#$&*
course PHY 201
09/03/2013 5:48pm
Were you able to determine from the data how many different ruler scales were used? If so, how many and how did you determine it. If not, why not?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
You will need to know this definition, word for word and symbol for symbol, starting now and for the rest of the course. The definition is about 19 words and a few symbols long and most of the words are single syllables:
Definition of average rate of change:
The average rate of change of A with respect to B is (change in A) / (change in B).
You should already recognize this definition as perhaps the most fundamental definition in calculus, though it could be asserted that the most fundamental definition also applies a limiting process to this definition.
You also need the following two definitions:
Average velocity is the average rate of change of position with respect to clock time.
Average acceleration is the average rate of change of velocity with respect to clock time.
Do your best with the next few questions, and explain your thinking on each one. Mistakes are acceptable, but not thinking is not.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
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.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
Now this is where things start to get a little tricky. Not everyone will be able to answer all these questions correctly. As long as you do your best thinking and express it in your answer, you'll be fine.
You should answer the following with the best of your common sense, thinking about what the questions mean rather than looking up formulas and explanations. The answers should come from you, not from some other source. And you should do your best to answer the questions without talking to your classmates, though once you have done your own thinking it would be great for you to discuss it with whomever you can.
Don't worry if you make a mistake. The important thing right now is for your instructor to see your thinking, and even more so for you to puzzle a bit over some of these questions. Even if your initial thinking is wrong, it will give you a foundation for understanding ideas when we cover them in class.
You know the ball started from rest in each trial. So it started with velocity zero.
You've just calculated the average velocities for the four trials.
Knowing that the ball starts from rest and knowing its average velocity, using only common sense and not some formula that might give you the right answer without requiring you to understand anything, explain the most reasonable approach you can think of to finding the final velocity.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
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?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
#$&*
Using your best estimate of the ball's final velocity for each of the four trials, what is the average acceleration for each? Show in detail how you get the average acceleration for the first trial, then just include the brief details of your calculation for each of the other three trials.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
#$&*
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.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course PHY 201
09/03/2013 5:48pm
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?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
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.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
Specifically apply this definition to find the average velocity of the ball in each of the four trials from Monday, assuming it traveled 60 cm during each interval of observation. Time was measured in cycles of your pendulum.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
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.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
Assuming you do know the final velocity and the count, how would you apply the definition of average rate of change and the definition of average acceleration to determine the acceleration of the ball?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
@&
count and ave. velocity would give you change in position
*@
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
@&
I don't think ave. vel. and count will do it. All you could get from ave. vel. and count would be change in position.
*@
#$&*
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.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
@&
Going up the ramp the initial velocity was not actually zero, but I wasn't clear on this point. We assume that your timing started just after the quick 'poke' I used to get the ball moving, so the ball was already in motion with some initial velocity.
*@
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
@&
(cm/cycle) / cycle is just fine. Mathematically this could also be written as (cm/cycle) * (1/ cycle) = cm/cycle^2.
*@
#$&*
I expect the last few questions above to have been fairly challenging. In a typical physics class at this level fewer than half the class would be able to answer them all correctly.
The questions below rely on skills you might or might not have developed, and might or might not recall. Give them your best thinking, so that at the very least you'll have the questions in your mind when we answer them in class.
By what percent do you estimate the average frequency of your counts might have varied between trials? Express your answer as the difference between the lowest and highest frequency, as a percent of the average of all the frequencies. Don't go looking up a technical definition of the word ""frequency"", which would probably confuse the whole issue. You probably have enough intuition about the meaning of that word to come up with a reasonable, if not profoundly accurate, estimate. You also shouldn't have to look up what we mean by the difference between the frequencies as a percent of the average frequency, but that terminology is well-defined, completely applicable and should not be confusing so if you've got to look it up it's OK.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
@&
That would be the appropriate calculation.
I'm not sure why you used 11 and 8.5 as representative frequencies of your counts. I would think that you would be able to achieve a more regular counting rhythm than that.
