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Aiswarya Ram Gupta Grade: 12
        

A block of mass 'm' is projected up an inclined pane of inclination θ with an initial velocity 'u'. If the coefficient of kinetic friction between the block and the pane is μ, the distance upto which the block will rise up the plane , before coming to rest, is given by (a) u2μ/2gsinθ  (b)  u2μ/2gcosθ  (c)  u2/4gsinθ  (d) u2/4gcosθ     .Please explain.

6 years ago

Answers : (5)

vikas askiitian expert
510 Points
										

friction force acts on the block in backward direction (down the plane),


f = uN                 (N is normal reaction)


N = mgcos@


f = umgcos@ 


one of the component of weight acts in backward direction & other perpendicular to plane...


Fb = mgsin@


total force in downward direction is F+f


 F(total) = umgcos@ + mgsin@


 manet = mg(ucos@+sin@)


   anet = g(ucos@+sin@)      .............1


now  , we can use , v2 = u2 - 2as                ( coz accleration is constant)


            finally v becomes 0 , so


    s = u2/2a


 plugging value of a from eq 1


  s = u2/2g(sin@+ucos@)


this is value of distance covered before stopping....

6 years ago
Aiswarya Ram Gupta
35 Points
										

thnku......bt dis answer is not given in the options...Frown

6 years ago
vikas askiitian expert
510 Points
										

may be they have taken some assumptions or ur q is not complete ....


can u tel me the ans of this q??

6 years ago
Aiswarya Ram Gupta
35 Points
										

answer given is  u2/4gsinθ.

6 years ago
vikas askiitian expert
510 Points
										

your q was in complete , this is the q & sol ....earlier this q was asked by kaushik in this forum..


 


Q=> A block slides down an inclined plane of slope angle  θ with constant velocity. It is then projected up the same plane with an initial velocity 'u'  plane of inclination  . How far up the incline will it move before coming to rest?


solution =>


lock moves down the plane with constant velocity it means net force is zero...


force due to friction (f) = mgsin@                              (@ is the angle of plane)


net retardation force when body is projected upward is (f+mgsin@)


 f = mgsin@ so


net retardation force = 2mgsin@


     ma = mgsin@


     a(retardation) = 2gsin@        .............1


 V2 = U2 - 2aS


finally velocity becomes 0 so


  U2 = 2aS


 S = U2/2a


    =u2/4gsin@

6 years ago
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