#$&*
phy121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
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Also conduct a total of 10 timings:
Conduct 5 timings for your setup with the ramp in its original direction. As accurately as possible, use the TIMER program to determine the time required for the ball to travel the length of the ramp.
Then conduct 5 more timings with the ramp reversed (i.e., move the dominoes to the other end, which will reverse the downward direction)..
To analyze your data, you may again find the data analysis program to be the quickest way to get results. However note that if you have sufficient skills with spreadsheets and/or computer algebra programs, you may at some point find that you might prefer to use them to perform some of the repetitive calculations.
First, find the positions of each of the marks newly made on your papers. Each position will be measured along a single axis, and will be relative to the origin point you have selected.
Report in the first line, in comma-delimited format, the first 3 positions, relative to the origin, obtained from the 10-cm trials for the 2-domino ramp.
If you place a copy of this line into the data window of the data analysis program and click the 'Change Rows To Columns' button the rows will change to columns and you can then click the Mean and Standard Deviation button to obtain the mean and standard deviation of these positions.
Do so and report the mean and standard deviation, in comma-delimited format, in the second line below.
---------->>>>> 10 cm 2 dom
Your answer (start in the next line):
#$&*
Using the same format report the same information for the first 20-cm trials on this ramp:
---------->>>>> 20 cm 2 dom
Your answer (start in the next line):
#$&*
Using the same format report the same information for the first 30-cm trials on this ramp:
---------->>>>> 30 cm 2 dom
Your answer (start in the next line):
#$&*
Flip a coin. If it comes up 'heads' then do the next step. If it comes up 'tails' skip the next step.
Using the same format report the same information for the 10-cm trials on the reversed ramp, still using the 2-domino stack:
---------->>>>> 10 cm 2 dom rev
Your answer (start in the next line):
#$&*
If you got 'heads' when you flipped the coin, do the next step. If it was 'tails' then skip.
Using the same format report the same information for the 20-cm trials on the reversed ramp:
---------->>>>> 20 cm 2 dom rev
Your answer (start in the next line):
#$&*
If you got 'heads' when you flipped the coin, do the next step. If it was 'tails' then skip.
Using the same format report the same information for the 30-cm trials on the reversed ramp:
---------->>>>> 30 cm 2 dom rev
Your answer (start in the next line):
#$&*
Using the same format report the same information for the 10-cm trials on the 4-domino setup, with the ramp in its original orientation:
---------->>>>> 10 cm 4 dom
Your answer (start in the next line):
14.6,14.7,14.2,14.7,14.4
#$&*
Using the same format report the same information for the 20-cm trials on this ramp:
---------->>>>> 20 cm 4 dom
Your answer (start in the next line):
19.1, 18.5, 18.6, 19.0, 19.3
#$&*
Using the same format report the same information for the 30-cm trials on this ramp:
---------->>>>> 30 cm 4 dom
Your answer (start in the next line):
23.8, 24.0, 23.9, 24.1, 24.1
#$&*
If you got 'heads' when you flipped the coin earlier, then you can skip. If it was 'tails' then do the next step..
Using the same format report the same information for the 10-cm trials on the reversed ramp, still using the 4-domino stack:
---------->>>>> 10 cm 4 dom rev
Your answer (start in the next line):
14.0,14.6,14.2,14.8,14.7
#$&*
If you got 'heads' when you flipped the coin earlier, then you can skip. If it was 'tails' then do the next step..
Using the same format report the same information for the 20-cm trials on the reversed ramp:
---------->>>>> 20 cm 4 dom rev
Your answer (start in the next line):
20.6, 21.3, 20.8, 21.2, 21.5
#$&*
If you got 'heads' when you flipped the coin earlier, then you can skip. If it was 'tails' then do the next step..
Using the same format report the same information for the 30-cm trials on the reversed ramp:
---------->>>>> 30 cm 4 dom rev
Your answer (start in the next line):
24.7,24.8, 25.3,25.2, 24.9
#$&*
Report here the mean and standard deviation of the straight-drop positions, which will be used with the mean and standard deviations of the landing positions your reported above to find horizontal projectile distance information in each set of trials.
