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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 \dots 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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