#$&*
course phy 201
9/2 7
130828We noted that distance, time and mass are the basic undefined quantities in first-semester physics. All other quantities are defined in terms of these three.
In addition to the definitions of average rate, average velocity and average acceleration we looked at and briefly discussed the law
F_net = m a
where m is a point mass, F_net is net force (the sum of all forces acting on the mass) and a is its acceleration,
and the definition
`dW = F_parallel * `ds.
(note that `d stands for Delta, the capital Greek letter that looks like an equilateral triangle and stands for 'change in').
`ds is change in position, F_parallel is how much of the force acts in the direction of motion, and `dW is the work done by the force as it acts through the change in position `ds.
Please provide your data by inserting it into the questions below, and answer the susequent questions. Submit your work through the Submit Work Form at
http://vhcc2.vhcc.edu/dsmith/submit_work.htm
(this link isn't written in Blackboard or in Outlook so it should work, as should other links on actual webpages).
I recommend that work these questions before the last minute. Your brain adapts better if you spread your thinking out.
I also recommend that you submit them when they are complete, rather than waiting until the last minute. This is so you can get my feedback on one thing before you move to another.
In any case, the last minute will be 6:00 p.m. next Tuesday.
Note that this deadline (as well as the advice to spread things out) also applies to your other assignments. There is no need to get them in by Sunday night since we don't have class on Labor Day.
If you have questions, use the Question Form at
http://vhcc2.vhcc.edu/dsmith/forms/question_form.htm .
Data submitted from Monday appear at the end of this document.
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 wasn't able to collect this data. I tried using cross multiplication for this data and I couldn't get an accurate number through or a few numbers that would match up. I also had the problem that on my data, I used a ruler at home and received my data in inches rather than in centimeters. so the cross multiplication through it way off.
Give your data for the four observation made today of the ball rolling up the ramp and back down.
The ball took 6 swings of the pendulum from the point of poking it and stopping it and 8 swings to roll back.
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 to come back down the ramp. I had less force because when it was being poked it only took 6, if you where to poke it from the other end, it would have went a lot faster, but it wouldn't have came back the other way.
How confident are you in your result?
About a 7 out of 10.
How confident do you think you'll be in the results obtained from the whole group?
Well, I was pretty confident about the table being tilted in the east and I was wrong, so I don't to get my hopes up.
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More, it is more data collected. about 50% 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?
Change in A/Change in B with respect to clock time
Explain how this calculation is consistent with your experience.
The change in a is 6 and the change in B is 8, the velocity is 0.75 with respect to clock time.
Explain how this calculation is consistent with formulas you've probably learned.
well, if it was constant the velocity would be one. so, like most formulas, if everything is normal, even, exact, the answer would be one.
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.
change in A is 60 cm and Change in B is 6 pendulum swings = a velocity of 10 cm/cycle in all trials except for the 3rd one one which is 60/5.5 =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 greater the steep, the higher the velocity, the lower the steep, the lower the velocity will be.
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?
The velocity would be the average rate of change. The higher the acceleration, the higher the steep, the higher the velocity.
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.
trail 1: 1 trail 2: 1 trail 3: 0.75 trail 4: 1
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.
About 25%, not every swing can be the same. There is a 0.25 difference in the velocities, so i'm thinking 25 % could be my variable in trails.
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
0.02
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
0.02
1.
length of first pendulum: 31.5cm one-minute count for first pendulum: 60 cycles
length of second pendulum: 15cm one-minute count for second pendulum: 82 cycles
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5.5 cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 5.0 cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 5.5 cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 5.5 cycles
3. I think it is tilted towards the east.
I think it is tilted toward the east because I had a faster time when the ramp was supported on the west side of the tabletop. I don't really think my data is very strongly supported because there are so many margins of error involved in this method of data collection.
A better way to measure how level the tabletop is would be to use a level. But if we were using another form of data collection, we could time the ball with a timer instead of using a pendulum - the timer would be more accurate than using my unpredictable hand.
1.
length of first pendulum: 41.85 units (I used the 3x reduced strip) one-minute count for first pendulum: 70 cycles
length of second pendulum: 20.9 units one-minute count for second pendulum: 96 cycles
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5.5 cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 5 cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 5 cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4.5 cycles
3.
Given the slightly longer duration for the ball to traverse the ramp west to east instead of east/west, I would summize the table top is slightly tilted more toward the west.
If the table top were truly level, the ball would roll with the same duration of pendulum cycles. Since my data shows the ball travelled a shorter duration of cycles when travelling east to west, it implies the table has a steeper slope toward the west wall.
