Smooth block is released at rest on a 45^@incline and then slides a distance d. If the time taken of slide on rough incline is n times as large as that to slide than on a smooth incline. Show that coefficient of friction. mu = (1- (1)/(n^2))

Smooth block is released at rest on a 45^@incline and then slides a di

1.	Smooth block is released at rest on a 45^@incline and then slides a distance d. If the time taken of slide on rough incline is n times as large as that to slide than on a smooth incline. Show that coefficient of friction. mu = (1- (1)/(n^2))
Answer» <html><body><p></p>Solution :When there is no friction, the block slides down the inclined plane with <a href="https://interviewquestions.tuteehub.com/tag/acceleration-13745" style="font-weight:bold;" target="_blank" title="Click to know more about ACCELERATION">ACCELERATION</a>. <br/>` a = g <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> theta `<br/>when there is friction, the downward acceleration of the block is <br/> ` a. =g (sin theta - mu <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> theta)` <br/>As the block slides a distance d in each case so <br/> ` d = 1/2 at^2 = 1/2 a.t.^2` <br/>`(a)/(a.) = (t.^2)/(t^2) = ((nt)^2)/(t^2) = n^2 " or"(g sin theta)/(g (sin theta -mu cos theta) )=n^2` <br/>Solving , we get (using ` theta =<a href="https://interviewquestions.tuteehub.com/tag/45-316951" style="font-weight:bold;" target="_blank" title="Click to know more about 45">45</a>^@` ) <br/>`mu = 1 - (1)/(n^2)`</body></html>