Millikan Experiment Based Marble Mass Homework

[orangegalaxies]

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!

 

[hutchphd]

First you need to understand Millikan's experiment and how this process is analogous to Millikan's method. What level course is this for?

 

[orangegalaxies]

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

 

[PeroK]

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:

11.0 g
11.1 g

What do you think about that?

 

[orangegalaxies]

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

 

[PeroK]

The difference in their masses is very small

That's a statement of fact. What do you think about that fact?

 

[Vanadium 50]

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?

 

[orangegalaxies]

That's a statement of fact. What do you think about that fact?

Does it probably mean they have the same number of marbles?

 

[orangegalaxies]

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

 

[PeroK]

Does it probably mean they have the same number of marbles?

Definitely. What about taking a fresh look at all the data you have?

 

[orangegalaxies]

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?

 

[PeroK]

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?

 

[orangegalaxies]

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.

 

[PeroK]

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.

 

[orangegalaxies]

If it has two marbles, what is the most (approx) each could weigh? Remember that the container must be at least 3g.

4g?

 

[PeroK]

4g?

So, how many does a container of 31-32g have?

 

[orangegalaxies]

So, how many does a container of 31-32g have?

Around 7 marbles? How can we assume the 11g one has 2 marbles though?

 

[PeroK]

Around 7 marbles?

Is it allowed to have 7 marbles?

How can we assume the 11g one has 2 marbles though?

To see whether that's a possibility.

 

[orangegalaxies]

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?

 

[PeroK]

Nope ahhh so it's just to test, like theoretical stuff?

It's called logic!

 

[orangegalaxies]

It's called logic!

Great! Thanks ~a lot~!

 

[Charles Link]

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.

 

[orangegalaxies]

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.

 

[orangegalaxies]

It's called logic!

what do i have to do next?

 

[Charles Link]

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.

 

[hutchphd]

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.

 

[kuruman]

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.

 

[orangegalaxies]

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 :')

 

[orangegalaxies]

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?

 

[hutchphd]

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?