By taking more trials in each direction and comparing the mean of each direction and each ramp placement. Also, if one person were to time the process using a stopwatch instead of a pendulum the data may be more precise.
""
1.
length of first pendulum: 52 cm one-minute count for first pendulum: 40
length of second pendulum: 28 cm one-minute count for second pendulum: 56
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 3
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 3
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 2.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 2.5
3. West
Whichever end of the table is lower, the ball would roll to that end faster. The faster the ball rolls, the less time it takes for the pendulum to swing.
Fairly certain. There, of course, is always the possibility for error, but I do not believe that their was much error in my observations
We could use better tools for measuring. (Ex. an electronic timer instead of a pendulum)
We could also measure precisely how far up the ramp to put the ball each time instead of just eyeballing it each time.""
1. length of first pendulum: 30cm one-minute count for first pendulum:102
length of second pendulum: 15cm one-minute count for second pendulum:72
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):
7 passes
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):
9 passes
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):
7passes
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):
7 passes
3.
Based on an average of my information, I believe the table is tilted towards the west.
I believe that my answer is supported by my data, the only variance would be a mistake in the data.
Using a time clock and doing the experiment more than just twice
1.
length of first pendulum: 64.5mm one-minute count for first pendulum: 55
length of second pendulum: 32.25mm one-minute count for second pendulum: 74
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 4
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 3.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 3.5
3.
Toward the west.
Because the first two trials took longer than the second two trials, the slope must be less steep when the ramp is supported on the west side. If the west side ramp is less steep than the right side ramp, the table overall must be inclined to the west.
Measure the tabletop's angle with a level.
1. length of first pendulum: 6.4 inches one-minute count for first pendulum:77
length of second pendulum: 3.2 inches one-minute count for second pendulum:99
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):6
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):6
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):5.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):6
3. I think the table is tilted toward the east because my West 5.5 rotation is the only one that was different.
My West rotation of 5.5 is the only one that was different of all my four trials, so i think it is tilted toward the opposite direction since it didn't take as long to get there.
To be more accurate, we would have to have a more controlled data. our pendulums were all different sizes and moving at different speeds. The distance, time, and mass were all undefined.
""
1. length of first pendulum: 40cm one-minute count for first pendulum: 60cycles
length of second pendulum: 20cm one-minute count for second pendulum: 84cycles
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.5cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4cycles
3. It seems to be tilted toward the west.
The ball would roll faster towards the direction the table is tilted towards, thus there would be less pendulum cycles when it rolls in that direction. The conclusion really isn't supported with very much certainty, because the tools to measure (and conduct the ball rolling) are very rudimentary and inaccurate and not the most precise.
By using stop watches instead of pendulums and using an incline that would have less defects that could make the ball's roll irregular. ""
**********************
1. length of first pendulum: 49.5 cm one-minute count for first pendulum: 60
length of second pendulum: 24.75 one-minute count for second pendulum: 84
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.75
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4
3. The tabletop is tilted towards west.
The count for the ball to roll east to west is lower than that of west to east. Hence it took the ball longer to go from west to east than from east to west. It can be deduced from that data that the table is tilted towards west. There is 80% certainty.
First, roll the ball just like we did and find out the direction it rolls towards. Then lift the table on the side which the ball rolled towards until the ball stops rolling, hence making it level. Then it could be said with 100% certainty which side the tabletop is tilted towards and even by how much.
1. length of first pendulum: one-minute count for first pendulum: 24cm; 60, 61, 61
length of second pendulum: one-minute count for second pendulum: 13.5cm 80, 78
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):5
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):5
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):4
3. West
It took less slightly less time to go from the east side to the west side than a previous measurement with the ramp in the same orientation.
Medium certainty.
By using different positions of each side of the table, slightly different balls, and by measuring ratios between times in each set.
1. length of first pendulum: 40cm one-minute count for first pendulum: 60cycles
length of second pendulum: 20cm one-minute count for second pendulum: 84cycles
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.5cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4cycles
3. The tabletop is almost certainly not level. According you your information, do you think it is tilted toward the east or toward the west?
It seems to be tilted toward the west.
The ball would roll faster towards the direction the table is tilted towards, thus there would be less pendulum cycles when it rolls in that direction. The conclusion really isn't supported with very much certainty, because the tools to measure (and conduct the ball rolling) are very rudimentary and inaccurate and not the most precise.
By using stop watches instead of pendulums and using an incline that would have less defects that could make the ball's roll irregular. "
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course phy 201
9/2 7
130828We noted that distance, time and mass are the basic undefined quantities in first-semester physics. All other quantities are defined in terms of these three.
