Since it’s a straight line, this implies proportionality. Now, there is the slight complication that the pulley does exert a force on your system, but it’s safe to ignore this and just picture everything in one-dimension. This can be separated into 2 main steps. The list looks like this: What if the situation is changed to this:

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Your logic treats both containers and objects as distinct. Probabilities, 7 items, 4 containers. Then the balls are dropped 7 at a time into each of 32 containers. The main issue was that the probability of these patterns is based on permutations instead of combinations. First calculate the number of ways 7 items can go into n bins, none empty, using this expansion series: Then I divided gravity by each calculated acceleration so I ended up with 6 new numbers.

Sign up using Facebook. Then, the numbers in the list can be expressed by S 7,k 32 k k! I dont understand exactly your question about the possible permutations of what?

Hopefully that is enough for you to see that what you discovered is Newton’s 2nd law. The distribution of homewok in the container is random. Then the balls are dropped 7 at a time into each of 32 containers.

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Then I divided gravity by each calculated acceleration so I ended up with 6 new numbers. The right-hand side is the total mass of the two-mass system multiplied by the its common acceleration.

First, your list of numbers are actually the number of ways of putting 7 distinct items, not identical items, into containers. I already have the answer for this, but wondering if there’s some efficient way to calculate this. So, I thought about this a little more, and I think some case-by-case work is probably inevitable.

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Physics Stack Exchange works best with JavaScript enabled. Is the probability of the distribution of black balls the same as you described? Similarly there are orderings for each case and for each case. Post as a guest Name. Verifying Newton’s 2nd Law Ask Question. For 5 trials the mass was increased. Thread starter rcgldr Start date Mar 20, Is the logic in my first post treating the items or containers as distinct: So taking one of the cases, suppose we have bin allocations: That might be appropriate for your application; I really don’t know enough puysics judge.

So perhaps for your situation you do need to consider the whole space of distinct items. The main issue was that the probability of these patterns is based on permutations instead of combinations.

Note homewwork 7 items into 4 containers is the same as rolling a 4 sided die 7 times and noting the outcome, so this method can be used for permutations or probability of rolling a die several times. IS all that is needed to verify it?

This can be separated into 2 main steps.

In one of my classes a mass 0. For example, with 4 bins used: The number of ways to do this would be 32x1x1x1x31x30x What if the situation is changed to this: Since it’s a straight line, this implies proportionality. The number of different distributions of identical objects was the point I was trying to answer; probability is another subject again. The hanging mass would be dropped and the acceleration of the mass on the airtrack would be calculated. Obviously for 7 items into a particular bin, there is only one option.