---------->>>>>
Your answer (start in the next line):
2.88, 0.45
#$&*
For each set of 5 trials you will now need to calculate the velocity of the ball as it comes off the ramp. There are various ways to calculate the velocity and its uncertainty. Here the velocity calculation for each setup will be based on the mean horizontal distances.
First calculate the mean horizontal distance traveled by the ball after leaving the end of the ramp, for each starting position on each setup (you had 3 starting positions for each setup).
• Report in the first line, in comma-delimited format, the mean horizontal distances for the 10-, 20- and 30-cm trials for the 2-domino setup with the original ramp orientation.
• In the second line use the same format to report the same information for the 2-domino setup with the reversed ramp orientation.
• In the third line report for the 4-domino setup with the original ramp orientation.
• In the fourth line report for the 4-domino setup with the reversed ramp orientation.
You will have skipped either the second or fourth setups. Just type 'skipped' for that line.
---------->>>>> mean horiz dist for each of 4 steps
Your answer (start in the next line):
skipped
skipped
14.52,18.9, 23.98
14.46,21.08, 24.98
#$&*
Using the 'Experiment-Specific Calculations' button of the data program, select 1, as you did in the preceding experiment, and respond with the information necessary to calculate the speed of the ball at the end of the ramp, based on the mean distance observed for your first set of 5 trials.
Repeat this process for each of the remaining 11 trials.
Report the resulting speeds in the box below, three speeds for each setup and ramp orientation, in the same order and the same format used in the preceding:
For the setup you skipped, just enter 'skipped'.
---------->>>>> ball speeds based on mean distances
Your answer (start in the next line):
14.52cm/0.2 s= 72.6 cm/s
18.9cm/0.2s= 94.5 cm/s
23.98cm/0.2 s= 119.9 cm/s
14.46 cm/0.2 s=72.3 cm/s
21.08cm/0.2 s=105.4 cm/s
24.98 cm/ 0.2 cm=124.9 cm/s
#$&*
@&
The 0.2 second has appeared here with no indication of how it was obtained or how it is related to your experimental setup or your data.
*@
Each speed should match the final velocity of the ball on the ramp. In each trial the ball rolled a known distance from rest. Our hypothesis is that the acceleration was uniform and depended only on the slope of the ramp.
Assuming uniform acceleration from rest through a 10-cm distance, with final velocity equal to that you just reported for the 2-domino setup, what would be the acceleration of the ball? Report that acceleration in the first line below, and starting in the second line explain how you obtained it and also explain what units resulted from your calculation:
---------->>>>> accel 10 cm 2 dom setup, explain
Your answer (start in the next line):
#$&*
You could easily and quickly repeat these calculations for the remaining 11 trials, and may do so if you wish. However, first click again on the 'Experiment-Specific Calculations' button, select 2, and enter when prompted the distance the ball moved down the ramp (10, 20 or 30 cm as required), the velocity reported previously for the trial, and the program will indicate the associated acceleration.
Using whatever means you believe will be most efficient, calculate the remaining accelerations.
Report the resulting accelerations below, three accelerations for each setup, in the same order and the same format used in the preceding box. Report three accelerations per line, separated by commas. You will report 4 lines, including one you can report as 'skipped'
---------->>>>> report accelerations
Your answer (start in the next line):
Skipped
skipped
#$&*
You can copy the contents of the previous box into the data analysis program, change rows to columns, and calculate the corresponding mean and standard deviation of the three accelerations reported for each of the four setups (for example, you have three accelerations on the first ramp; you will find the mean and standard deviation of these three quantities).
Using the program or another means of your choosing, calculate and report these results in four lines, in each line giving the mean and standard deviation of the acceleration. Then starting in a new line briefly explain what your results mean and how they were obtained.
---------->>>>>
Your answer (start in the next line):
#$&*
What are the uncertainties in the information used to calculate distances, velocities and accelerations in this analysis?
How much uncertainty do you think there is in the acceleration results?
Specifically, what do you believe to be the percent uncertainty in the accelerations calculated here? That is, give the typical uncertainty as a percent of the typical acceleration. As best you can, explain how you can determine these uncertainties based on uncertainties in the original data.
