max h

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A ball of mass m slides down a smooth inclined plane which forms a loooop of radius R.At what height it will leave the track and to what max. height it will rise afterwards

#Physics #Mechanics

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Abhishek Priyam ·2009-01-02 21:54:49

writing energy conservation..

mg2R=1/2mv²+mgR(1+cosÎ¸)......

balancing force where it will leave the surface..

mg.cosÎ¸=mv²/R...

From two equations..

cosÎ¸=2/3

so it will leave surface at a height of R(1+cosÎ¸)=5R/3

with velocity.. v=√2gR/3
in the direction shown below..

velocity is making Î¸ with horizintal...
thereafter parabolic path so max ht there is say h

Hence the answer..

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skygirl ·2009-01-02 22:01:41

this cos inverse 2/3 is a magic angle.

75% i get this angle.. wenever i do these kinda sums.. !

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Abhishek Priyam ·2009-01-02 22:03:56

yes in these not 75% but 95% one get this and in friction tan^-1Î¼

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skygirl ·2009-01-03 19:38:54

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max h

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