Your 'conservation of momentum' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your optional message or comment: **
resubmit v2.0
could you check my work so far, especially the box labeled with $$$$$ and ****
** Distances from edge of the paper to the two marks made in adjusting the 'tee'. **
.35 cm, .4cm
.4 cm
+-.05
** Five horizontal ranges of uninterrupted large ball, mean and standard deviation and explanation of measuring process: **
12.9, 13.2, 13.4, 13.6, 13.62,
13.34, 0.3011
to obtain my results i rolled the big ball down the incline and allowed it to hit the floor. I marked where it hit the floor each time.
** 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. **
9.9, 10.3, 10.5, 11.1, 11.5 ( big ball )
12.2, 12.3, 12.6, 12.8, 13.1 ( small ball )
12.60, 0.3674 ( small ball )
10.66, 0.6387 ( big ball )
** Vertical distance fallen, time required to fall. **
62.42 cm - ball 1, 62.78 cm - ball 2
.357 s, .358 s
To determine just how far the balls feel I used Pyth Theory. The distance from the table to the floor was 61.5 cm (A^2). I then took the avg distance (B^2). I added A^2 + B ^2 and received C^2. I took the squareroot of C^2 and got the total distance.
61.5 ^ 2 + 10.66 ^ 2 = square root of ( 3782.25 + 113.64 ) = 62.42 cm
61.5 ^ 2 + 12.60 ^ 2 = square root of ( 3782.25 + 158.76 ) = 62.78 cm
To determine the time I used an equation for uniform acceleration:
x = x 0 + v 0 t + 1 / 2 a t ^ 2
62.42 = 0 + 0 + 1/2 * 980 cm / s ^2 * t ^ 2
.357 = t
x = x 0 + v 0 t + 1 / 2 a t ^ 2
62.78 = 0 + 0 + 1/2 * 980 cm / s ^2 * t ^ 2
.358 = t
Note: you told me that Pyth Theory would not work here, but I could keep this stat just because it is close enough to the exact value.
** 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. **
$$$$$$UNSURE OF ANSWERS HERE...I will try to explain how I obtained these values the best I can so you can asst me (sorry I had to spread these out on more than one line)
***LINE ONE***
(length of ramp / time) 29.68 cm / s
(length 1st ball travels from ramp to edge of table = 4 cm) / .357 s = 11.20 cm/s
(length 2nd ball travels from straw to edge of table = 2 cm / .358 s = 5.59 cm/s
To get the horizontal velocity of a ball, you should be dividing the horizontal distance traveled during the .36 seconds of its fall to the floor by the .36 sec it takes. This gives you horizontal displacement / time interval = ave horiz velocity. Since horiz velocity is very nearly constant, this will be very nearly equal to the velocity immediately after the collision.
You don't report any horizontal ranges of 4 cm or 2 cm, so it's not clear where those numbers come from.
***LINE TWO***
10.66 + 0.6387 = 11.30 cm / .357 = 31.65 cm/s
10.66 - 0.6387 = 10.02 cm / .357 = 28.07 cm/s
***LINE THREE***
Length big ball travels from ramp to edge of table
velocity should remain consistent w/ velocity going down ramp = 28.68 cm/s
***LINE FOUR***
distance/duration = 2 cm / .357 = 5.6 cm/s
It doesn't take .357 sec for the ball to travel the 2 cm to the edge of the table
** 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 = m v
m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2
u1, u2, v1 and v2 are all quantities you should have determined from your data, in the preceding set of calculations
** 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. **
** Diameters of the 2 balls; volumes of both. **
** How will magnitude and angle of the after-collision velocity of each ball differ if the first ball is higher? **
** Predicted effect of first ball hitting 'higher' than the second, on the horizontal range of the first ball, and on the second: **
** 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: **
** What percent uncertainty in mass ratio is suggested by this result? **
** 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? **
5 hours so far
** Optional additional comments and/or questions: **
See my notes on what you've done so far.