A car negotiates a bend of radius 20m with an acceleration of 12m/s^2 .What is the maximum speed the car can attain without skidding?


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Question Number 30613 by NECx last updated on 23/Feb/18

$A c a r n e g o t i a t e s a b e n d o f r a d i u s$ $20 m w i t h a n a c c e l e r a t i o n o f$ $12 m / s^{2} . W h a t i s t h e m a x i m u m$ $s p e e d t h e c a r c a n a t t a i n w i t h o u t$ $s k i d d i n g ?$
Commented by NECx last updated on 24/Feb/18

$p l e a s e h e l p$
	Answered by mrW2 last updated on 25/Feb/18

	$v_{m a x} = \sqrt{a r} = \sqrt{12 \times 20} = 15.5 m / s = 56 k m / h$
	Commented by NECx last updated on 25/Feb/18

	$c a n I k n o w h o w y o u g o t t h e$ $f o r m u l a p l e a s e ?$
	Commented by mrW2 last updated on 25/Feb/18

	$t h e c a r c a n r e a c h a n a c c e l e r a t i o n f r o m$ $a = 12 m / s^{2}, t h a t m e a n s a f r i c t i o n$ $c o e e f f i c i e n t b e t w e e n t i r e s a n d g r o u n d$ $i s μ = \frac{a}{g} = 1.2 . w h e n t h e c a r g o e s$ $i n t o t h e c u r v e a n d i t s s p e e d i n c r e a s e s,$ $a p a r t o f t h e f r i c t i o n s h o u l d b e l e f t f o r$ $t h e c e n t r i f u g a l f o r c e, t h a t m e a n s$ $w i t h i n c r e a s i n g s p e e d t h e a c c e l e r a t i o n$ $s h o u l d b e d e c r e a s e d . w h e n t h e c a r$ $o b t a i n s t h e m a x . s p e e d t h e a c c e l e r a t i o n$ $s h o u l d b e z e r o a n d t h e c o m p l e t e$ $f r i c t i o n f o r c e c a n b e a v a i a b l e f o r t h e$ $c e n t r i f u g a l f o r c e, i . e .$ $m \frac{v_{m a x}^{2}}{r} = μ m g = {m a}_{m a x}$ $\Rightarrow v_{m a x} = \sqrt{{r a}_{m a x}} = \sqrt{20 \times 12} = 15.5 m / s$
	Commented by mrW2 last updated on 25/Feb/18

	Commented by mrW2 last updated on 25/Feb/18

	$a t p o i n t 1 :$ $f = {m a}_{m a x}$ $a t p o i n t 2 :$ $f = \sqrt{{(m a)}^{2} + {(m \frac{v^{2}}{r})}^{2}} = m \sqrt{a^{2} + {(\frac{v^{2}}{r})}^{2}}$ $a t p o i n t 3 :$ $f = m \frac{v_{m a x}^{2}}{r}$
	Commented by NECx last updated on 25/Feb/18

	$w o w . . . T h a n k s s o m u c h .$ $I r e a l l y l o v e i t w h e n y o u e x p l a i n$ $w i t h t h e a i d o f d i a g r a m s .$ $T h a n k s o n c e a g a i n .$
	Commented by mrW2 last updated on 27/Feb/18

	$D o e s m y a n s w e r m a t c h w i t h t h a t i n$ $y o u r b o o k ?$
	Commented by NECx last updated on 06/Mar/18

	$y e s s i r .$
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