*@
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
@&
The frequency of your count is how many counts you make in a given time period. So for example we could agree on a 5-second interval. Counting a series of 5-second intervals, your counts might be 17, 15, 16, 14, 17.
It appears than the counts were all pretty much within 10% of the mean, so we would conjecture that the frequency of our count did not vary by more that 10%.
*@
#$&*
course PHY 201
09/03/2013 5:48pm
Were you able to determine from the data how many different ruler scales were used? If so, how many and how did you determine it. If not, why not?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
You will need to know this definition, word for word and symbol for symbol, starting now and for the rest of the course. The definition is about 19 words and a few symbols long and most of the words are single syllables:
Definition of average rate of change:
The average rate of change of A with respect to B is (change in A) / (change in B).
You should already recognize this definition as perhaps the most fundamental definition in calculus, though it could be asserted that the most fundamental definition also applies a limiting process to this definition.
You also need the following two definitions:
Average velocity is the average rate of change of position with respect to clock time.
Average acceleration is the average rate of change of velocity with respect to clock time.
Do your best with the next few questions, and explain your thinking on each one. Mistakes are acceptable, but not thinking is not.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
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.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
Now this is where things start to get a little tricky. Not everyone will be able to answer all these questions correctly. As long as you do your best thinking and express it in your answer, you'll be fine.
You should answer the following with the best of your common sense, thinking about what the questions mean rather than looking up formulas and explanations. The answers should come from you, not from some other source. And you should do your best to answer the questions without talking to your classmates, though once you have done your own thinking it would be great for you to discuss it with whomever you can.
Don't worry if you make a mistake. The important thing right now is for your instructor to see your thinking, and even more so for you to puzzle a bit over some of these questions. Even if your initial thinking is wrong, it will give you a foundation for understanding ideas when we cover them in class.
You know the ball started from rest in each trial. So it started with velocity zero.
You've just calculated the average velocities for the four trials.
Knowing that the ball starts from rest and knowing its average velocity, using only common sense and not some formula that might give you the right answer without requiring you to understand anything, explain the most reasonable approach you can think of to finding the final velocity.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
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?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
#$&*
Using your best estimate of the ball's final velocity for each of the four trials, what is the average acceleration for each? Show in detail how you get the average acceleration for the first trial, then just include the brief details of your calculation for each of the other three trials.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
#$&*
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.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course PHY 201
09/03/2013 5:48pm
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?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
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.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
Specifically apply this definition to find the average velocity of the ball in each of the four trials from Monday, assuming it traveled 60 cm during each interval of observation. Time was measured in cycles of your pendulum.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
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.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
Assuming you do know the final velocity and the count, how would you apply the definition of average rate of change and the definition of average acceleration to determine the acceleration of the ball?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
@&
count and ave. velocity would give you change in position
*@
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
@&
I don't think ave. vel. and count will do it. All you could get from ave. vel. and count would be change in position.
*@
#$&*
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.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
@&
Going up the ramp the initial velocity was not actually zero, but I wasn't clear on this point. We assume that your timing started just after the quick 'poke' I used to get the ball moving, so the ball was already in motion with some initial velocity.
*@
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
@&
(cm/cycle) / cycle is just fine. Mathematically this could also be written as (cm/cycle) * (1/ cycle) = cm/cycle^2.
*@
#$&*
I expect the last few questions above to have been fairly challenging. In a typical physics class at this level fewer than half the class would be able to answer them all correctly.
The questions below rely on skills you might or might not have developed, and might or might not recall. Give them your best thinking, so that at the very least you'll have the questions in your mind when we answer them in class.
By what percent do you estimate the average frequency of your counts might have varied between trials? Express your answer as the difference between the lowest and highest frequency, as a percent of the average of all the frequencies. Don't go looking up a technical definition of the word ""frequency"", which would probably confuse the whole issue. You probably have enough intuition about the meaning of that word to come up with a reasonable, if not profoundly accurate, estimate. You also shouldn't have to look up what we mean by the difference between the frequencies as a percent of the average frequency, but that terminology is well-defined, completely applicable and should not be confusing so if you've got to look it up it's OK.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
@&
That would be the appropriate calculation.