---------->>>>> uncertainties in accelerations, how estimated
Your answer (start in the next line):
#$&*
Do your results appear to support the hypothesis that acceleration is independent of velocity or position on the 2-domino setups?
Do your results appear to support the hypothesis that acceleration is independent of velocity or position on the 4-domino setups?
---------->>>>> support or reject hypotheses
Your answer (start in the next line):
#$&*
Report the 5 time intervals you obtained for the system in its original orientation, in comma-delimited format on the first line. Report the mean and standard deviation of those time intervals in comma-delimited format on the second line.
Then using similar format report on the third and fourth lines the same information for the system with the ramp reversed.
---------->>>>> 5 time intervals original orientation, *&$*&$
Your answer (start in the next line):
#$&*
Based on `dt = mean - standard deviation then on `dt = mean + standard deviation, calculate the upper and lower limits on the acceleration in the setup with the ramp in its original position.
Repeat for the setup with the ramp reversed.
Report your results below, each line consisting of the lower and upper limit for one setup, in comma-delimited format. You will have two such lines, which you should report in the order requested above.
---------->>>>>
Your answer (start in the next line):
#$&*
Are these acceleration ranges consistent with the results previously obtained for the 10-, 20- and 30-cm trials on the corresponding ramps? Would you have more faith in the results of your timing or in the results obtained from projectile behavior?
---------->>>>>
Your answer (start in the next line):
#$&*
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I am struggling with what to do next... I am confused
@&
It took me a minute to spot this implied question, which should have appeared before the #$&* mark, and which should have been accompanied by a series of question marks.
I'm afraid I might have missed other questions, as I could easily have missed this one. Be sure to use the specified formats to avoid this possibility.
*@
@&
I believe you were to have timed the ball, obtaining mean time down the ramp and standard deviation of your timings.
For each series of timings:
If the time `dt down the ramp is mean + standard deviation, then what is the ball's acceleration on the ramp?
If the time `dt down the ramp is mean - standard deviation, then what is the ball's acceleration on the ramp?
These calculations will give you limits on the ball's acceleration.
You will also have found accelerations based on the ball's final velocity, as calculated from its projectile behavior in previous steps.
You are asked whether the results for your accelerations, found by the two methods, are consistent. You might or might not have trouble interpreting this question, but I want to see your best interpretation before giving you much additional guidance on what is meant by the word 'consistent'. I will say this much: two experimental results are consistent if it is possible, with a high level of certainty, to conclude that both results could have been obtained within the limits of the uncertainties of the experiment.
*@
** **
Using the 'Experiment-Specific Calculations' button of the data program, select 1, as you did in the preceding experiment, and respond with the information necessary to calculate the speed of the ball at the end of the ramp, based on the mean distance observed for your first set of 5 trials.
Repeat this process for each of the remaining 11 trials.
Report the resulting speeds in the box below, three speeds for each setup and ramp orientation, in the same order and the same format used in the preceding:
For the setup you skipped, just enter 'skipped'.
---------->>>>> ball speeds based on mean distances
Your answer (start in the next line):
14.52cm/0.2 s= 72.6 cm/s
18.9cm/0.2s= 94.5 cm/s
23.98cm/0.2 s= 119.9 cm/s
14.46 cm/0.2 s=72.3 cm/s
21.08cm/0.2 s=105.4 cm/s
24.98 cm/ 0.2 cm=124.9 cm/s
#$&*
Each speed should match the final velocity of the ball on the ramp. In each trial the ball rolled a known distance from rest. Our hypothesis is that the acceleration was uniform and depended only on the slope of the ramp.
Assuming uniform acceleration from rest through a 10-cm distance, with final velocity equal to that you just reported for the 2-domino setup, what would be the acceleration of the ball? Report that acceleration in the first line below, and starting in the second line explain how you obtained it and also explain what units resulted from your calculation:
---------->>>>> accel 10 cm 2 dom setup, explain
Your answer (start in the next line):
#$&*
*#&!*#&!
@&
Check my notes and let me know if I've managed to clarify the situation and answer your question.
*@