The Sphinx's Lair

byebye

Q: Swapping 3 rooks in a 3x3 grid

1:11 AM

0

This puzzle was inspired by this one: Swapping rooks in a 4x4 board What is the least number of moves required to swap black and white rooks? Rooks move using standard chess rules (vertically or horizontally), but you do not need to alternate players.

Q: Logic puzzle: 19 balls and a scale

1:36 AM

0

You have 19 balls that are identical in all ways, except one ball is either heavier or lighter than the rest. With a balance scale, how could you determine in three weighings which one the odd ball? and whether it’s lighter or heavier?( in a systematic way)

logical-deduction enigmatic-puzzle arithmetic

Q: Math Puzzle #01 (remade from Math Tapestry Puzzle)

2:26 AM

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The Puzzle is just above this message. The check mark will be whoever can get the lowest pair possible. The smallest pair will be decided by the average of the numbers.

mathematics

3:45 AM

Okay, I've finished all parts of the Making Of post except "Logistical Steps"

Time to look in my grid's revision history :)

1:20 PM

0

Q: 19 balls and a scale

You are given 19 identical looking balls and a two sided scale. One of the balls ism different either lighter or heavier. Using 4 weighings of the scale How can you determine which ball is odd and whether it's lighter or heavier?

strategy weighing

Q: 2 weird problems I came across

1:45 PM

0

A man accused of murder hires a lawyer who is always believed by the court to be telling the truth. The prosecution's attorney says that if the accused man committed the murder, he had an accomplice. The defence lawyer says that this affirmation is not true. Did the lawyer help his client by say...

logical-deduction liars

Q: The ID of my next Zoom meeting

2:35 PM

1

My friend is inviting me to a Zoom meeting. Rather the sending me the ID for it, he sent me the following 10 IDs. "Each of these numbers has precisely two digits which are identical, and exactly in the same position, to two digits in the correct ID for the meeting", he told me. My friend claims t...

mathematics

3:33 PM

@GarethMcCaughan, any updates on the CCCC?

matt

6:42 PM

@bobble same, my biology labs have just been things like "count the things in 3 random squares and average them all and then count them all up" and "make an arch out of ice cubes"

@bobble apparently not

7:26 PM

CCCC: Quaint rubbish, the tail end of someone's stuff from long ago (8)

Sorry about the slowness. @bobble The problem is scarcely ever that I've forgotten about it.

no problem! glad to see it up

matt

7:39 PM

hmm

North Læraðr

11:15 PM

Hm, "quaint" and "from long ago" can have awfully similar meanings

11:28 PM

Physics help, again: how can you measure the velocity & acceleration of an elevator, while inside it with a spring, meterstick, stopwatch, and set of weights?

Well, famously you can't measure its velocity.

well, then what about acceleration?

I need to calculate v_max and a when at v_max

Acceleration is indistinguishable from gravity. How would you measure the gravitational acceleration?

and my teacher has gone over literally nothing about springs

Calculate F_grav with the weight of the objects & g

So, just to return to the thing about velocity, because it's important: if you are inside a box that's moving with constant velocity v then there is literally nothing you can do to distinguish that from being inside a box that isn't moving at all. There actually isn't any physically-detectable difference -- aside from interactions with things outside the box that might be moving in different ways.

If the elevator has a glass window or something so that you can see the outside, of course it's a different matter.

11:32 PM

I know that the elevator will start at rest (v = 0), accelerate to v_max, and then decelerate to rest

the question specifically says no windows

(You're then measuring the velocity relative to what's outside, but that's all you can Oh, wait, you have extra information about what it's doing.

)

This is feeling like a puzzle where I wasn't taught the necessary background information :(

What do you know about springs?

There's something called a spring constant which is N/m

And do you know what it means?

11:34 PM

but again, my teacher hasn't taught us ANYTHING about springs, but this workbook is due tomorrow

and no, not entirely sure what the spring constant is

That's OK -- you don't need to know very much about springs.

Did you ever learn something called Hooke's law?

Nope

Should I google?

OK then, so that's the one thing you need to know about springs :-).

You could ask Google if you like, or I can just tell you.

tell me i'm lazy :)

So the behaviour of a spring (at least as long as the forces on it aren't too large) is completely determined by two things. (1) Its length when nothing's stretching or squeezing it. Call that L. (2) Its spring constant. There's probably a standard name for that but I'm not sure what; let's call it k, which might even be standard.