I'm not sure why you used 11 and 8.5 as representative frequencies of your counts. I would think that you would be able to achieve a more regular counting rhythm than that.
*@
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
@&
The frequency of your count is how many counts you make in a given time period. So for example we could agree on a 5-second interval. Counting a series of 5-second intervals, your counts might be 17, 15, 16, 14, 17.
It appears than the counts were all pretty much within 10% of the mean, so we would conjecture that the frequency of our count did not vary by more that 10%.
*@
#$&*
course PHY 201
09/03/2013 5:48pm
Were you able to determine from the data how many different ruler scales were used? If so, how many and how did you determine it. If not, why not?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
You will need to know this definition, word for word and symbol for symbol, starting now and for the rest of the course. The definition is about 19 words and a few symbols long and most of the words are single syllables:
Definition of average rate of change:
The average rate of change of A with respect to B is (change in A) / (change in B).
You should already recognize this definition as perhaps the most fundamental definition in calculus, though it could be asserted that the most fundamental definition also applies a limiting process to this definition.
You also need the following two definitions:
Average velocity is the average rate of change of position with respect to clock time.
Average acceleration is the average rate of change of velocity with respect to clock time.
Do your best with the next few questions, and explain your thinking on each one. Mistakes are acceptable, but not thinking is not.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
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.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
Now this is where things start to get a little tricky. Not everyone will be able to answer all these questions correctly. As long as you do your best thinking and express it in your answer, you'll be fine.
You should answer the following with the best of your common sense, thinking about what the questions mean rather than looking up formulas and explanations. The answers should come from you, not from some other source. And you should do your best to answer the questions without talking to your classmates, though once you have done your own thinking it would be great for you to discuss it with whomever you can.
Don't worry if you make a mistake. The important thing right now is for your instructor to see your thinking, and even more so for you to puzzle a bit over some of these questions. Even if your initial thinking is wrong, it will give you a foundation for understanding ideas when we cover them in class.
You know the ball started from rest in each trial. So it started with velocity zero.
You've just calculated the average velocities for the four trials.
Knowing that the ball starts from rest and knowing its average velocity, using only common sense and not some formula that might give you the right answer without requiring you to understand anything, explain the most reasonable approach you can think of to finding the final velocity.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
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?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
#$&*
Using your best estimate of the ball's final velocity for each of the four trials, what is the average acceleration for each? Show in detail how you get the average acceleration for the first trial, then just include the brief details of your calculation for each of the other three trials.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
#$&*
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.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course PHY 201
09/03/2013 5:48pm
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?By measuring out and timing the pendulums as listed, then comparing the results with each different list.
#$&*
Give your data for the four observation made today of the ball rolling up the ramp and back down.
To go up: 11
To go back down: 8.5
#$&*
According to your results did the ball take longer go up the ramp or longer to come back down? Explain your reasoning.
Unless I labelled my results wrong, this shows that the ball took longer to go up the ramp than to come back down. This is because the time was shorter and thus it took less time.
#$&*
How confident are you in your result?
I would be more confident if I was certain I labelled my results correctly, or confident about the accurate of my timings.
#$&*
How confident do you think you'll be in the results obtained from the whole group?
Much more confident. The more data (usually) the more accurate the conclusion.
#$&*
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More. Much more.
#$&*
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.
According to the definition of average rate of change, then, what is the calculation for velocity?
velocity = (change in position) / (change in clock time)
#$&*
Explain how this calculation is consistent with your experience.
With an equal change of position, if the change in clock time is smaller, the velocity will be higher. More miles per hour, for example. If the change in clock time is larger, the demonator of the fraction is larger, and the velocity decreases.
