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A ball of mass m is released from A inside a
smooth wedge of mass m as shown in fig.
What is the speed of the wedge when the ball reaches point B?

Asked by chandanbr6004 2nd November 2017, 5:50 PM
Answered by Expert
Answer:
begin mathsize 12px style l o s s space i n space p o t e n t i a l space e n e r g y equals space g a i n space i n space k i n e t i c space e n e r g y
P E space a t space p o i n t space B equals K E space b e f o r e space s l i d i n g plus K E space w h i l e space s l i d i n g left parenthesis h o r i z o n t a l space plus v e r t i c a l space c o m p o n e n t right parenthesis
m g r cos 45 equals 1 half m v squared plus 1 half m left parenthesis v subscript 1 cos 45 minus v right parenthesis squared plus 1 half m left parenthesis v subscript 1 sin 45 right parenthesis squared
g fraction numerator r over denominator square root of 2 end fraction equals v over 2 squared plus 1 half left parenthesis v subscript 1 over 2 squared minus 2 fraction numerator v v subscript 1 over denominator square root of 2 end fraction minus v subscript 1 squared right parenthesis plus fraction numerator 1 over denominator 2 square root of 2 end fraction v subscript 1 squared space minus negative negative negative negative 1

f r o m space p r i n c i p l e space o f space c o n v e r s a t i o n space o f space l i n e a r space m o m e n t u m space a t space p o i n t space B
i n i t i a l space m o m e n t u m equals f i n a l space m o m e n t u m space a t space B
m v equals m left parenthesis v subscript 1 cos 45 minus v right parenthesis
v subscript 1 equals 2 square root of 2 V
p u t space i n space space e q u a t i o n space 1 space comma space w e space g e t
v squared equals 3 square root of 2
V equals square root of fraction numerator g r over denominator 3 square root of 2 end fraction end root

o p t i o n space 1 end style
Answered by Expert 4th December 2017, 11:43 AM
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