In addition to the definitions of average rate, average velocity and average acceleration we looked at and briefly discussed the law
F_net = m a
where m is a point mass, F_net is net force (the sum of all forces acting on the mass) and a is its acceleration,
and the definition
`dW = F_parallel * `ds.
(note that `d stands for Delta, the capital Greek letter that looks like an equilateral triangle and stands for 'change in').
`ds is change in position, F_parallel is how much of the force acts in the direction of motion, and `dW is the work done by the force as it acts through the change in position `ds.
Please provide your data by inserting it into the questions below, and answer the susequent questions. Submit your work through the Submit Work Form at
http://vhcc2.vhcc.edu/dsmith/submit_work.htm
(this link isn't written in Blackboard or in Outlook so it should work, as should other links on actual webpages).
I recommend that work these questions before the last minute. Your brain adapts better if you spread your thinking out.
I also recommend that you submit them when they are complete, rather than waiting until the last minute. This is so you can get my feedback on one thing before you move to another.
In any case, the last minute will be 6:00 p.m. next Tuesday.
Note that this deadline (as well as the advice to spread things out) also applies to your other assignments. There is no need to get them in by Sunday night since we don't have class on Labor Day.
If you have questions, use the Question Form at
http://vhcc2.vhcc.edu/dsmith/forms/question_form.htm .
Data submitted from Monday appear at the end of this document.
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 wasn't able to collect this data. I tried using cross multiplication for this data and I couldn't get an accurate number through or a few numbers that would match up. I also had the problem that on my data, I used a ruler at home and received my data in inches rather than in centimeters. so the cross multiplication through it way off.
Give your data for the four observation made today of the ball rolling up the ramp and back down.
The ball took 6 swings of the pendulum from the point of poking it and stopping it and 8 swings to roll back.
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 to come back down the ramp. I had less force because when it was being poked it only took 6, if you where to poke it from the other end, it would have went a lot faster, but it wouldn't have came back the other way.
How confident are you in your result?
About a 7 out of 10.
How confident do you think you'll be in the results obtained from the whole group?
Well, I was pretty confident about the table being tilted in the east and I was wrong, so I don't to get my hopes up.
Would you expect to be more or less confident in the data from the whole group? How much more or less?
More, it is more data collected. about 50% 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?
Change in A/Change in B with respect to clock time
Explain how this calculation is consistent with your experience.
The change in a is 6 and the change in B is 8, the velocity is 0.75 with respect to clock time.
Explain how this calculation is consistent with formulas you've probably learned.
well, if it was constant the velocity would be one. so, like most formulas, if everything is normal, even, exact, the answer would be one.
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.
change in A is 60 cm and Change in B is 6 pendulum swings = a velocity of 10 cm/cycle in all trials except for the 3rd one one which is 60/5.5 =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 greater the steep, the higher the velocity, the lower the steep, the lower the velocity will be.
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?
The velocity would be the average rate of change. The higher the acceleration, the higher the steep, the higher the velocity.
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.
trail 1: 1 trail 2: 1 trail 3: 0.75 trail 4: 1
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.
About 25%, not every swing can be the same. There is a 0.25 difference in the velocities, so i'm thinking 25 % could be my variable in trails.
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of velocity be off?
0.02
If the frequency for a trial was off by 2%, by what percent would the resulting calculation of acceleration be off?
0.02
1.
length of first pendulum: 31.5cm one-minute count for first pendulum: 60 cycles
length of second pendulum: 15cm one-minute count for second pendulum: 82 cycles
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5.5 cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 5.0 cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 5.5 cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 5.5 cycles
3. I think it is tilted towards the east.
I think it is tilted toward the east because I had a faster time when the ramp was supported on the west side of the tabletop. I don't really think my data is very strongly supported because there are so many margins of error involved in this method of data collection.
A better way to measure how level the tabletop is would be to use a level. But if we were using another form of data collection, we could time the ball with a timer instead of using a pendulum - the timer would be more accurate than using my unpredictable hand.
1.
length of first pendulum: 41.85 units (I used the 3x reduced strip) one-minute count for first pendulum: 70 cycles
length of second pendulum: 20.9 units one-minute count for second pendulum: 96 cycles
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5.5 cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 5 cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 5 cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4.5 cycles
3.
Given the slightly longer duration for the ball to traverse the ramp west to east instead of east/west, I would summize the table top is slightly tilted more toward the west.
If the table top were truly level, the ball would roll with the same duration of pendulum cycles. Since my data shows the ball travelled a shorter duration of cycles when travelling east to west, it implies the table has a steeper slope toward the west wall.
By taking more trials in each direction and comparing the mean of each direction and each ramp placement. Also, if one person were to time the process using a stopwatch instead of a pendulum the data may be more precise.
