Banked Circular Motion (1 Viewer)

[MongMan]

Banked circular motion. How should I be setting out my solutions to these problems?
Cambridge Ex 7.6
1) A car has no tendency to slip when travelling at a speed of v ms^-1. round a section of track of radius 100m which is banked at an angle of 12'. Find the speed of the car.

want v, r=100m ø=12'

___
| . /
|ø/T
|/

Tsinø = mv^2/r
Tcosø = mg

tanø = v^2/rg
v^2 = rgtanø

Is this kind of solution grossly oversimplified? How should I be setting out this kind of problem?

 

[cutemouse]

How are you resolving forces?

There's two ways to do this: Resolving forces down the plane and perpendicular to plane OR resolving forces horizontally and vertically.

In either case you should have a 'F' variable for the sideways slipping/frictional force, which is zero if there is no sideways slipping.

Yes your working out is atrocious.

 

[MongMan]

How are you resolving forces?

There's two ways to do this: Resolving forces down the plane and perpendicular to plane OR resolving forces horizontally and vertically.

In either case you should have a 'F' variable for the sideways slipping/frictional force, which is zero if there is no sideways slipping.

Yes your working out is atrocious.

Is this a troll? It's practically exactly the same as the Cambridge solution I just downloaded.

 

[cutemouse]

Well geez, thanks for calling me a troll when I was trying to help you!

And secondly, Cambridge is a pile of crap for mechanics.

And thirdly, you should have a sideways frictional force in your working, incase the question asks you to work it out.

But nevermind that, I aint going to be helping you if you're going to just blow it back in my face again like that.

 

[cutemouse]

If you were going to do to it properly, here's how.

Resolve forces by drawing the appropriate vector diagrams... Then:

Resolving forces down plane:

mv^2/r * cosθ = F + mgsinθ

For no sideways slipping F=0

So mv^2/r* cosθ= mgsinθ

So tanθ = v^2/rg

So then sub values in etc.


Or you could do this by resolving forces horizontally and vertically, which is a bit more difficult... but if the question asks you to do it this way then you have to.

 

[MongMan]

Sorry bro. And thanks.

I'm starting to notice that cambridge is shit for mechanics. I don't think Fitzpatrick is much better either. What should I be looking at for a good explanation?

mv^2/r * cosθ = F + mgsinθ

I tend to avoid cosøing my mv^2/rs and sinøing my mg's. Gets confusing

How about drawing vectors for F and N (generic F triangle, and N going off on normal), and then saying
Nsinø + Fcosø = mvv/r
Ncosø - Fsinø =mg

and then stating "Negate F=0"?

 

[cutemouse]

I'm starting to notice that cambridge is shit for mechanics. I don't think Fitzpatrick is much better either. What should I be looking at for a good explanation?

The Coroneos 4U supplement. But people say that Patel is good too, I still think Coroneos is better though.

I tend to avoid cosøing my mv^2/rs and sinøing my mg's. Gets confusing

But it's easier that way and you'd be wasting time if you did it the long way and the question didn't ask for it.

How about drawing vectors for F and N (generic F triangle, and N going off on normal), and then saying
Nsinø + Fcosø = mvv/r
Ncosø - Fsinø =mg

and then stating "Negate F=0"?

You could... But F=0 only applies when there is no sideways frictional force.

But what if the question asks you to find F when there is sideways slipping that occurs?

 

[untouchablecuz]

The Coroneos 4U supplement. But people say that Patel is good too, I still think Coroneos is better though.


But it's easier that way and you'd be wasting time if you did it the long way and the question didn't ask for it.



You could... But F=0 only applies when there is no sideways frictional force.

But what if the question asks you to find F when there is sideways slipping that occurs?

Nsinø + Fcosø = mv²/r [1]
Ncosø - Fsinø =mg [2]

[1]*cosø-[2]sinø

i.e Nsinøcosø+Fcos²ø-Ncosøsinø+Fsin²ø=mv²cosø/r-mgsinø

F=mv²cosø/r-mgsinø=m(v²/r-gtanø)

 

[untouchablecuz]

The Coroneos 4U supplement. But people say that Patel is good too, I still think Coroneos is better though.


But it's easier that way and you'd be wasting time if you did it the long way and the question didn't ask for it.



You could... But F=0 only applies when there is no sideways frictional force.

But what if the question asks you to find F when there is sideways slipping that occurs?

Nsinø + Fcosø = mv²/r [1]
Ncosø - Fsinø =mg [2]

[1]*cosø-[2]*sinø

i.e Nsinøcosø+Fcos²ø-Ncosøsinø+Fsin²ø=mv²cosø/r-mgsinø

F=mv²cosø/r-mgsinø=mcosø(v²/r-gtanø)

 

[00iCon]

Terry Lee!!! but they stopped printing

 

[cutemouse]

Terry Lee!!! but they stopped printing

Uhh, Terry Lee isn't that good for Mechanics either.

 

[untouchablecuz]

i used cambridge for mechanics and it wasnt that bad

 

[00iCon]

Uhh, Terry Lee isn't that good for Mechanics either.

How about: No textbook is good for mechanics, and the best way to understand it is to do engineering studies as well.

 

[addikaye03]

Uhh, Terry Lee isn't that good for Mechanics either.

What book did you use then hero?

 

[cutemouse]

What book did you use then hero?

No need to patronise me

As for your question:

The Coroneos 4U supplement.

 

[cutemouse]

How about: No textbook is good for mechanics, and the best way to understand it is to do engineering studies as well.

The Coroneos 4U supplement is pretty decent IMO. The font however put some people off. But a solid book

 

[jchoi]

Sorry bro. And thanks.

I'm starting to notice that cambridge is shit for mechanics. I don't think Fitzpatrick is much better either. What should I be looking at for a good explanation?


I tend to avoid cosøing my mv^2/rs and sinøing my mg's. Gets confusing

How about drawing vectors for F and N (generic F triangle, and N going off on normal), and then saying
Nsinø + Fcosø = mvv/r
Ncosø - Fsinø =mg

and then stating "Negate F=0"?

Cambridge is shit for everything but for the challenging questions and exercises. Fitz should really be good enough for mechanics, that's if you have a proper teacher that introduces the topic to you nicely.