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A body slides down an inclined with 45 inclination, twice the time taken to slide is equal to the time taken for the same distance in absence of friction.find co efficient of friction

A body slides down an inclined with 45 inclination, twice the time taken to slide is equal to the time taken for the same distance in absence of friction.find co efficient of friction

Grade:11

1 Answers

Rahul Verma
45 Points
7 years ago
In presence of friction,
mg\sin 45 - \mu N = ma
= mg/\sqrt{2} - \mu mg = ma
a = g/\sqrt{2} - \mu g
time taken to slide (t_{1}), using eq of motion,
s = \frac{1}{2} at_{1}^{2}
t_{1} = \sqrt{\frac{2s}{a}}
t_{1} = \sqrt{\frac{2s}{\frac{g}{\sqrt{2} }- \mu g}}
 
in abscence of friction 
mg\sin 45 = ma
a = g\sin 45
a = g/\sqrt{2}
similarly
t2 = \sqrt{\frac{2s}{a}}
t_{2} = \sqrt{\frac{2s}{\frac{g}{\sqrt{2}}}}
as per question
t1 = 2t2
\mu =\frac{0.75}{\sqrt{2}}

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