Snow Day Blog

Last Tuesday, I decided to venture outside to my front porch and test conservation of momentum. I determined that the simplest method was to throw a snowball at a ball. I dug out a volleyball from my room, and a slightly-dusty cooking scale from our kitchen cabinet.  Using the scale, I found the approximate masses of the volleyball and the snowball. The volleyball weighted 260 grams and the snowball weighed 50 grams. I converted these to kilograms and got .260kg and .05kg. I threw the snowball at the volleyball…

… and missed.
I tried again…

… that's better.

I inserted the video in LoggerPro and used the program to find the velocities of the snowball and the volleyball. Everything was negative, so I flipped the axis in my calculations to eliminate the negatives for simplicity. Using LoggerPro, I found the average velocities in the x-direction for the snowball and the volleyball. The initial x velocity of the snowball was 5.362745475 m/s. The final x velocity of the volleyball was 0.6531473279 m/s. The volleyball was initially at rest so its initial momentum was 0. The snowball burst apart on impact so there was no real way to measure its final momentum. I just said it was 0.

pi = pf

m1v1i + m2v2i = m1v1f + m2v2f

m1= mass of the snowball = .05kg

m2 = mass of the volleyball = .260kg

pix = initial momentum in the x-direction

pfx = final momentum in the x-direction

pix = .05(5.362745475) + 0 = 0.26813727375 kgm/s

pfx = 0 + .260(0.6531473279) = 0.169818305254 kgm/s

Magnitude: 0.317389121385 kgm/s

Then, I found the average velocities in the y-direction. The snowball’s initial y velocity was 5.095071793 m/s and the volleyball’s final y velocity was 0.07838227402 m/s. Once again, I said the initial momentum of the volleyball was 0 and the final momentum of the snowball was 0.

piy = initial momentum in the y-direction

pfy = final momentum in the y-direction

piy = .05(5.095071793) + 0 = 0.25475358965 kgm/s

pfy = 0 + .260(0.07838227402) = 0.0203793912452 kgm/s

Magnitude:  0.255567429511 kgm/s

If momentum was conserved, the magnitude of the initial momentum would equal the magnitude of the final momentum. While the two values I calculated are close, they are not equal.

Some causes of this may be:

• Errors in measurements
• Rounding
• Errors in the velocity of the volleyball
• The points in LoggerPro were inaccurate because it was difficult to locate the center of the volleyball each time
• The snowball breaking apart

A major cause of this discrepancy may be a loss of energy. This makes sense since upon impact, the snowball burst apart. Energy would have went into sending the bits of snow flying in different directions instead of into the volleyball. This lost amount of kinetic energy can be determined.

I found the magnitudes of the velocities of the snowball and the volleyball. The magnitude of the initial velocity of the snowball was 7.3972153953672 m/s, and the magnitude of the final velocity of the volleyball was .65783372733804 m/s.

KEi of snowball + KEi of volleyball - KE lost = KEf of snowball + KEf of volleyball

KE = ½ mv2

½(.05)(7.3972153953672)2 + 0 + KElost = 0 + ½(.260)(.65783372733804)2

1.36796989014 - KElost = 0.056256877667

KElost = 1.31171301247 J

So 1.31171301247 J of energy were lost in the collision between the snowball and the volleyball.

This little experiment was pretty neat, even if my hands were near frozen solid after. It was interesting to see what we're studying in class applied in the real world, as cold as it may be.