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Question Number 145751 by ajfour last updated on 07/Jul/21

Commented by ajfour last updated on 07/Jul/21

$F i n d t h e m i n i m u m e n e r g y t h a t$ $n e e d b e e x p e n d e d b y p u l l i n g$ $o n o n e o f t h e c a r p e t s w i t h$ $a f o r c e (m a y v a r y) i n t h e$ $s h o w n d i r e c t i o n t o d e t a c h$ $t h e m c o m p l e t e l y f r o m o n e$ $a n o t h e r . B o t h c a r p e t s h a v e$ $m a s s m a n d f r i c t i o n c o e f f .$ $f o r e v e r y s u r f a c e i s u n i f o r m$ $a n d e q u a l t o μ .$
Commented by ajfour last updated on 09/Jul/21

$?$
Commented by ajfour last updated on 10/Jul/21

$I d u n n o w, s i r, i^{'} v e p u t t h e$ $q u e s t i o n a s k i n g t h e m i n i m u m$ $e n e r g y r e q u i r e d t o d e t a c h t h e$ $c a r p e t s f r o m o n e a n o t h e r b y$ $a p p l y i n g f o r c e i n t h e s h o w n$ $w a y : t o w h i c h c a r p e t ? t h a t$ $a l s o n e e d b e f o u n d o u t .$
Commented by mr W last updated on 10/Jul/21

$t h e f o r c e i s a c t e d o n t h e l o w e r c a r p e t,$ $r i g h t ?$
	Answered by mr W last updated on 10/Jul/21

	$a s s u m e w e p u l l o n t h e u p p e r c a r p e t .$ $s a y t h e o v e r l a p p i n g l e n g t h o f b o t h$ $c a r p e t s i s x .$ $t o t a l f r i c t i o n a c t i n g o n t h e u p p e r$ $c a r p e t i s μ m g, n o m a t t e r h o w l a r g e$ $x i s .$ $s u c h t h a t t h e u p p e r c a r p e t m o v e s,$ $F ⩾ μ m g$ $o n t h e l o w e r c a r p e t :$ $a c t i n g f r i c t i o n o n t h e c o n t a c t s u r f a c e$ $t o u p p e r c a r p e t i s \frac{x}{b} \times μ m g .$ $f r i c t i o n o n i t s c o n t a c t s u r f a c e t o$ $g r o u n d i s μ m g + \frac{x}{b} \times μ m g, w h i c h i s$ $a l w a y s l a r g e r t h a n t h e a c t i n g f r i c t i o n$ $o n i t s u p p e r s u r f a c e, t h a t m e a n s t h e$ $l o w e r c a r p e t {d o e s n}^{'} t m o v e .$ $t o t a l e n e r g y n e e d e d t o d e t a c h b o t h$ $c a r p e t s c o m p l e t e l y i s t h e n$ $E ⩾ F \times b = μ m g b$
	Commented by ajfour last updated on 10/Jul/21

	$T h a n k s s i r, i {h a d n}^{'} t t h o u g h t$ $c a r e f u l l y, b e t t e r q u e s t i o n$ $w o u l d b e i f t h e g r o u n d w e r e$ $f r i c t i o n l e s s .$
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