11:36 PM

Okay

If you stretch the spring to have length L+x, then the force you have to exert to do that (= the force with which the spring pulls the ends inward again) equals kx.

The fact that there is such a k -- i.e., extension and force are proportional -- is Hooke's law.

so delta-L = x, and F = delta-L * k

Yes.

For real springs, if you stretch or squash them too far/hard then this law breaks down in various interesting ways.

I'm assuming this is an ideal spring

And of course some spring-like things don't work in compression but do in tension. (Think about, say, a length of elastic.)

Yup.

So, if you hang a mass m on a spring with given values of L and k, what happens to the length of the spring?

11:39 PM

F = mg, F = delta-L * k, mg = delta-L * k, delta-L = mg/k

probably should have made those separate

OK. Congratulations, you have invented the weighing scale.

cool!

Now, suppose the elevator is accelerating upward with acceleration a. What happens to your spring while that happens?

I don't know, this is the part I have trouble reasoning about

The forces present are confusing to me

OK. Forget about "doing physics" and answer this: When you're in an elevator and it starts moving upwards, what does it feel like?

11:42 PM

Like I'm being pushed down

(I think. haven't been in elevators recently)

What if it starts accelerating downwards?

(Just trying to build a little intuition here.)

Like gravity is less, a bit like floating

Right.

But why? Gravity isn't actually less

So in fact there's no way to distinguish, from inside the elevator, between (1) gravity acting in a particular direction and (2) accelerating in the opposite direction. This is called the "Principle of Equivalence", and it was first formalized by a chap you might have heard of called Albert Einstein.

11:45 PM

Okay, I'm with you so far

So. Suppose the elevator is accelerating upward with acceleration a. What do you reckon is the equivalent thing that could happen to gravity to make it feel the same?

g becomes g + a

(It's a bit unnecessary to formulate all this in terms of what would happen to gravity, but I think it's not a bad way to think about it. We'll talk briefly about another way later.)

Right. So what's the length of your spring now?

delta-L = m(g + a)/k?

Right.

What about when the acceleration goes the other way (when it's slowing down from v_max to 0 again)?

11:48 PM

delta-L = m(g - a)/k

OK. So, which of these things can you measure?

And which do you already know?

m, k (outside the elevator), delta-L, and g is constant

Are you allowed to do preliminary experiments outside the elevator to measure things?

And are you told the value of m?

I think. The weights have known mass, and I calculated the spring constant (not really understanding what it was) beforehand.

Do you mean some earlier bit of the question said that you did an experiment that ends up finding the spring constant?

11:51 PM

Yes, there was a previous question that was just weights, meterstick, and spring. I got k from there

(didn't think it was important to mention. sorry)

OK. (You can actually do without that, by being a bit sneaky with your measurements inside the elevator. But apparently there's no need :-).)

Right. So, it seems to me that from the things you know and the things you can measure it's pretty straightforward to find out the value of a at any moment.

There's a bit of a difficulty around the fact that when the acceleration changes the spring can't really respond instantaneously, but I assume we're supposed to ignore that issue :-).

Assume long enough elevator ride for evening out, I guess

Are you told that the elevator accelerates with constant acceleration from v=0 up to v=v_max, and then decelerates with constant acceleration from v=v_max down to v=0 again?

Nope

(I'm guessing yes.)

Oh.

So in that case do you have a way of recording from instant to instant what the acceleration is? Because you're going to need to do some numerical integration if you want to get velocities out of this...

That seems slightly unlikely to be what they have in mind; you might want to double-check whether constant acceleration is implied somewhere.

11:55 PM

chegg.com/homework-help/questions-and-answers/…

^^ you can read the problem

I think that phrase "the upward acceleration a that the elevator has as its speed increases to maximum" implies that a is constant.

Okay, that is good. I wasn't sure if it counted.

OK. So it seems to me you have everything you need to find a.

So I start stopwatch, then measure initial a.

Once a changes (the spring goes haywire), I record the time

And then measure second a.

It looks to me as if they haven't actually asked you to measure what happens as it slows down again.

11:57 PM

measure a = take delta-L and calculate

why do I have a stopwatch?