Compare your submission with the following document and, if necessary, self-critique your work.

In order to self-critique, submit a copy of your original submission, inserting revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).

Note that the quality of this video was intentionally limited. 

• The 'blurriness' here was obvious.
• Though it isn't always as obvious to our perception, any instrument you use is similarly blurry at some level of precision. 
• Even the most precise instrument has its limits.
• The main purpose of this exercise is to quantify the blurriness, i.e., the uncertainties, in the present measurements.

The questions posed on the Seed Question were as follows, with commentary in bold:

• How accurately do you think you can measure the time between two events using the TIMER program?

 

Your answer to this question should have consisted of a decimal number representing the number of seconds of uncertainty your timing using the program, and you should explain why you believe this number to be a reasonable estimate of the uncertainty.

• What is the shortest time interval you think you would be able to measure with reasonable accuracy? </p>
 

Your answer to this question should have been a decimal number representing the shortest time interval you believe could be timed accurately. 

Your answer should be accompanied by an explanation of why you believe it to be reasonable.

Note that the time interval specified in your answer to the present question should be shorter than the time you specified in the first question.  You can't reasonably time an interval that is shorter than your uncertainty in timing.

• How does the percent error in timing intervals change as the time between the events gets smaller? </p>
 

You should look through the recommended calculations at the end of this document and consider whether your answer to this question is consistent with the pattern that emerges from those questions.

STUDENT SOLUTION

I did this by if my intervals change by .2 per every second .2/1.0s = 20% error if the time is lessoned between
intervals .1/1.0s = 10% error..

so the error is decreasing, I juse want top make sure I am corret in thinking here???????????

INSTRUCTOR RESPONSE

You're on the right track and you're doing some very good thinking.

However the size of the uncertainty doesn't generally decrease as intervals get shorter.

For example your neurological response does not get better with shorter intervals. So you can't expect the uncertaintly associated with that response to decrease.

• If you have, say, an uncertainty of .1 second when timing a 2-second interval then you have a 5% uncertainty.
• Assuming you have the same uncertainty when timing a 1-second interval, the the uncertainty is .1 sec / (1 sec) = .10, or 10%.
• The shorter the interval the greater the uncertainty is as a percent of the timing.
  
   
• Similarly, even if your neurological response was very consistent (say to within a millisecond, which isn't really possible), the .01 second uncertainty in the timer itself would be the same for any interval. The shorter the interval, the greater percent that .01 second would be (e.g., .01 s / (2 s) = .005 = 0.5%, whereas .01 s / (1 s) = .01 or 1%).

• How accurately are you able to measure the positions of the ball and the pendulum in the initial video?

Your answers here should include numerical estimates of your uncertainties and an explanation of how your estimates are based on what you saw on the video.  If they weren't, consider the following questions:

• You can be very sure that your positions weren't accurate to within +- 1/8 inch.  What is it about the videos that makes it impossible to determine positions to within 1/8 inch?
• You can be equally sure that your positions were accurate to within +- 10 inches.  How can you justify this conclusion in terms of the videos?
• You can be very sure that your times weren't accurate to within +- .0001 second.  What is it about the videos that makes you sure of this?
• You can be very sure that your times were accurate to within +- 1 second.  What is it about the videos that makes you sure of this?

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Recommended calculations:

Answers to many of the following calculations are given at the end of the page.

Answer the following questions about percents:

• What is 2 percent of 50?
• What is .5 percent of 20?
• What percent of 50 is 2?
• What percent of 10 is 2?
• 50 is .2 percent of what number?
• 20 is 5 percent of what number?

Suppose you a single cycle of a four pendulums.  Assume that your timing is accurate to within +- .1 second.  Another way of saying the same thing is to say that the uncertainty in the timing is +- .1 second.

• If a cycle takes about 5 seconds, what percent of this time is the .1 second uncertainty?  This quantity is called the percent uncertainty in the measurement.
• If a cycle takes about 2 seconds, what percent of this time is the .1 second uncertainty?
• If a cycle takes about .5 seconds, what percent of this time is the .1 second uncertainty?

What happens to the percent uncertainty as the time required for a cycle decreases?  Can you explain why this is the case?

Answers to some of the calculations:

2 percent of 50 is .02 * 50 = 1

.5 percent of 20 is .005 * 20 = .1

If we divide 2 by 50 we get 2 / 50 = .04, which is 4%.  So 2 is 4% of 50.

If we divide 2 by 10 we get 2 / 10 = .2, which is 20%.  So 2 is 20% of 10.

.2 percent of a number is .002 multiplied by the number.  Call the number x.  If .2 percent x is 50, then .002 * x = 50 and x = 50 / .002 = 25 000.

5 percent of an unknown number x is .05 * x.  If 5 percent of this number is 20, the .05 * x = 20 and x = 20 / .05 = 400.

If we divide .1 sec by 5 sec we get .1 sec / (5 sec) = .02, so .1 sec is 2 % of 5 sec.

If we divide .1 sec by 2 sec we get .1 sec / (2 sec) = .05, so .1 sec is 5 % of 2 sec.

If we divide .1 sec by .5 sec we get .1 sec / (.5 sec) = .2, so .1 sec is 20 % of .05 sec.