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What is the velocity of block B?

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Asked by sumayiah2000 10th November 2019, 7:39 PM
Answered by Expert
Answer:
Figure shows the blocks-pulley arrangement as given in question. It is given that block-A moves towards left with speed 10 m/s.
 
Let L be the length of connecting rope between the blocks. Let l be the length of rope between block-A and pulley .
 
Then ( L - l ) will be the length between pulley and block-B.
 
Let a be the distance from pulley-point O to block-A and h is the vertical height from floor to pulley.
 
Then we have ,  l = ( a2 + h2 )1/2 ..................(1)
 
If we differentiate eqn.(1),  dl/dt = [ a / ( a2 + h2 )1/2 ] (da/dt) = ( cos 37 ) (da/dt) = 0.8 × 10 m/s = 8 m/s
 
Similarly on the other side, we have, ( L - l ) = ( b2 + h2 )1/2  .....................(2)
 
If we differentiate eqn.(2), we get,  -dl/dt = [ b / ( b2 + h2 )1/2 ] (db/dt) = cos53 (db/dt) = 0.6 (db/dt) 
 
Hence ,  (db/dt) = -8/0.6 = -13.33 m/s
 
Hence block-B will move with speed 13.33 m/s towards left
 
Answered by Expert 10th November 2019, 11:07 PM
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