Math Is Fun Forum

Thanks, Bob, although I'm having second thoughts;

Two examples later and my method didn't seem to work, and theirs did;

6x^2 + 11x -10

P.S. Is there a BBCode for superscript that works here?

Thanks

Thanks.

So the nth root of x = x^1/n ?

Thanks, Bob. When you say ‘effectively weightless’ are you referring to his apparent weight as opposed to his true weight (terms I’ve just come across)?
So if the cable breaks his apparent weight, the weight he ‘feels’(?), the weight he ‘seems’ to be(?); but his true weight his what it always is regardless of other factors, like acceleration, i.e, the gfs of 10N/kg times his mass of 90kg?

I’m told this isn’t actually freefall because of the force of friction involved; is that correct?

So the air, being matter, stuff with mass, accelerates too, at -10m/s/s?
You said he’d have no way of telling that he wasn’t able to float; so he isn’t able to float?

Do you mean 20m/s/s on top of the 10m/s/s due to gravity? Or 20m/s/s in total (10 due to gravity, 10 due to it’s motor/whatever)?

Ah, so he is floating, floating up. Why? Why isn’t he being pulled down at 10m/s/s due to the gfs?

10 due to the gfs, 10 due to the motor/whatever?

The force on him from the ceiling is 90(20-10)?

I think I’m partly getting that, but I’ll need to try harder to grasp it better.

I’m not quite sure I’ve followed the above to get here but 10-2(90)=720 which I think was the correct answer to my original question.

Rise up in the reference frame of your body? From the reference frame of a viewing platform would your organs remain stationary for a moment while you plummet, like a gory episode of The Road Runner?

Thanks, Bob.

I asked chatgpt about it.

I said,

"If inertia is 'an object's tendency to resist acceleration', and increasing velocity alters that tendency, then inertia must depend, at least partially, on velocity."

It replied with,

"And you're not wrong — if we use that broad, intuitive definition of inertia.

And then it got complicated, with how Newton actually defined things like mass, and acceleration, in terms of F=ma, etc.

I think I'll leave it for now, let it brew, and come back to it later. Thanks for your help with this one.

Fascinating. And mind-bending. For me at least.

So you, Bob, are driving a train, east at 6m/s.

And I’m driving a trolley east at 6m/s, parallel to you.

From the reference frame of your train I’m at rest.

And in your reference frame no force is required to stop me, because I’m already at rest? Even though we both know a force would be required to stop me in the reference frame of the ground beneath me?

Thanks, Bob

So now we view the trolley in the second example in the reference frame of the train moving at 6m/s in the same direction as the trolley.
To stop the trolley in 2s;

F=ma
F=100kg(-3m/s/s)
F=-300N

But if we view the trolley in the second example in the reference frame of the train why not view the trolly in the first example from that reference frame?
It was moving at 6m/s with reference to the ground. Now it’s moving at 0m/s with reference to the train.
But we still want to stop it in 2s.
So,

F=ma
F=100kg(a)

What do we put for ‘a’?

A=(v-u)/t
A=(0-0)/2
A=0/2
A=0

So,

F=100kg(0)
F=0N
But we know that a force of >0N would be required to stop the trolley, don’t we?

“I just used those as examples.  There's no limit to the number of possible frames.”

Thanks, Bob. I thought that might be the case, but wanted to be sure.

“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”

Do you mean something like;

Train heading west at 6m/s relative to ground.
Trolley on platform heading west at 12/ms relative to ground.
Trolley in reference frame of train = 6m/s west
(12m/s – 6m/s)?

Bob, you said,

“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.”

Wouldn’t we have reference frames without all of that? Wouldn’t we have reference frames if the Universe consisted solely of a static Earth?
On a static Earth you could still, for example, be seated on a railway platform, at rest with reference to the person sharing the bench with you; while a person on a moving train, at rest with reference to the person sharing the seat with her, would be moving with reference to you; and they could see themselves as at rest with you moving away from them. And someone could be running along the aisle of the train to catch the buffet car before it closed, etc, etc. Wouldn’t that amount to several reference frames?

Hello, ktesla39. Yes, it is fun, especially for me, as I've often never used any kind of code before.

Question for you, and Bob, and anyone else reading this. Have you memorised all the commands/tags/whatever it is you call the bracketed thingys, and now when you use it is as simple as typing any kind of text?

P.S. Why is this block of yellow text called 'inserted text'?

Thanks, Bob

Thanks, Phil

(You are in bold and italics respectively because I'm practicing my BBcode)