Physics

Mechanics

Easy

Question

$text A bomb shell explodes into end text 3 text pieces having masses end text 1 Kg comma 2 Kg text and end text m Kg text respectively. end text T h e space 2 K g space a n d space 1 K g space text masses fly off with velocities end text 8 ms to the power of negative 1 end exponent text and end text 12 ms to the power of negative 1 end exponent text along end text Y text and end text X text -axes respectively. The third one flies off with speed of end text 40 ms to the power of negative 1 end exponent. space text The total mass of end text t h e space s h e l l space i s$

0.35Kg
3.5Kg
45Kg
0.45Kg

The correct answer is: 3.5Kg

$text The resultant momentum of two pieces flying in end text X text and end text Y text axis is, end text P equals square root of m subscript 1 superscript 2 u subscript 1 superscript 2 plus m subscript 2 superscript 2 u subscript 2 superscript 2 end root equals square root of left parenthesis 12 right parenthesis squared plus left parenthesis 16 right parenthesis squared end root equals 20 therefore P plus m cross times 40 equals 0 comma text where end text to the power of straight prime m to the power of straight prime text is mass of third piece. end text therefore m equals 20 over 40 equals 1 half equals 0 times 5 kg therefore text Total mass of the shell end text equals straight m subscript 1 plus straight m subscript 2 plus straight m equals 1 plus 2 plus 0 times 5 equals 3 times 5 kg$

$T w o space p a r t i c l e s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a r e space c o n n e c t e d space b y space a space l i g h t space a n d space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space f i x e d space p u l l e y. space I n i t i a l l y comma space t h e space p a r t i c l e space m subscript 1 space m o v e s space w i t h space a space v e l o c i t y space v subscript 0 w h e n space t h e space s t r i n g space i s space n o t space t a u t. space N e g l e c t i n g space f r i c t i o n space i n space a l l space c o n t a c t i n g space s u r f a c e s comma space f i n d space t h e space v e l o c i t i e s space o f space t h e space p a r t i c l e s space m subscript 1 space a n d space m subscript 2 space j u s t space a f t e r space t h e space s t r i n g space i s space t a u t.$

PhysicsMechanics

Mechanics

Physics

$A space p l a t e space o f space m a s s space M space i s space h e l d space a t space r e s t space b y space f i r i n g space b u l l e t s space f r o m space b e l o w. space E a c h space b u l l e t space h a s space a space m a s s space m space v e l o c i t y space u space left parenthesis u p right parenthesis space j u s t space b e f o r e space h i t t i n g space a n d space s t o p s space a f t e r space h i t t i n g space t h e space p l a t e space f o r space a space m o m e n t space a n d space f a l l s. space D e t e r m i n e space t h e space n u m b e r space o f space b u l l e t s space s t r i k i n g space t h e space p l a t e space p e r space u n i t space t i m e.$

PhysicsMechanics

Mechanics

Physics

$A space m a c h i n e space g u n space c a n space f i r e space b u l l e t s space o f space 50 space g r a m s space a t space a space s p e e d space o f space 2000 space m space s to the power of negative 1 end exponent semicolon space t h e space m a n space h o l d i n g space t h e space g u n space c a n space e x e r t space a n space a v e r a g e space f o r c e space o f space 200 space N space a g a i n s t space t h e space g u n. space C a l c u l a t e space t h e space m a x i m u m space n u m b e r space o f space b u l l e t s space w h i c h space h e space c a n space f i r e space p e r space m i n u t e.$

PhysicsMechanics

Mechanics

Physics

$A space 3.00 space k g space s t e e l space b a l l space s t r i k e s space t h e space w a l l space w i t h space a space s p e e d space o f space 10.0 space m space divided by space s space a t space a n space a n g l e space o f 60 to the power of 0 space w i t h space t h e space s u r f a c e. space I t space b o u n c e s space o f f space w i t h space t h e space s a m e space s p e e d space a n d space a n g l e. space I f space t h e space b a l l space i s space i n space c o n t a c t space w i t h space t h e space w a l l space f o r space 0.200 space s comma space w h a t space i s space t h e space a v e r a g e space f o r c e space e x e r t e d space b y space t h e w a l l space o n space t h e space b a l l ?$

PhysicsMechanics

Mechanics

Physics

$A space b a l l space o f space m a s s space 1 space k g space i s space a t t a c h e d space t o space a n space i n e x t e n s i b l e space s t r i n g. space T h e space b a l l space i s space r e l e a s e d space f r o m space t h e space p o s i t i o n space s h o w n space i n space f i g u r e. space F i n d space t h e space i m p u l s e space i m p a r t e d space b y space t h e space s t r i n g space t o space t h e space b a l l space i m m e d i a t e l y space a f t e r space t h e space s t r i n g space b e c o m e s space t a u t.$

PhysicsMechanics

Mechanics

Physics

$A space m a s s space 2 space m space r e s t s space o n space a space h o r i z o n t a l space t a b l e. space I t space i s space a t t a c h e d space t o space a space l i g h t space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space s m o o t h space p u l l e space a n d space c a r r i e s space a space m a s s space m space a t space t h e space o t h e r space e n d. space I f space t h e space m a s s space m space i s space r a i s e d space v e r t i c a l l y space t h r o u g h space a space d i s tan c e space h space a n d space i s space t h e n space d r o p p e d. space w h a t space i s space t h e s p e e d space w i t h space w h i c h space t h e space m a s s space 2 space m space b e g i n s space t o space r i s e ?$

