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Question Number 169658 by Tawa11 last updated on 05/May/22

Commented by mr W last updated on 05/May/22

$f r i c t i o n a l f o r c e = a c t i v e f o r c e a p p l i e d$ $o n c a r t o n$ $\Rightarrow f r i c t i o n a l f o r c e = 150 N$ $A n s w e r A i s c o r r e c t .$
Commented by Tawa11 last updated on 05/May/22

$Ohh, God bless you sir .$
	Answered by kapoorshah last updated on 06/May/22

	$f r i c t i o n a l f o r c e = c o e f f i c i e n t o f f r i c t i o n \times n o r m a l f o r c e$ $= η_{k} \times (m \times g)$ $= 0.4 \times 51 \times 9.8$ $= 199.92 N$ $s i n c e f r i c t i o n a l f o r c e i s g r e a t e r t h a n t h e$ $s l i d i n g f o r c e t h e c a r t o n i s n o t m o v i n g .$ $s o t h e f r i c t i o n a l f o r c e = η_{s} \times m \times g$ $= 0.5 \times 51 \times 9.8$ $= 249.9 N$ $\approx 250 N$ $a n s w e r : C$
	Commented by mr W last updated on 06/May/22

	$a s f a r a s t h e c a r t o n {d o e s n}^{'} t m o v e,$ $t h e r e a c t t w o f o r c e s o n t h e c a r t o n$ $i n h o r i z o n t a l d i r e c t i o n :$ $t h e a c t i v e f o r c e F = 150 N a n d$ $t h e r e a c t i v e f o r c e w h i c h i s t h e$ $f r i c t i o n f o r c e f .$ $s i n c e b o t h f o r c e s a r e i n e q u i l i b r i u m,$ $t h e y m u s t b e o f s a m e s i z e, b u t o p p o s i t e$ $i n t h e d i r e c t i o n, i . e .$ $f = F = 150 N . \Rightarrow A n s w e r A .$ $c e r t a i n l y f m u s t b e s m a l l e r t h a n$ $μ_{s} N = μ_{s} m g = 0.5 \times 51 \times 9.81 = 250 N,$ $o t h e r w i s e t h e c a r t o n b e g i n s t o m o v e .$ $s i n c e f = 150 < 250, i t m e a n s t h a t t h e$ $c a r t o n r e a l l y {d o e s n}^{'} t m o v e .$
	Commented by kapoorshah last updated on 06/May/22

	$t h e a n s w e r i s C$
	Commented by mr W last updated on 06/May/22

	$t h e n y o u s h o u l d e x p l a i n h o w t h e$ $f o l l o w i n g i s t r u e :$
	Commented by mr W last updated on 06/May/22

	Commented by Tawa11 last updated on 06/May/22

	$Sir mrW . I understand your solution since the time you solved it .$ $The carton does not move, then f = f_{r} = 150 N .$ $God bless you sir .$
	Commented by Tawa11 last updated on 06/May/22

	$at kapoorshah sir . Thanks for your time .$ $I reason like you before, but am sure 250 N is not correct .$ $That was why I posted the question to the forum .$ $And sir mrW has cleared by doubt . [Ans = 150 N]$
	Commented by mr W last updated on 06/May/22

	$s o m e t h i n g e l e m e n t a r y a b o u t f r i c t i o n :$ $b e f o r e a n o b j e c t m o v e s, t h e$ $f r i c t i o n i s c a l l e d s t a t i c f r i c t i o n . i t$ $i s N O T a c o n s t a n t f o r c e! i t i s j u s t a$ $r e a c t i o n f o r c e . i f y o u {d o n}^{'} t a p p l y$ $a f o r c e a n t h e o b j e c t t o a t t e m p t t o$ $m o v e i t, t h e f r i c t i o n i s z e r o . a s f a r$ $a s t h e f o r c e y o u a r e a p p l y i n g o n i t$ $i s l e s s t h a n t h e m a x i m a l p o s s i b l e$ $s t a t i c f r i c t i o n, w h i c h i s c a l c u l a t e d$ $b y f_{m a x} = μ_{s t a t i c} N, t h e o b j e c t {d o e s n}^{'} t$ $m o v e a n d t h e f r i c t i o n f o r c e f w h i c h$ $i s a c t u a l l y a c t i n g o n t h e o b j e c t i s$ $a l w a y s e q u a l t o t h e a c t i v e f o r c e F y o u$ $a r e a p p l y i n g o n t h e o b j e c t, i . e . f = F .$ $w h e n y o u i n c r e a s e t h e a c t i v e f o r c e F$ $u n d r e a c h t h e m a x i m a l p o s s i b l e$ $s t a t i c f r i c t i o n f o r c e f_{m a x} = μ_{s t a t i c} N,$ $t h e o b j e c t b e g i n s t o m o v e . o n c e a n$ $o b j e c t m o v e s, t h e r e a c t s a l w a y s a$ $f r i c t i o n f o r c e o n t h e o b j e c t, t h i s$ $f r i c t i o n i s c a l l e d k i n e t i c f r i c t i o n,$ $w h i c h i s c a l c u l a t e d b y f_{k i n e t i c} = μ_{k i n e t i c} N .$ $i t i s a l w a y s t h e r e a n d i s c o n s t a n t, a s$ $f a r a s t h e o b j e c t m o v e s . t h e$ $m a x i m a l s t a t i c f r i c t i o n w h i c h m u s t$ $b e o v e r c o m e t o m a k e a n o b j e c t m o v e$ $i s l a r g e r t h a n t h e k i n e t i c f r i c t i o n .$ $w e c a n e x p e r i e n c e t h i s i n o u r$ $d a i l y l i f e : t o m a k e a n o b j e c t t o s t a r t$ $t o m o v e i s m o r e h a r d t h a n j u s t t o$ $k e e p i t m o v e .$ $w h e n t h e o b j e c t b e g i n s t o m o v e, y o u$ $c a n r e d u c e t h e f o r c e y o u a p p l y o n i t t o$ $k e e p i t m o v i n g c o n s t a n t l y . w h e n$ $y o u {d o n}^{'} t r e d u c e t h e f o r c e, t h e o b j e c t$ $w i l l g e t a n a c c e l e r a t i o n f r o m y o u r$ $f o r c e a n d g e t s f a s t e r a n d f a s t e r,$ $b e c a u s e t h e f r i c t i o n (k i n e t i c) f o r c e$ $a c t i n g o n i t i s s m a l l e r t h a n t h e f o r c e$ $y o u a r e a p p l y i n g .$
	Commented by Tawa11 last updated on 06/May/22

	$God bless you sir . I really appreciate your time .$
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