A car starts from rest and uniformly accelerates for 1 km, travels with uniform velocity for 98 km and brakes and stop after travelling another 1 km. Consider the above experiment being done on 2 different roads 1st roads has higher coefficient of friction for car for all types than 2nd road. Compare energy consumed in 2 cases, which one consumes more energy and why?


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Question Number 3463 by prakash jain last updated on 13/Dec/15

$A car starts from rest and uniformly$ $accelerates for 1 km, travels with uniform$ $velocity for 98 km and brakes and stop$ $after travelling another 1 km .$ $Consider the above experiment being done$ $on 2 different roads 1 st roads has higher$ $coefficient of friction for car for all types$ $than 2 nd road .$ $Compare energy consumed in 2 cases, which one$ $consumes more energy and why ?$
Commented by prakash jain last updated on 13/Dec/15

$Same car is used on both tracks . All other$ $things equal only friction changes .$
	Answered by Yozzii last updated on 13/Dec/15

	$T h e e n e r g y W e x p e n d e d b y a b o d y m o v i n g a g a i n s t$ $f r i c t i o n a l f o r c e f i s W = f d w h e r e d = d i s t a n c e$ $t r a v e l l e d f o r w h i c h f a c t s .$ $I n s i t u a t i o n s o f m o t i o n a l o n g a r o a d$ $w i t h a c e r t a i n c o e f f i c i e n t o f f r i c t i o n μ,$ $f t a k e s a m a x i m u m v a l u e o f μ R, w h e r e$ $R = n o r m a l r e a c t i o n o n b o d y b y t h e r o a d .$ $∴ W = μ R d . I f d a n d R a r e c o n s t a n t o n l y,$ $\Rightarrow W \propto μ .$ $R = m g b y {N e w t o n}^{'} s 3 r d L a w o f M o t i o n$ $w h e r e m = m a s s o f b o d y, g = a c c e l e r a t i o n$ $d u e t o g r a v i t y (d e p e n d e n t u p o n p l a n e t$ $w h e r e t h e e x p e r i m e n t i s h e l d) .$ $I n b o t h c a s e s d = c o n s t a n t (100 k m) a n d a n y$ $v a l i d c o m p a r i s o n m u s t h a v e t h e$ $e x p e r i m e n t p e r f o r m e d w i t h i d e n t i c a l$ $c a r s o n t h e s a m e t r a c k, s o t h a t R i s c o n s t a n t .$ $S i n c e W \propto μ, t h e t r a c k w i t h h i g h e r μ$ $i n c u r s h i g h e r e n e r g y c o n s u m p t i o n o n$ $a g i v e n c a r .$
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