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course Phy 201
9/3 11am
1.Were you able to determine from the data how many different ruler scales were used? If so, how many and how did you determine it. If not, why not?I think I was able to determine that there were three different ruler scales used. I did think it was a little difficult to determine the scale because I didn’t know how closely others measured their dominoes and how they counted they’re pendulums. I determined how many were used to the best of my ability by scaling the other measurements by my own measurements and the ruler I used.
2. Give your data for the four observation made today of the ball rolling up the ramp and back down.
I counted 7 cycles up the ramp and 10 cycles back down the ramp.
I only got one trial for this because I thought we only did one real trial for the ball rolling up and down. I did have four measurements from a previous day when we did exercises with the ball however.
3. According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
It took longer for the ball to roll back down the ramp than it did for the ball to roll up the ramp because I counted 7 cycles back up and 10 back down. This likely happened because the ball was propelled up the ramp and before it could come back down, it had to come to a complete stop and come back down only using gravity.
4. How confident are you in your result?
I am fairly confident in my result, but I wouldn’t put all my confidence in the data I collected unless I did it multiple times and corroborated with others.
5. How confident do you think you'll be in the results obtained from the whole group?
I think I could be pretty confident in the results obtained by the group. Whatever the majority of the class says is probably generally correct.
6. Would you expect to be more or less confident in the data from the whole group? How much more or less?
I think I would be much more confident in the data obtained by the class than with my own, lone data.
You will need to know this definition, word for word and symbol for symbol, starting now and for the rest of the course. The definition is about 19 words and a few symbols long and most of the words are single syllables:
Definition of average rate of change: The average rate of change of A with respect to B is (change in A) / (change in B).
You should already recognize this definition as perhaps the most fundamental definition in calculus, though it could be asserted that the most fundamental definition also applies a limiting process to this definition.
You also need the following two definitions:
Average velocity is the average rate of change of position with respect to clock time.
Average acceleration is the average rate of change of velocity with respect to clock time.
Do your best with the next few questions, and explain your thinking on each one. Mistakes are acceptable, but not thinking is not.
7. According to the definition of average rate of change, then, what is the calculation for velocity?
The calculation for velocity would be:
Change of position/clock time
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Change in position is correct, but 'clock time' is not. You need two clock times, or a measurement of the difference between two clock times, to calculate an average velocity according to the definition.
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Position would be how far the ball rolled.
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position is where the ball is at an instant; it isn't how far it rolled.
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Clock time would be how long it took the ball to roll that far using pendulum cycles.
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A clock time is a single time read on a running clock. Clock time can not be used to calculate an average rate according to this definition.
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Explain how this calculation is consistent with your experience.
If I correctly understand what this question is asking for, it is consistent with my experience with the ball. The position of ball is how far the ball rolled in the trial and the clock time is how long it took it to travel a certain distance on the ramp.
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Your use of the terms 'position' and 'clock time' are not consistent with the definition of average velocity. Easily enough adapted, but they must be expressed correctly.
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Explain how this calculation is consistent with formulas you've probably learned.
I’m really not sure that I know any other formulas that would be consistent with this one other than the other formulas we went over in class. For example, the formula for average acceleration seems strongly related to average velocity because it actually uses velocity in the definition. They also seems related because they are both based off the principles of average rate of change.
Specifically apply this definition to find the average velocity of the ball in each of the four trials from Monday, assuming it traveled 60 cm during each interval of observation. Time was measured in cycles of your pendulum.
First Trial: 60cm/5.5 cycles = 10.91 cm/cycle
Second Trial: 60cm/5.0 cycles = 12 cm/cycle
Third Trial: 60cm/5.5 cycles = 10.91 cm/cycle
Fourth Trial 60cm/5.5 cycles = 10.91 cm/cycle
Now this is where things start to get a little tricky. Not everyone will be able to answer all these questions correctly. As long as you do your best thinking and express it in your answer, you'll be fine.
