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The coeff of friction b/w the block A of mass m and triangular wedge B of mass M is @. There is no friction b/w the wedge and the plane. If the system (blockA + wedge B) is released so that there is no sliding b/w A and B, show that the max possible inclination theta is equals to tan -1 @.


The coeff of friction b/w the block A of mass m and triangular wedge B of mass M is @. There is no friction b/w the wedge and the plane. If the system (blockA + wedge B) is released so that there is no sliding b/w A and B, show that the max possible inclination theta is equals to tan -1 @.

Grade:12

1 Answers

pratham ashish
9 Points
12 years ago
hi, if there no frctn b/n B & PLANE then, accelrn of (A+B) wud be g sin(theta). along the plne indwnward diectn, now cosider the A w.r.t B forces on A 1) psuedo f = m* gsin(theta) upward along th pln 2) gravity = mg vertical dwnwrd 3)max. friction force = @*{mg-mg sin^2(theta)} mg sin^2(theta) is vertical compnent of psuedo f {mg-mg sin^2(theta)} = total dwn force horizontal comp of psuedo f = mg*sin(theta)* cos(theta) now in limiting case max frctn f = mg cos^2(theta) => @*mg {1- sin^2(theta)}=mg*sin(theta)*cos(theta) => @ = tan(theta) => theta = tan^-1@.

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