Math Is Fun Forum

Oh yes,certainly.   I just used those as examples.  There's no limit to the number of possible frames.

Bob

Have I told you where to look for a long list of these?

Go to help and you'll find it in the third thread.

The thread existed long before I joined but it was hidden. I stumbled on it one day and copied it into the post in help.me
The whereabouts of the original is a mystery but I've added to my version so that's the place to go.

Do I know them all? Certainly not!  I don't fill my head with stuff like that

No idea  why they are given those names. Someone thought it was a good name I guess.

Bob

Italics means sloping

Emphasis means bold

Monster?  Nay! Admin have super powers to disintegrate unwanted characters.  And a character has two meanings; both of which are vulnerable.
B

Latex commands are 'called' by inserting them between the opening and closing command math

It used to be possible to suppress the action be using another bbcode command, code, but it seems to no longer work, probably happened when the forum switched to a new server.  So I'll leave off the first open bracket and the last close bracket to avoid the code interpreter trying to action the code.  Then I'll repeat but with all the brackets, so you can see what the command does.

math] commands here [/math

So to make a simple fraction

math] \frac{3}{4} [/math

Here's an integral

math] \int_0^\infty x^{x+2} + \alpha x .dx [/math

Years ago the member Dross wrote a tutorial to get people started https://www.mathisfunforum.com/viewtopic.php?id=4397

and others added to the thread.  I find the code commands are blacked out now and some other commands no longer work but there's still a lot of useful stuff here.  I go there if I want something I haven't used before eg. the infinity in the line above.

You can also do an internet search for the right command but this can be frustrating as not all are implemented here.

^ for to the power of works simply if followed by a single character eg

math] x^7 [/math

but if you want a more complicated power the power must be enclosed in {}

math] x^{y + 7} [/math

Otherwise this happens

If you see some Latex and want to see the underlying commands just click on it.

Hope that gets you started.

Bob

Usually I can answer your questions based on what I was taught and passed on in my own teaching.  This one is the exception. In all the Newtonian mechanics and physics questions I have encountered, inertia has never occurred.

I had to go up in my loft and get down all my old texts on applied maths and physics.  Some just refer to Newton and  basically say bodies possess the property of inertia, that is they do not accelerate unless acted upon by an external force. 

I also tried googling the units for inertia. I got two answers:

Mass is a measure of an object's inertia. The more mass an object has, the more inertia it has.

The SI unit for inertia is kilogram-meter squared (kg⋅m²). While the term "inertia" is often used to refer to an object's resistance to changes in motion, the actual concept of resistance to change is often referred to as moment of inertia. The moment of inertia is a measure of how an object resists rotational acceleration.

The first is inertia as it applies to linear motion and the second to rotating objects. 

The measure of linear kinetic energy is 1/5 . m . v^2 and for rotating objects 1/2 . I / w^2 where I is the moment of inertia and w the angular velocity.

We're not the only ones confused. Have a look at this thread :

https://physics.stackexchange.com/quest … n-stopping

So there we are. Everyone is confused and there's no one answer.

LATER EDIT: I've given this some over-night thought.  For an object with zero or uniform velocity it's inertia is because of its mass.  More mass, more inertia.  It's actual velocity is irrelevant.  The Earth rotates on its axis, and around the Sun, which in turn, rotates around the centre of the Galaxy, which is moving relative to other galaxies.  That's why we have the concept of frames of reference.

If you consider that trolley going at various speeds, then, yes, the amount of force to reduce that velocity to zero will vary, but that doesn't alter its inertia. It just gives you the means to do the calculation.  If you set up a frame of reference that travels at 6 m/s in the second case, then the trolley is only travelling at 6 m/s relative to that frame and so can be 'brought to rest' in the frame with the same effort as the first case.

Momentum gives you a way to measure the force required, but I showed in a previous post that impulse is just a way of applying v = u + at to determine F.

Bob

It looks like a homework assignment. As a teacher I'd prefer that members don't just do the work for someone.  You could see if you can write a program but don't post it. That way if RegJose comes back with a request for specific help you're well prepared even if your version isn't quite what the assignment requires.

Bob

A C function is a computer program routine written in the language C.

This scenario is clearly artificial as no business person would, given the choice, send out all of the product that is in low supply whilst restricting amounts of the product in plentiful supply.  That's a topsy turvy law of supply and demand. I conclude this is a homework assignment.

On this forum we don't do people's homework.  If,  RegJose, you have most of the code written, but are stuck over one issue, post what you've done and perhaps someone will be able to help with that.

Bob

hi Filte1943

Welcome to the forum.

I'm not very confident with series limits but I'll have a go.

The ratio test is

Where a(n) is the general term of the series.

If L < 1 then the series converges.

In your case:

This will tend to 1 from below. The ratio test is inconclusive in such a case.

LATER EDIT: Found this: https://math.stackexchange.com/question … o-infinity

Bob

hi paulb203

Good to hear from you.

Your answer is correct.  The working obviouly works but there are one thing not quite right about what you've written.

Back to basics:

So 11.9 isn't in Newtons as it's an impulse not a force.  What are the units for impulse? Ns  ie Newton seconds. So you are not subtracting Newtons from Ns.  The equation underlying this calculation is

I had

That gives V = 47 m/s

Bob

I learnt it as conservation of momentum.  Your calculation is correct.  But should need to add emphasis concerning direction.

So start by declaring you are taking East as the positive direction and end by stating the combined object travels East at 2/3 m/s.

Bob

What you call it isn't important.  The calculation is

Decide on a positive direction (either will do but then use it throughout).

As the objects are travelling towards each other one v will be + and the other - .

Bob

hi again.

I've partly answered your other number base question.  But this one ??? Did you just throw together some numbers to ask this?

In any number case the column headings are n^3    n^2    n    and units.
The only digits that are allowed are those smaller than n.

So

would never occur. 5 and 8 don't exist as digits in base 5.

Bob

If you want more help on number bases you could look here:

https://www.mathsisfun.com/numbers/bases.html

or post again, but not in this area of the forum, but rather in the help me section.

Bob