Once in a lifetime opportunity :-)

Fr33b1rd wrote:

For sexyget

First find centipetal force at 100 km/h:

Fc= mV^2/r

Fc = mV^2/60

V = 27.8 m/s

Fc= m * (27.8)^2 / 60 = 12.88 * m

So now we know the centripetal force is greater than the component of gravity

We need to know the component of centripetal force which will tend to make the car slide up the slope (all this Fu).

Fu = 12.88 * m * cos θ

So if curve is banked, the slope is such that Fu = gravitational force pulling car down the slope.

Fd (gravity component down the slope) = mg * sin θ

mg * sin θ = 12.88 * m * cos θ

9.8 * sin θ = 12.88 cos θ
sin θ / cos θ = tan θ= 12.88/ 9.8 θ = 52.7 degrees

Now the range of speeds:

Note: "m" cancels out.

Maximum speed is where friction force = centripetal force upslope - gravity force downslope

Maximum speed:
Frictional force = 0.30 * normal force
Frictional force = 0.30 * [mg cos θ + (mV^2/60) sin θ)]
Force upslope = (mV^2/60) cos θ - mg sin θ

0.30 * [9.8 * cos 52.7 + (V^2/60) sin 52.7)] = (V^2/60) cos52.7 - 9.8 sin 52.7

0.30 (5.94 + 0.013 * V^2) = 0.011 * V^2 - 7.8

1.78 + .004 * V^2 = .011 * V^2 - 7.8

.007 * V^2 = 15.6

V = 47.2 m/s = 170 km/h (maximum speed)

Now repeat exercise for minimum speed, where
friction force + centripetal force upslope. = gravity force downslope

Anything else?

Ha Ha Freebird well done! I found this myself last night at 3am! Yahooooooooo

SG69

Didn't find it anywhere... got a degree in maths and physics. Glad you already have an answer though.

I was good at maths at school... but not that good

heyyyy!

minxywitch wrote:

heyyyy!

Hi minxywitch, if you want to chat, join us in the Good Morning/Afternoon/Night thread

I like problems like that they’re great fun(as far as school work goes) its only basic maths/ physics (As level) but it seems harder as this would be broken up into 2 questions in an exam. It’s much more fun when you have to think about the steps :)

grr jumped the gun and pressed post too quick,

by basic i  meant basic as far as maths and physics go.

and i forgot to say hello to smooth one, so hello:p

hiya folks, hope you are all well.

SmoothOne wrote:

thanks sweetlove.  hope you are well

and great avatar btw

aw thank you very much

my pleasure, so how's your day been?

if you want to chat theres the good morning/afternoon.... thread

Tha'ts me told lol. ok post your answer there

heya and welcome x

Hi SmoothOne - a belated welcome from me

Thanks SS and JG, hope to see you guys about.  Site seems to be promising so far

hi smoothone. x

hi smooth and thanks for reminding me of maths from 6th form

thought i would never see anything like that again.