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: **
I do not understand how to find the horizontal range. I have looked at previous experiments, for example, experiment 6, and I still do not know how to find the horizontal range. It this the same as the horizontal velocity? Should i use the timer program to find the times of the motion down the ramp and time of fall? And should i measure the distances down the ramp and of the fall? I do not know what information to use and what equation to put the information in to find the horizontal range. Could you please help me with this and maybe guide me through the process of finding it so i can do this experiment correctly? thank you for your time!
** Distances from edge of the paper to the two marks made in adjusting the 'tee'. **
** Five horizontal ranges of uninterrupted large ball, mean and standard deviation and explanation of measuring process: **
** 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. **
** Vertical distance fallen, time required to fall. **
** 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. **
** 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. **
** 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? **
** Optional additional comments and/or questions: **
Let me know if you didn't get my email addressing your questions. Here is a copy of what I sent you:
The horizontal range of the ball is the horizontal distance it travels while in free fall from the edge of the ramp, or point of collision (whichever applies) to the floor. You measure it by measuring straight-drop positions (below the edge of the ramp or below the point of collision, depending on which ball you are measuring in which part of the experiment) and landing positions, as you did in previous experiments involving the projectile behavior of the ball.
The Timer program is not useful in this experiment. From distance of fall and horizontal range you determine final velocity on the ramp, which is all that matters. Time spent on the ramp is irrelevant, as is the distance down the ramp.
You are using horizontal ranges to find the velocity of the first ball before collision, and the velocities of the two balls after collision.