max h

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

4 Answers

33
Abhishek Priyam ·

writing energy conservation..

mg2R=1/2mv2+mgR(1+cosθ)......

balancing force where it will leave the surface..

mg.cosθ=mv2/R...

From two equations..

cosθ=2/3

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

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

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

Hence the answer..

:)

1
skygirl ·

this cos inverse 2/3 is a magic angle.

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

33
Abhishek Priyam ·

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

[3]

1
skygirl ·

[3]

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