Millikan Experiment Based Marble Mass Homework

AI Thread Summary
The discussion revolves around the calculations related to the mass of marbles in containers, using data from a physics homework assignment based on the Millikan experiment. The user initially calculated an average marble mass of 20.33 g, which was deemed incorrect given the constraints of the problem. Participants suggested reevaluating the data, emphasizing the importance of grouping containers with similar masses and considering the experimental uncertainty. They also pointed out that the mass of each marble should be estimated around 4.5 g, with the empty container weighing at least 3 g. The conversation highlights the need for logical reasoning and careful analysis of the provided data to arrive at a consistent solution.
orangegalaxies
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Homework Statement
Determine the mass of one marble and the container, given the mass of 10 different containers that contain an unknown number of marbles in them. After finding the mass of one marble, and the empty container, use this data to find how many marbles were in each container.

I then have to answer these questions
- Would having more containers make this easier?
- Would having a large variety of quantity make this easier?
- How does this relate to Millikan's experiment?
- What are some sources of error?
Relevant Equations
I don't believe I require any equations to solve this problem except the average one:
Average = sum of numbers/number of numbers
I arranged the masses in ascending order:
11.0 g
11.1 g
20.6 g
21.4 g
21.5 g
25.7 g
25.8 g
25.9 g
31.6 g
31.9 g

I found the average mass of the marbles: 22.65 g

I found the difference in masses of the marbles:
0.1 g
9.5 g
0.8 g
0.1 g
4.2 g
0.1 g
0.1 g
5.7 g
0.3 g

I found the average of the differences: 2.32 g

I subtracted both the averages to find the mass of one marble: 20.33 g. This doesn't make sense since the smallest mass of a container + the marbles = 11.0 g. A single marble on its own can't be 20.33 g. Some additional info I got was that there is a maximum of 5-6 marbles in one container and the empty container weighs at least 3 g.

I would really appreciate help on where I went wrong and how I can go about answering the rest of the questions. Thank you!
 
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First you need to understand Millikan's experiment and how this process is analogous to Millikan's method. What level course is this for?
 
hutchphd said:
First you need to understand Millikan's experiment and how this process is analogous to Millikan's method. What level course is this for?
12th class physics
 
orangegalaxies said:
I would really appreciate help on where I went wrong and how I can go about answering the rest of the questions. Thank you!
This is perhaps a tough question, as you may actually have to think about what to do.

First, let's look at these two measurements:

orangegalaxies said:
11.0 g
11.1 g

What do you think about that?
 
PeroK said:
This is perhaps a tough question, as you may actually have to think about what to do.

First, let's look at these two measurements:
What do you think about that?
The difference in their masses is very small
 
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orangegalaxies said:
The difference in their masses is very small
That's a statement of fact. What do you think about that fact?
 
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orangegalaxies said:
I found the average of the differences

Why? What good do you think this will do you? How do you intend to use this number?
 
PeroK said:
That's a statement of fact. What do you think about that fact?
Does it probably mean they have the same number of marbles?
 
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Vanadium 50 said:
Why? What good do you think this will do you? How do you intend to use this number?
My teacher gave us this hint to get started so I followed it. I don't understand why since the resulting mass is too big
 
  • #10
orangegalaxies said:
Does it probably mean they have the same number of marbles?
Definitely. What about taking a fresh look at all the data you have?
 
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  • #11
PeroK said:
Definitely. What about taking a fresh look at all the data you have?
I see that there are some other masses that have a difference of 0.1 so I can probably assume they also have the same number of marbles, eg:

21.4 g
21.5 g

25.7 g
25.8 g
25.9 g

Is it too much to assume the 11.0 and 11.1 masses contain the minimum number of marbles?
 
  • #12
orangegalaxies said:
I see that there are some other masses that have a difference of 0.1 so I can probably assume they also have the same number of marbles, eg:

21.4 g
21.5 g

25.7 g
25.8 g
25.9 g

Is it too much to assume the 11.0 and 11.1 masses contain the minimum number of marbles?
Does it say anything about there being at least one marble in each case?

Do you think you could have two marbles in a container of approx 11g?
 
  • #13
PeroK said:
Does it say anything about there being at least one marble in each case?

Do you think you could have two marbles in a container of approx 11g?
Yeah I don't see why it can't have two marbles. For sure, each case should have at least one in it.
 
  • #14
orangegalaxies said:
Yeah I don't see why it can't have two marbles. For sure, each case should have at least one in it.
If it has two marbles, what is the most (approx) each could weigh? Remember that the container must be at least 3g.
 
  • #15
PeroK said:
If it has two marbles, what is the most (approx) each could weigh? Remember that the container must be at least 3g.
4g?
 
  • #16
orangegalaxies said:
4g?
So, how many does a container of 31-32g have?
 
  • #17
PeroK said:
So, how many does a container of 31-32g have?
Around 7 marbles? How can we assume the 11g one has 2 marbles though?
 