#$&*
Explain how this calculation is consistent with formulas you've probably learned.
distance = rate * time can be re-worded as
(change in position) = velocity * (change in clock time)
or, by dividing through by (change in clock time),
velocity = (change in position)/ (change in clock time)
#$&*
Specifically apply this definition to find the average velocity of the ball in each of the four trials from Monday, assuming it traveled 60 cm during each interval of observation. Time was measured in cycles of your pendulum.
Going up the ramp:
velocity = (60 - 0) / (11 - 0)
velocity = 60 / 11
velocity = 5.45 cm/cycle
Going down the ramp:
velocity = (60 - 0) / (8.5 - 0)
velocity = 60 / 8.5
velocity = 7.06 cm/cycle
#$&*
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.
If the ball starts at 0 and ends at a velocity x, then averaging the two would result in (0 + x) / 2, or half the final velocity. Assuming the ball maintains uniform acceleration, the final velocity will be double the average velocity.
For the specific ramp trials we did, going up the hill began and ended at velocity 0. The final velocity was 0. Going down the ramp had a final velocity of 14.12, based on the previous paragraph's hypothesis.
#$&*
Assuming you do know the final velocity and the count, how would you apply the definition of average rate of change and the definition of average acceleration to determine the acceleration of the ball?
If I know the final velocity, and the count, then:
Using the count and the final velocity, I could determine the change in position.
@&
count and ave. velocity would give you change in position
*@
Using the count and the change in position, I could next determine the average velocity.
Using the average velocity and the count, I could determine the average acceleration of the ball.
@&
I don't think ave. vel. and count will do it. All you could get from ave. vel. and count would be change in position.
*@
#$&*
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.
acceleration = (change in velocity) / (change in clock time)
To go up ramp:
acceleration = 0 - 0 / Anything = 0 (Because it accelerated and then deccelerated, cancelling each-other out)
@&
Going up the ramp the initial velocity was not actually zero, but I wasn't clear on this point. We assume that your timing started just after the quick 'poke' I used to get the ball moving, so the ball was already in motion with some initial velocity.
*@
To go down ramp:
acceleration = (14.12 - 0) / (8.5 - 0) = 14.12 / 8.5 = 1.66 (cm/cycle)/cycle (is there a better way to write the units for acceleration?)
@&
(cm/cycle) / cycle is just fine. Mathematically this could also be written as (cm/cycle) * (1/ cycle) = cm/cycle^2.
*@
#$&*
I expect the last few questions above to have been fairly challenging. In a typical physics class at this level fewer than half the class would be able to answer them all correctly.
The questions below rely on skills you might or might not have developed, and might or might not recall. Give them your best thinking, so that at the very least you'll have the questions in your mind when we answer them in class.
By what percent do you estimate the average frequency of your counts might have varied between trials? Express your answer as the difference between the lowest and highest frequency, as a percent of the average of all the frequencies. Don't go looking up a technical definition of the word ""frequency"", which would probably confuse the whole issue. You probably have enough intuition about the meaning of that word to come up with a reasonable, if not profoundly accurate, estimate. You also shouldn't have to look up what we mean by the difference between the frequencies as a percent of the average frequency, but that terminology is well-defined, completely applicable and should not be confusing so if you've got to look it up it's OK.
11 - 8.5 = 2.5
(11 + 8.5) / 2 = 9.75
2.5 / 9.75 = x / 100
x = 25.6
25.6percent
@&
That would be the appropriate calculation.
I'm not sure why you used 11 and 8.5 as representative frequencies of your counts. I would think that you would be able to achieve a more regular counting rhythm than that.
*@
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
2%? I do not know how to get this answer.
#$&*
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
I'm still confused about what exactly frequency is, to be honest. Would it still be 2%? How would I go about calculating this?
#$&*
"
@&
The frequency of your count is how many counts you make in a given time period. So for example we could agree on a 5-second interval. Counting a series of 5-second intervals, your counts might be 17, 15, 16, 14, 17.
It appears than the counts were all pretty much within 10% of the mean, so we would conjecture that the frequency of our count did not vary by more that 10%.
*@