Particle Accelerator

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Guru Vishnu

05:08

@JohnRennie: Hi sir. Good morning :-)

John Rennie

@GuruVishnu hi :-)

Guru Vishnu

@JohnRennie: Are you free now sir?

John Rennie

Yes

Guru Vishnu

Ok sir. Just a continuation of yesterday's discussion.

The first green one gives the correct answer whereas the second red box gives the incorrect one.

John Rennie

OK ... ?

Guru Vishnu

05:11

@JohnRennie Why is the component of one velocity along the another gives the correct result whereas the other way round gives the incorrect one?

How exactly does the second method fail? And what differentiates it from the first one?

John Rennie

Consider what happens when $\theta = 90°$. At this instant the mass is moving tangentially to the the string i.e. we momentarily have circular motion. Yes.

@GuruVishnu hello?

Guru Vishnu

@JohnRennie Hi sir.

@JohnRennie I understood so far.

John Rennie

05:27

So at this moment $dL/dt = v = 0$ and $u \ne 0$.

Guru Vishnu

@JohnRennie I didn't get why is $v=0$; isn't it non-zero all the time sir?

It's something an external agent like a motor maintains...

John Rennie

Consider this instant i.e. when the string is vertical. What is $dL/dt$ ?

Guru Vishnu

@JohnRennie On a L-t graph, as the block moves left to right, we get an extrema when the string is perpendicular to the surface. And hence the derivative is zero.

John Rennie

Yes, so if the block is moving horizontally we must have $v = 0$.

Guru Vishnu

Now I get your statement. I thought it was something like assuming $\theta$ to be a constant like I did yesterday which eventually led to the incorrect answer.

John Rennie

05:37

What this actually means is that $v/u = 0$ so if $v$ remains constant that would mean $u \to \infty$.

Guru Vishnu

@JohnRennie How could that be possible then? This looks like a simple experimental setup and how could we go faster than the speed of light, sir?

John Rennie

In a real experiment if we held $v$ constant we we need to apply an increasing force as $\theta \to 90°$ and the block would lift up off the base.

Guru Vishnu

Ok sir.

John Rennie

If we had some form of rails keeping the block moving horizontal then as $\theta \to 90°$ the force we would need to keep $v$ constant would go to infinity.

Guru Vishnu

Ok sir. This seems much better to me.

But how to relate this with my confusion?

@JohnRennie sir?

John Rennie

05:45

I'm not really sure what your confusion is ...

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