calculate the "best angle" (1 Viewer)

[:: ck ::]

ok heres a question... i don't even know if it's still in the syllabus or not but im curious on how to answer it ... >.<

"A car of mass 1000 kg travels around a curve in a road with radius 200 m at 100 km/h

Calculate :
a) The best angle to the horizontal to bank the road; and
b) The reaction force applied by the road to the car when the car is banked at this angle.

 

[Suvat]

maybe this should go in the 4u maths forum...

 

[Constip8edSkunk]

its not... but its in 4U maths. If you do it, you will learn it in thecircular motion topic.

basically draw a force diagram and resolve vectors verically and horizontally to get smultaneous eqn, which can b solved

eg.
where N is the normal and @ the angle of the banked track, with 0 friction
vertically: mg=Ncos@ ......[1]
horizontally: mv^2/r=Nsin@......[2]
[2]/[1] : v^2/gr = tan@ , to find @
[1]^2+[2]^2: m^2(g^2+(v/r)^2) = N^2 , to find N

edit: lol i shouldve wrote a 1 sentence reply like suvat hehe

 

[:: ck ::]

thx skunk

4unit eh... mmm looks like i'll be doing that stuff next year~ T.T

 

[Ragerunner]

If I saw that question in my HSC,

I'll be saying a big "WHAT THE ####??!!"

 

[Rahul]

Originally posted by :: ryan.cck ::
4unit eh... mmm looks like i'll be doing that stuff next year~ T.T

yep, mechanics will be one of the last topics you will do, if not the last [before harder 3u]

 

[...]

all this is taken out of the syllabus..

 

[Rahul]

ryan, did you get this out of an old physics book? seems like it is from the old syllabus, as mentioned above.

 

[Dash]

Me is drunk I say sir....
Dis aint gunna be in ur hsc god dam man!!
Cool down n screw the hsc! Its a piece of shitty DOGGGG!!!!!
I have no idea what I'm on about......
Bah......... la la la la la... time to get sobre.................................

 

[:: ck ::]

oOoo *phew*

mm i got it in a tutorin test i was late to class and all i heard was that u didn need to know how to do that particular questoin for hsc

 

[wogboy]

It isn't in the HSC Physics syllabus, but if you're still curious find out how to solve it, look at the attached diagram:

1. Identify all the forces acting on the body, and draw it onto a diagram:

- Weight force (W = mg, vertically down);
- Normal reaction force (N, diagonally upwards, perpendicular to the surface of the road)
- We'll neglect friction.

Also identify the net force acting on the mass, which is the centriperal force C = mv^2 / r, pointing towards the centre of the tracks.

2. If you add the vectors W and N you should get the vector C. (W + N = C). Draw up a vector diagram lke the one I attached.

3. From the vector diagram, work out the angle required using some simple geometry and trigonometry.

You can see that:
tan@ = C / W = (mv^2 / r)/(mg)
= v^2 / rg

(note that the mass cancels out, so the angle is independent of the mass)

a)
r = 200m, v = 100 km/h = 27.78 m/s, g = 9.8 m/s^2

tan@ = (27.78)^2 / (200 * 9.8)
so @ = 21.49 degrees

b)
m = 1000 kg

N^2 = C^2 + W^2 (Pythagoras' theorem)

N = sqrt(C^2 + W^2)
= sqrt[(mv^2 / r)^2 + (mg)^2]
= 10532 N

 

[:: ck ::]

woah shit ~!!

cool ... soundz... easy.. haha

thx wogboy