  • #18
orangegalaxies said:
Around 7 marbles?
Is it allowed to have 7 marbles?

orangegalaxies said:
How can we assume the 11g one has 2 marbles though?
To see whether that's a possibility.
 
  • #19
PeroK said:
Is it allowed to have 7 marbles?To see whether that's a possibility.
Nope ahhh so it's just to test, like theoretical stuff?
 
  • #20
orangegalaxies said:
Nope ahhh so it's just to test, like theoretical stuff?
It's called logic!
 
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  • #21
PeroK said:
It's called logic!
Great! Thanks ~a lot~!
 
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  • #22
It may interest the OP that Millikan had oil droplets whose mass could be measured/estimated that also carried a small electrical charge that varied from perhaps one to as many as 10 or 15 electrons. By seeing how the oil drop responded when placed in an electric field of known value, he was able to determine what the charge was that was on each of the oil drops, with some small but significant uncertainty. The charge that was on each oil drop he determined to be a small integer multiple of ## 1.602 E-19 ## Coulombs. In his original experiment, he did not have 3 decimal place accuracy=his data perhaps was something like this data with the marbles=you need to sift through some experimental error to take an educated guess at what is the most likely mass of each marble.

One item that I think may affect things is that it said the containers were different=there is no guarantee that every one of them is 3 grams.
 
  • #23
Charles Link said:
It may interest the OP that Millikan had oil droplets whose mass could be measured/estimated that also carried a small electrical charge that varied from perhaps one to as many as 10 or 15 electrons. By seeing how the oil drop responded when placed in an electric field of known value, he was able to determine what the charge was that was on each of the oil drops, with some small but significant uncertainty. The charge that was on each oil drop he determined to be a small integer multiple of ## 1.602 E-19 ## Coulombs. In his original experiment, he did not have 3 decimal place accuracy=his data perhaps was something like this data with the marbles=you need to sift through some experimental error to take an educated guess at what is the most likely mass of each marble.

One item that I think may affect things is that it said the containers were different=there is no guarantee that every one of them is 3 grams.
The containers are all the same, it's the number of marbles in them that are different. All the containers were opaque film canisters.
 
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  • #24
PeroK said:
It's called logic!
what do i have to do next?
 
  • #25
This one can be solved with a quick look at the data. Precise refinements take extra work, but you should be able to look over the data quickly, with a pretty good idea of what the mass of one marble is.

Note: There appears to be a large experimental uncertainty in the data that they supplied you with, on the order of +/-.3 grams or thereabouts.
 
  • #26
You are told that there are six or fewer marbles in any (identical) container and that the container mass is at least 3 grams. But your initial guess clearly gives 7 marbles Try again.
 
  • #27
orangegalaxies said:
what do i have to do next?
It helps to be organized.
First group together the containers (if any) that have the same number of marbles to within experimental uncertainty.
Second take all the possible differences between containers that you have identified as having different numbers of marbles. Why take differences and how do they help you guess the mass of one marble?
Third check that your guess is consistent with all the other pieces of information you have. If inconsistent, go back to step 2.
Fourth figure out the mass of the container.
 
  • #28
hutchphd said:
You are told that there are six or fewer marbles in any (identical) container and that the container mass is at least 3 grams. But your initial guess clearly gives 7 marbles Try again.
hmmm okay so for the 31-32 g container, i did 31-3 and then divided this by 4, but this is wrong like you said. I'm not sure as to what else i can do :')
 
  • #29
kuruman said:
It helps to be organized.
First group together the containers (if any) that have the same number of marbles to within experimental uncertainty.
Second take all the possible differences between containers that you have identified as having different numbers of marbles. Why take differences and how do they help you guess the mass of one marble?
Third check that your guess is consistent with all the other pieces of information you have. If inconsistent, go back to step 2.
Fourth figure out the mass of the container.
Step 1: Based on the data, the containers that could have the same number of marbles are the ones that weigh:
11.0 g
11.1 g

21.4 g
21.5 g

25.7 g
25.8 g
25.9 g

Step 2: I already found the differences in mass, could you explain more on what I need to do?
 
  • #30
Please show all the data (where are the 31.5g samples?). Get organized please. Then suppose the marbles are ~4g. Does this work? What is the weight of the empty?
 
  • #31
hutchphd said:
Please show all the data (where are the 31.5g samples?). Get organized please. Then suppose the marbles are ~4g. Does this work? What is the weight of the empty?
Masses of all 10 containers in ascending order:
11.0 g
11.1 g
20.6 g
21.4 g
21.5 g
25.7 g
25.8 g
25.9 g
31.6 g
31.9 g

Largest mass: 31.9 g
Approx weight of one marble: 4 g
Mass of empty container: minimum of 3 g

(31.9 - 3)/4 = 7 marbles in largest container

This is wrong, I don't follow what you are saying, can you please explain?
 
