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Yesterday I learned about optimum speed. My teacher told that optimum speed is the speed with which one can take turns on banked road without wear and tear.

$v_0=\sqrt{rg\tan\theta} $, $v_0$= optimum speed, $r$= radius, $g$= gravitational constant

Then he asked us to find out what will happen if the speed of a vehicle on a slope is less than optimum speed and how it is useful.

I don't know what will happen but as it is on slope so i guess i can't move upward.But if it can't move upward than how will it be useful?

Can anyone help?

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    $\begingroup$ Is upward the only useful direction? $\endgroup$
    – RedGrittyBrick
    Commented Aug 10, 2014 at 15:40
  • $\begingroup$ @RedGrittyBrick I have just tried to show in what way i was thinking, but my teacher told no need of direction because vehicle will be stationary!! $\endgroup$
    – Freddy
    Commented Aug 11, 2014 at 4:25
  • $\begingroup$ Why did i got down vote, can anyone explain it to me? $\endgroup$
    – Freddy
    Commented Aug 11, 2014 at 16:06

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Think of what happens when the speed is more than optimal? Now imagine the reverse effect when it is less that optimal.

Physics and engineering are about learning an effect or process and then exploring its limits. Here the teacher is trying to prompt you into thinking about when happens when the speed is too low. At the limit the speed would be zero. Surely you can do a free body diagram and see what happens then.

On the other hand, it is the situation where the speed is two high. At the limit consider zero friction (like on super ice) and do a Free Body Diagram to explore this situation.

In the end you will understand why there is a speed, called critical in banked turns and what delicate balance happens when this speed is observed.

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    $\begingroup$ My teacher showed a small derivation with free body diagram and derived that coefficient of static friction is equal to $\tan\theta$ so whenever $\tan\theta\le$coefficient of static friction we can park a vehicle on a slope! $\endgroup$
    – Freddy
    Commented Aug 11, 2014 at 4:24
  • $\begingroup$ Its all about learning through exploration that leads to understanding. $\endgroup$
    – John Alexiou
    Commented Aug 11, 2014 at 12:39

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