PhysicsMechanics

Mechanics

Physics

$A space p a r t i c l e space o f space m a s s space 1 k g space i s space a t t a c h e d space t o space a space s t r i n g space o f space l e n g t h space 5 m. space T h e space s t r i n g space i s space a t t a c h e d t o space a space f i x e d space p o i n t space O. space I t space i s space r e l e a s e d space f r o m space t h e space p o s i t i o n space a s space s h o w n space i n space f i g u r e. space C a l c u l a t e t h e space i m p u l s e space d e v e l o p e d space i n space t h e space s t r i n g space w h e n space i t space b e c o m e s space t a u t.$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

$A space b o b space o f space m a s s space M space i s space s u s p e n d e d space b y space a n space i n e x t e n s i b l e space s t r i n g. space A space p a r t i c l e space o f space m a s s space m comma space m o v i n g space w i t h space v e l o c i t y space v subscript 0 space s t r i k e space t h e space b o b space a s space s h o w n space i n space t h e space f i g u r e. space I f space t h e space p a r t i c l e space c o m e s space t o space r e s t space j u s t space a f t e r space c o l l i s i o n comma space t h e n space c a l c u l a t e space text velocity of the bob just after collision. end text$

PhysicsMechanics

Mechanics

Physics

$A space b o b space o f space m a s s space M space i s space s u s p e n d e d space b y space a n space i n e x t e n s i b l e space s t r i n g. space A space p a r t i c l e space o f space m a s s space m comma m o v i n g space w i t h space v e l o c i t y space v subscript 0 space s t r i k e space t h e space b o b space a s space s h o w n space i n space t h e space f i g u r e. space I f space t h e space p a r t i c l e space c o m e s space t o space r e s t space j u s t space a f t e r space c o l l i s i o n comma space t h e n space c a l c u l a t e space i m p u l s e space o f space t e n s i o n space i n space t h e space s t r i n g$

PhysicsMechanics

Mechanics

Physics

$A space t i m e space v a r y i n g space f o r c e comma space F equals 2 space t space i s space a c t i n g space o n space a space p a r t i c l e space o f space m a s s space 2 space k g space m o v i n g space a l o n g x space minus a x i s. space v e l o c i t y space o f space t h e space p a r t i c l e space i s space 4 space m space divided by space s space a l o n g space n e g a t i v e space x space minus a x i s space a t space t i m e t equals 0 comma space F i n d space t h e space v e l o c i t y space o f space t h e space p a r t i c l e space a t space t h e space e n d space o f space 4 space s$

PhysicsMechanics

Mechanics

Physics

$A space b a l l space o f space m a s s space 200 space g space i s space p r o j e c t e d space w i t h space a space v e l o c i t y space o f space 30 space m space divided by space s space a t space 30 to the power of 0 space f r o m space h o r i z o n t a l. space U sin g space t h e space c o n c e p t space o f space i m p u l s e comma space f i n d space c h a n g e space i n space v e l o c i t y space i n space 2 space s T a k e space g equals 10 space m space divided by space s space squared$

PhysicsMechanics

Mechanics

Physics

$T o space w h a t space m a x i m u m space h e i g h t space w i l l space t h e space b l o c k space r i s e$

PhysicsMechanics

Mechanics

Physics

$A space s m a l l space b l o c k space o f space m a s s space m space equals space 1 space k g space i s space p l a c e d space o v e r space a space w e d g e space o f space m a s s space M space equals space 4 space k g space a s space space s h o w n space i n space f i g u r e. space M a s s space m space i s space r e l e a s e d space f r o m space r e s t space A l l space s u r f a c e s space a r e space s m o o t h. space O r i g i n space O space i s space a s space s h o w n comma space left parenthesis g space equals space 10 space m divided by s squared right parenthesis F i n a l space v e l o c i t y space o f space t h e space w e d g e space i s.......... m divided by s$

PhysicsMechanics

Mechanics

Physics

$bold italic P bold italic a bold italic s bold italic s bold italic a bold italic g bold italic e bold colon A space b l o c k space o f space m a s s space 1 space k g space i s space m o v i n g space t o w a r d s space a space m o v a b l e space w e d g e space o f space m a s s space 2 space k g space a s space s h o w n space i n space f i g u r e. space A l l space s u r f a c e s space a r e space s m o o t h. space W h e n space t h e space b l o c k space l e a v e s space t h e space w e d g e f r o m space t o p comma space i t s space v e l o c i t y space i s space m a k i n g space a n space a n g l e space theta space equals space 30 º space w i t h space h o r i z o n t a l. T h e space v a l u e space o f space v subscript 0 space i n space m divided by s space i s space$

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0.35Kg
3.5Kg
45Kg
0.45Kg

The correct answer is: 3.5Kg

Related Questions to study

$T o space w h a t space m a x i m u m space h e i g h t space w i l l space t h e space b l o c k space r i s e$

$T o space w h a t space m a x i m u m space h e i g h t space w i l l space t h e space b l o c k space r i s e$

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0.35Kg3.5Kg45Kg0.45Kg

The correct answer is: 3.5Kg

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0.35Kg
3.5Kg
45Kg
0.45Kg