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The sphere at P is given a downward velocity v o and swings in a vertical plane at the end of a rope of l = 1 m attached to a support at O. The rope breaks at angle 30° from horizontal, knowing that it can withstand a maximum tension equal to three times the weight of the sphere. The value of v o will be: ( g =π 2 m/s 2 )

   The sphere at P is given a downward velocity vo and swings in a vertical plane at the end of a rope of l = 1 m attached to a support at O.


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The rope breaks at angle 30° from horizontal, knowing that it can withstand a maximum tension equal to three times the weight of the sphere. The value of vo will be: ( g =π2 m/s2)

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

applying energy conservaion

1/2 mvo2 + mglsin@ = 1/2 mv     ................1

 

when bob is at @ = 30 then

T - mgsin30 = mv2/l

T =3mg so

mv2 = 5mgl/2   ..............2

from 1 & 2

we get

1/2 mvo2 = 5mgl/4 - mgl/2 = 3mgl/4

vo = (3gl/2)1/2 = 3.8m/s

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