You should answer the following with the best of your common sense, thinking about what the questions mean rather than looking up formulas and explanations. The answers should come from you, not from some other source. And you should do your best to answer the questions without talking to your classmates, though once you have done your own thinking it would be great for you to discuss it with whomever you can.
Don't worry if you make a mistake. The important thing right now is for your instructor to see your thinking, and even more so for you to puzzle a bit over some of these questions. Even if your initial thinking is wrong, it will give you a foundation for understanding ideas when we cover them in class.
You know the ball started from rest in each trial. So it started with velocity zero.
You've just calculated the average velocities for the four trials.
Knowing that the ball starts from rest and knowing its average velocity, using only common sense and not some formula that might give you the right answer without requiring you to understand anything, explain the most reasonable approach you can think of to finding the final velocity.
The final velocity is when you’re finished with your trial and starting velocity is 0 (which you have given). You would have to find the position (how far it traveled) of the object as well as the count (how long it took to get there) at the end of your trial. To calculate this you would have to somehow take into account the initial and final. For example, the formulas that read something like “change in x = x final - x initial.” I’m just not sure how to proceed as to how to find the correct answer for final velocity.
Assuming you do know the final velocity and the count, how would you apply the definition of average rate of change and the definition of average acceleration to determine the acceleration of the ball?
Average ROC = (Change in A)/(Change in B)
Ave. Accl. = Ave. ROC of velocity WRT clock time
To find the acceleration of the ball you would use the known final velocity and divide by the count since you know it as well.
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You are wandering a little ways from the definition.
If
Average ROC = (Change in A)/(Change in B)
Ave. Accl. = Ave. ROC of velocity WRT clock time
then what specifically would you have to calculate to get the average rate of change of velocity with respect to clock time?
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Using your best estimate of the ball's final velocity for each of the four trials, what is the average acceleration for each? Show in detail how you get the average acceleration for the first trial, then just include the brief details of your calculation for each of the other three trials.
First trial: Since I’m really unsure as to how to calculate final velocity, I’m going to assume I can use the average velocity in this. To calculate the average acceleration I would say [10.91 (velocity)] / [5.5 (clock time) = 1.98 cm/cycle
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Not bad.
However what are the units of your 10.91, and what are the resulting units of acceleration?
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Second trial: 12/5.0 = 2.4 cm/cycle
Third trial: 10.91/5.5 = 1.98 cm/cycle
Fourth trial: 10.91/5.5 = 1.98 cm/cycle
I expect the last few questions above to have been fairly challenging. In a typical physics class at this level fewer than half the class would be able to answer them all correctly.
The questions below rely on skills you might or might not have developed, and might or might not recall. Give them your best thinking, so that at the very least you'll have the questions in your mind when we answer them in class.
By what percent do you estimate the average frequency of your counts might have varied between trials? Express your answer as the difference between the lowest and highest frequency, as a percent of the average of all the frequencies. Don't go looking up a technical definition of the word ""frequency"", which would probably confuse the whole issue. You probably have enough intuition about the meaning of that word to come up with a reasonable, if not profoundly accurate, estimate. You also shouldn't have to look up what we mean by the difference between the frequencies as a percent of the average frequency, but that terminology is well-defined, completely applicable and should not be confusing so if you've got to look it up it's OK.
If I understand correctly, then I calculated that the frequency of my trial was off by about 9%.
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
I would estimate that the velocity would be off by at least 4% because you’re combining the time and the position which would probably both be off by about 2%.
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
Acceleration would be off by even more because you use the 4% off and combine it with another two percent off, so I might guess that it would be off by 8% or more.
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Definitely on the right track here. However since the change in clock time is used only once in calculating ave vel, you would have only a 2% error in that result. The additional use of the change in clock time when calculating acceleration would add another 2%, very much along the lines of your reasoning.
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You need to be just a little clearer about your quantities and definitions, but you've made a very good effort here and you're on track. Check my notes.
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