Your work on conservation of momentum has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Distances from edge of the paper to the two marks made in adjusting the 'tee'.
10.2
75.3
My measurements might not very accurate because I first off do not know if I have set up the experiment correctly. Also, it is hard to measure exactly the distance from the top of the tee to the floor.
Five horizontal ranges of uninterrupted large ball, mean and standard deviation and explanation of measuring process:
14.3, 14.6, 14.2, 13.9, 14.4
14.28, .2588
To get the marks, I placed a carbon piece of paper on a plain white sheet and allowed the ball to hit the carpon paper when it fell off the ramp so that it would make a mark. I then measured the mark from the edge of the paper. To get the mean and standard deviation, I put the numbers into the data program.
Five horizontal ranges observed for the second ball; corresponding first-ball ranges; mean and standard deviation of the second-ball ranges; mean and standard deviation of ranges for the first ball.
10.9, 11.3, 11.1, 11.5, 11.3
13.8, 14.1, 14.0, 14.3, 14.2
According to your data here, it appears that the first-ball ranges were not much different than before, when the first ball did not collide with the second ball.
The first ball almost certainly would have traveled significantly less distance when colliding with the second ball. Can you clarify how you obtained these measurements?
11.22, .2280
14.08, .1924
To find these measurements, I used a similar procedure as before. I used the carbon paper to make the marks and then measured from the end of the paper to the marks. In order to specify which marks went together, I numbered them 1 through 5.
Vertical distance fallen, time required to fall.
73.4
.703125
To find the distance through which the two balls fell after collision, I measured from the place where the collision occured and the floor when they hit. To determine the time required to fall from this distance to rest, I used the timer program.
Velocity of the first ball immediately before collision, the velocity of the first ball after collision and the velocity of the second ball after collision; before-collision velocities of the first ball based on (mean + standard deviation) and (mean - standard deviation) of its uninterrupted ranges; same for the first ball after collision; same for the second ball after collision.
20.31, 20.02, 15.96
14.5388, 14.0212
14.2724, 13.8876
11.448, 10.992
First ball momentum before collision; after collision; second ball after collision; total momentum before; total momentum after; momentum conservation equation. All in terms of m1 and m2.
p = m1 (20.31 cm/s)
p = m1 (20.02 cm/s)
p = m2 (15.96 cm/s)
m1(20.31 cm/s) + m2(0 cm/s)
m1(20.02 cm/s) + m2(15.96 cm/s)
m1(20.31 cm/s) + m2(0 cm/s) = m1(20.02 cm/s) + m2(15.96 cm/s)
Equation with all terms containing m1 on the left-hand side and all terms containing m2 on the right; equation rearranged so m1 appears by itself on the left-hand side; preceding the equation divided by m2; simplified equation for m1 / m2.
m1(20.31 cm/s) - m1(20.02 cm/s) = m2(15.9 cm/s) - m2(0 cm/s)
m1 = m2(54.8276 cm/s)
m1/m2 = 54.8276
m1/m2 = 15.9 / 0.29
This is stating that for every .29 kg of mass of the second ball, there is 15.9 kg of mass of the first ball.
Diameters of the 2 balls; volumes of both.
3.2, 1.3
10.7233, 1.7698
How will magnitude and angle of the after-collision velocity of each ball differ if the first ball is higher?
If the center of the first ball is higher than the center of the second, it could cause the second ball to travel in a different path than expected. It would probably cause the ball to travel straight down. The speed will be less than what they would be if the centers were at the same height. The direction of the after collision would be pointed straight downward rather than out a little bit. If the center of the second ball is higher than the center of the first, then the second ball would probably travel in a more outward direction. The speed would probably be greater than if the centers were at the same height.
Predicted effect of first ball hitting 'higher' than the second, on the horizontal range of the first ball, and on the second:
The horizontal range of the first ball would probably would probably be the same as it always is. The horizontal range of the second however would probably be shorter than regular.
ratio of masses using minimum before-collision velocity for the first ball, maximum after-collision velocity for the first ball, minimum after-collision velocity of the second:
m1/m2 = -43.758
Take the momentum from the minimum before collision velocity of the first ball and set it equal to the total of the maximum after collision velocity for the first ball and the minimum after collision velocity of the second ball. Then, you solve to get m1/m2.
What percent uncertainty in mass ratio is suggested by this result?
80%
What combination of before-and after-collision velocities gives you the maximum, and what combination gives you the minimum result for the mass ratio?
In symbols, what mass ratio is indicated if the before-collision velocity of ball 1 is v1, its after-collision velocity u1 and the after-collision velocity of the 'target' ball is u2?
Derivative of expression for m1/m2 with respect to v1.
If the range of the uninterrupted first ball changes by an amount equal to the standard deviation, then how much does the predicted value of v1 change? If v1 changes by this amount, then by how much would the predicted mass ratio change?
Complete summary and comparison with previous results, with second ball 2 mm lower than before.
Vertical drop of the second ball, its mean horizontal range and the slope of the line segment connecting the two centers; the velocity given by the program based on mean; velocity interval for 2-mm decrease in 2d-ball height; velocity interval from the original run at equal heights; difference in the mean-based velocities; is new velocity significantly different than original?
Your report comparing first-ball velocities from the two setups:
Uncertainty in relative heights, in mm:
Based on the results you have obtained to this point, argue for or against the hypothesis that the uncertainty in the relative heights of the balls was a significant factor in the first setup.
How long did it take you to complete this experiment?
Optional additional comments and/or questions:
Most of your analysis looks very good, but I posed a question above about your reported ranges. Can you clarify by submitting a copy of this document, and inserting your clarification (or question, if you have one), marked with asterisks **** so I can easily identify it?