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physics

mechanics

Easy

Question

$A space p a r t i c l e space i s space m o v i n g space i n space a space c i r c l e space w i t h space u n i f o r m space s p e e d space v. space space I n space m o v i n g space f r o m space a space p o i n t space t o space a n o t h e r space d i a m e t r i c a l l y space o p p o s i t e space p o i n t$

$T h e k i n e t i c e n e r g y c h a n g e s b y (1 / 2) m v^{2}$
$T h e m o m e n t u m c h a n g e s b y 2 m v$
$T h e k i n e t i c e n e r g y c h a n g e s b y m v^{2}$
$T h e m o m e n t u m c h a n g e s b y m v$

The correct answer is: $T h e m o m e n t u m c h a n g e s b y 2 m v$

$M o m e n t u m space c h a n g e s space b y space 2 m v space b u t space k i n e t i c space e n e r g y space r e m a i n s space s a m e.$

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$A space p r o t o n space o f space m a s s space 1.6 space cross times space 10 to the power of negative 27 space end exponent k g space g o e s space r o u n d space i n space a space c i r c u l a r space o r b i t space o f space r a d i u s space 0.10 space m space u n d e r space a space c e n t r i p e t a l space f o r c e space o f space 4 space cross times space 10 to the power of negative 13 space space end exponent N. space space t h e n space t h e space f r e q u e n c y space o f space r e v o l u t i o n space o f space t h e space p r o t o n space i s space a b o u t$

$A space p r o t o n space o f space m a s s space 1.6 space cross times space 10 to the power of negative 27 space end exponent k g space g o e s space r o u n d space i n space a space c i r c u l a r space o r b i t space o f space r a d i u s space 0.10 space m space u n d e r space a space c e n t r i p e t a l space f o r c e space o f space 4 space cross times space 10 to the power of negative 13 space space end exponent N. space space t h e n space t h e space f r e q u e n c y space o f space r e v o l u t i o n space o f space t h e space p r o t o n space i s space a b o u t$

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$A n space a t h l e t e space c o m p l e t e s space o n e space r o u n d space o f space a space c i r c u l a r space t r a c k space o f space r a d i u s space 10 space m space i n space 40 space s e c. space space T h e space d i s tan c e space c o v e r e d space b y space h i m space i n space 2 space m i n space 20 space s e c space i s$

$A n space a t h l e t e space c o m p l e t e s space o n e space r o u n d space o f space a space c i r c u l a r space t r a c k space o f space r a d i u s space 10 space m space i n space 40 space s e c. space space T h e space d i s tan c e space c o v e r e d space b y space h i m space i n space 2 space m i n space 20 space s e c space i s$

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$T h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space t y r e s space a n d space t h e space r o a d space i s space 0.25. space space T h e space m a x i m u m space s p e e d space w i t h space w h i c h space a space c a r space c a n space b e space d r i v e n space r o u n d space a space c u r v e space o f space r a d i u s space 40 space m space w i t h o u t space s k i d d i n g space i s space left parenthesis a s s u m e open g equals 10 m s to the power of negative 2 end exponent close parentheses$

$T h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space t y r e s space a n d space t h e space r o a d space i s space 0.25. space space T h e space m a x i m u m space s p e e d space w i t h space w h i c h space a space c a r space c a n space b e space d r i v e n space r o u n d space a space c u r v e space o f space r a d i u s space 40 space m space w i t h o u t space s k i d d i n g space i s space left parenthesis a s s u m e open g equals 10 m s to the power of negative 2 end exponent close parentheses$

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$A space m o t o r space c y c l e space d r i v e r space d o u b l e s space i t s space v e l o c i t y space w h e n space h e space i s space h a v i n g space a space t u r n. space space T h e space f o r c e space e x e r t e d space o u t w a r d l y space w i l l space b e$

$A space m o t o r space c y c l e space d r i v e r space d o u b l e s space i t s space v e l o c i t y space w h e n space h e space i s space h a v i n g space a space t u r n. space space T h e space f o r c e space e x e r t e d space o u t w a r d l y space w i l l space b e$