  • #32
orangegalaxies said:
Step 2: I already found the differences in mass, could you explain more on what I need to do?
As I already said,
kuruman said:
Why take differences and how do they help you guess the mass of one marble?
As implied by what I said, what you need to do is first figure out what the difference in masses is equal to and, once you answer that, guess the mass of one marble. The number should be consistent with you already know or is given.
 
  • #33
orangegalaxies said:
hmmm okay so for the 31-32 g container, i did 31-3 and then divided this by 4, but this is wrong like you said. I'm not sure as to what else i can do :')
Why did you do this? Container+marbles masses at 32g. There are at most 6 marbles by question. What is minimum possible mass of container?
 
  • #34
kuruman said:
As I already said,

As implied by what I said, what you need to do is first figure out what the difference in masses is equal to and, once you answer that, guess the mass of one marble. The number should be consistent with you already know or is given.
The difference in masses:
0.1 g
9.5 g
0.8 g
0.1 g
4.2 g
0.1 g
0.1 g
5.7 g
0.3 g

Average difference in masses: 2.32 g

Is this then the mass of one marble? Ahhhh it won't work for the larger marbles so I don't think so
 
  • #35
hutchphd said:
Why did you do this? Container+marbles masses at 32g. There are at most 6 marbles by question. What is minimum possible mass of container?
3 g. Pls chill, I'm new to these concepts, not an expert so I won't be able to understand things unless you explain them. My teacher is crappy and won't explain either.
 
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  • #36
I think that 3 gram minimum is inaccurate, and is resulting in extra confusion. I estimate the container to be closer to 2 grams.
 
  • #37
Charles Link said:
I think that 3 gram minimum is inaccurate, and is resulting in extra confusion. I estimate the container to be closer to 2 grams.
hmmmm. these are the values my teacher gave me...
 
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  • #38
Apologies. You almost got it but you need to choose best values from noisy data:
orangegalaxies said:
Largest mass: 31.9 g
Approx weight of one marble: 4 g
Mass of empty container: minimum of 3 g

(31.9 - 3)/4 = 7 marbles in largest container

This is wrong, I don't follow what you are saying, can you please explain?
Can't be 7 marbles by definition. Mass of marble is more like 4.5, Try another guess. It won't be perfect.

Now make guess and plot mass vs # marbles for all data points.
 
  • #39
If you look at the data, at first glance, (I'm sure you observed it as well), there appears to be increments of between 4.5 and 5 grams. There is a jump from 11 to 21, but with a small sample, it's not surprising that the 16 is absent.
 
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  • #40
hutchphd said:
Apologies. You almost got it but you need to choose best values from noisy data:
Can't be 7 marbles by definition. Mass of marble is more like 4.5, Try another guess. It won't be perfect.

Now make guess and plot mass vs # marbles for all data points.
Can you explain how you got 4.5 g?

Assuming each marble is 4.5, and the empty container is 3:

Mass : Number of marbles
11.0 g = ~2
11.1 g = ~2
20.6 g = ~4
21.4 g = ~4
21.5 g = ~4
25.7 g = ~5
25.8 g = ~5
25.9 g = ~5
31.6 g = ~6
31.9 g = ~6
 
  • #41
Charles Link said:
If you look at the data, at first glance, (I'm sure you observed it as well), there appears to be increments of between 4.5 and 5 grams. There is a jump from 11 to 21, but with a small sample, it's not surprising that the 16 is absent.
Yeah you're right that is a patterm
 
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  • #42
I just spotted something else=they give you the weight of the container to be at least 3 grams=it might even be large enough to make the 11 g have just one marble=my previous post on this being inaccurate and possibly 2 grams was incorrect.
 
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  • #43
Charles Link said:
I think that 3 gram minimum is inaccurate, and is resulting in extra confusion. I estimate the container to be closer to 2 grams.
I disagree I think it is more like 6g. The problem says >3.
 
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  • #44
hutchphd said:
I disagree I think it is more like 6g. The problem says >3.
see my post 42 :)
 
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  • #45
Charles Link said:
I just spotted something else=they give you the weight of the container to be at least 3 grams=it might even be large enough to make the 11 g have just one marble=my previous post on this being inaccurate and possibly 2 grams was incorrect.
This is also true yeah
 
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  • #46
Yes Now the OP needs to graph the data, draw the best linear fit. Slope gives marble mass, intercept gives container mass
 
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  • #47
hutchphd said:
Yes Now the OP needs to graph the data, draw the best linear fit. Slope gives marble mass, intercept gives container mass
graph the differences in masses?
 
  • #48
Graph y=total measured mass vs. x=number of marbles
y value for x=0 gives mass of container.
 
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  • #49
Your eyeball and ruler will draw the "best" line pretty well. Gives the best fit to all the data.
 
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  • #50
is there a way to solve this problem without graphing? my teacher never mentioned graphing, they only said you need to find the averages. they are a pretty bad teacher tbh but i wanted to confirm
 

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