0.055 kg m/s

While this collision appears to be an inelastic collision, I wanted to confirm this information. In an inelastic collision, we know kinetic energy is not conserved. We could check if this collision was an inelastic collision using the formula Einitial = Efinal for both balls. If it is an inelastic collision, like I suspect, this equation will not be true. Since the balls went straight up after, the final energy is potential energy. This requires a height, which was very hard to measure exactly in this situation, so I am going to take an educated, VERY approximated, guess about the height of the ball. 

In this picture, which is about the peak height of the ball, the balls appear to be double my height in the air. I am 5'4, so the ball's height is ABOUT 10 feet 8 inches in the air. This is about 3.25 meters. 

KE = PE 
(1/2 mv^2) + (1/2 mv^2) = 2 *(mgh)  
(1/2 *  0.0929 *0.688 ^2) + (1/2 * 0.0929 * 0.4028 ^2)  = 2 * 0.0929 * 9.8 * 3.25 
0.02199  + 0.0075 = 2 * 2.958 
0.0295 J = 5.916 J 

This statement is not true, proving this collision to be an inelastic collision. There are a lot of areas where this could have gone wrong, including the measurement of the balls height and the fact that the balls hit me and my mom at different points, which affected the measurement of the velocity in logger pro. However, the difference in energy is so vast that even with these errors, this collision can still be proven to be an elastic collision. 

As we learned in class, momentum is conserved in this collision, but energy is not. This energy was lost through sound, by pushing me and my mom back when we collided, possibly friction between the balls, and in more areas. 

If our velocities were increased and we ran faster at one another, the balls would have gone higher into the air, and we most likely would have been pushed back further, maybe even being knocked on to the ground. My brother and I tested this theory afterwards, running almost full speed at one another. He got knocked down and the balls went flying in opposite directions, mine going as far as into the street, proving this theory. 



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