""
1.
length of first pendulum: 52 cm one-minute count for first pendulum: 40
length of second pendulum: 28 cm one-minute count for second pendulum: 56
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 3
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 3
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 2.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 2.5
3. West
Whichever end of the table is lower, the ball would roll to that end faster. The faster the ball rolls, the less time it takes for the pendulum to swing.
Fairly certain. There, of course, is always the possibility for error, but I do not believe that their was much error in my observations
We could use better tools for measuring. (Ex. an electronic timer instead of a pendulum)
We could also measure precisely how far up the ramp to put the ball each time instead of just eyeballing it each time.""
1. length of first pendulum: 30cm one-minute count for first pendulum:102
length of second pendulum: 15cm one-minute count for second pendulum:72
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):
7 passes
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):
9 passes
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):
7passes
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):
7 passes
3.
Based on an average of my information, I believe the table is tilted towards the west.
I believe that my answer is supported by my data, the only variance would be a mistake in the data.
Using a time clock and doing the experiment more than just twice
1.
length of first pendulum: 64.5mm one-minute count for first pendulum: 55
length of second pendulum: 32.25mm one-minute count for second pendulum: 74
2.
first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 4
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 3.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 3.5
3.
Toward the west.
Because the first two trials took longer than the second two trials, the slope must be less steep when the ramp is supported on the west side. If the west side ramp is less steep than the right side ramp, the table overall must be inclined to the west.
Measure the tabletop's angle with a level.
1. length of first pendulum: 6.4 inches one-minute count for first pendulum:77
length of second pendulum: 3.2 inches one-minute count for second pendulum:99
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):6
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):6
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):5.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):6
3. I think the table is tilted toward the east because my West 5.5 rotation is the only one that was different.
My West rotation of 5.5 is the only one that was different of all my four trials, so i think it is tilted toward the opposite direction since it didn't take as long to get there.
To be more accurate, we would have to have a more controlled data. our pendulums were all different sizes and moving at different speeds. The distance, time, and mass were all undefined.
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1. length of first pendulum: 40cm one-minute count for first pendulum: 60cycles
length of second pendulum: 20cm one-minute count for second pendulum: 84cycles
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.5cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4cycles
3. It seems to be tilted toward the west.
The ball would roll faster towards the direction the table is tilted towards, thus there would be less pendulum cycles when it rolls in that direction. The conclusion really isn't supported with very much certainty, because the tools to measure (and conduct the ball rolling) are very rudimentary and inaccurate and not the most precise.
By using stop watches instead of pendulums and using an incline that would have less defects that could make the ball's roll irregular. ""
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1. length of first pendulum: 49.5 cm one-minute count for first pendulum: 60
length of second pendulum: 24.75 one-minute count for second pendulum: 84
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.75
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4.5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4
3. The tabletop is tilted towards west.
The count for the ball to roll east to west is lower than that of west to east. Hence it took the ball longer to go from west to east than from east to west. It can be deduced from that data that the table is tilted towards west. There is 80% certainty.
First, roll the ball just like we did and find out the direction it rolls towards. Then lift the table on the side which the ball rolled towards until the ball stops rolling, hence making it level. Then it could be said with 100% certainty which side the tabletop is tilted towards and even by how much.
1. length of first pendulum: one-minute count for first pendulum: 24cm; 60, 61, 61
length of second pendulum: one-minute count for second pendulum: 13.5cm 80, 78
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west):5
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east):5
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west):5
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east):4
3. West
It took less slightly less time to go from the east side to the west side than a previous measurement with the ramp in the same orientation.
Medium certainty.
By using different positions of each side of the table, slightly different balls, and by measuring ratios between times in each set.
1. length of first pendulum: 40cm one-minute count for first pendulum: 60cycles
length of second pendulum: 20cm one-minute count for second pendulum: 84cycles
2. first trial (ramp supported on west side of tabletop, wide end of ramp directed to west): 5cycles
second trial (ramp supported on west side of tabletop, wide end of ramp directed to east): 4.5cycles
third trial (ramp supported on east side of tabletop, wide end of ramp directed to west): 4cycles
fourth trial (ramp supported on east side of tabletop, wide end of ramp directed to east): 4cycles
3. The tabletop is almost certainly not level. According you your information, do you think it is tilted toward the east or toward the west?
It seems to be tilted toward the west.
The ball would roll faster towards the direction the table is tilted towards, thus there would be less pendulum cycles when it rolls in that direction. The conclusion really isn't supported with very much certainty, because the tools to measure (and conduct the ball rolling) are very rudimentary and inaccurate and not the most precise.
By using stop watches instead of pendulums and using an incline that would have less defects that could make the ball's roll irregular. "
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