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$A space c a r space i s space m o v i n g space w i t h space h i g h space v e l o c i t y space w h e n space i t space h a s space a space t u r n. space space A space f o r c e space a c t s space o n space i t space o u t w a r d l y space b e c a u s e space o f space$

$A space c a r space i s space m o v i n g space w i t h space h i g h space v e l o c i t y space w h e n space i t space h a s space a space t u r n. space space A space f o r c e space a c t s space o n space i t space o u t w a r d l y space b e c a u s e space o f space$

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$T h e space m a x i m u m space v e l o c i t y space left parenthesis i n space m s – 1 right parenthesis space w i t h space w h i c h space a space c a r space d r i v e r space m u s t space t r a v e r s e space a space f l a t space c u r v e space o f space r a d i u s space 150 space m space a n d space c o e f f i c i e n t space o f space f r i c t i o n space 0.6 space t o space a v o i d space s k i d d i n g space i s space$
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$A space p a r t i c l e space m o v e s space w i t h space c o n s tan t space s p e e d space v space a l o n g space a space c i r c u l a r space p a t h space o f space r a d i u s space r space a n d space c o m p l e t e s space t h e space c i r c l e space i n space t i m e space T. space T h e space a c c e l e r a t i o n space o f space t h e space p a r t i c l e space i s$

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$I f space a space c y c l i s t space m o v i n g space w i t h space a space s p e e d space o f space 4.9 space m divided by s space o n space a space l e v e l space r o a d space c a n space t a k e space a space s h a r p space c i r c u l a r space t u r n space o f space r a d i u s space 4 space m comma space t h e n space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space c y c l e space t y r e s space a n d space r o a d space i s$

$I f space a space c y c l i s t space m o v i n g space w i t h space a space s p e e d space o f space 4.9 space m divided by s space o n space a space l e v e l space r o a d space c a n space t a k e space a space s h a r p space c i r c u l a r space t u r n space o f space r a d i u s space 4 space m comma space t h e n space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space c y c l e space t y r e s space a n d space r o a d space i s$

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$A space p o i n t space m a s s space m space i s space s u s p e n d e d space f r o m space a space l i g h t space t h r e a d space o f space l e n g t h space l comma space f i x e d space a t space O comma space i s space w h i r l e d space i n space a space h o r i z o n t a l space c i r c l e space a t space c o n s tan t space s p e e d space a s space s h o w n. space space F r o m space y o u r space p o i n t space o f space v i e w comma space s t a t i o n a r y space w i t h space r e s p e c t space t o space t h e space m a s s comma space t h e space f o r c e s space o n space t h e space m a s s space a r e space$

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PhysicsMechanics

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PhysicsMechanics

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$L e t open vertical bar stack straight A subscript 1 with rightwards arrow on top close vertical bar equals 3 comma open vertical bar stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5 text and end text open vertical bar stack straight A subscript 1 with rightwards arrow on top plus stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5. space space T h e space v a l u e space o f open parentheses 2 stack straight A subscript 1 with rightwards arrow on top plus 3 stack straight A subscript 2 with rightwards arrow on top close parentheses times open parentheses 3 stack straight A subscript 1 with rightwards arrow on top minus 2 stack straight A subscript 2 with rightwards arrow on top close parentheses text is end text$

$L e t open vertical bar stack straight A subscript 1 with rightwards arrow on top close vertical bar equals 3 comma open vertical bar stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5 text and end text open vertical bar stack straight A subscript 1 with rightwards arrow on top plus stack straight A subscript 2 with rightwards arrow on top close vertical bar equals 5. space space T h e space v a l u e space o f open parentheses 2 stack straight A subscript 1 with rightwards arrow on top plus 3 stack straight A subscript 2 with rightwards arrow on top close parentheses times open parentheses 3 stack straight A subscript 1 with rightwards arrow on top minus 2 stack straight A subscript 2 with rightwards arrow on top close parentheses text is end text$

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