Question

A uniform ladder of mass m and length l leans at an angle $\Theta$ against a frictionless wall. A person of mass M climbs 90% of the way to the top (at 0.9l). Find an expression for the minimum coefficient of static friction needed to keep the ladder from slipping.

Answer 1

Friction less wall Mg .0.51 mg -0.90 А f net R & R se the reaction forces on the Ladder by the floor and the wall. Leff be the force of friction and M the coefficient of static friction. inf=UR As the ladder is at rest Equating the vertical forces R = mg + Mg R,= (t Mg Equating the horizontal forces = f As there is zero torque acting on the

its the net torque on the ladder is zero, so A taking moment of forces about point R, xo + fxo + mg xosssoul & rg xo gesmo -Ry Lusg=0 . 0.5mglsoil + o.anglsiid = Rx lcoso IR = 0.5 mg suid + 0.9 Mg suid R = gtano (0.5m +0.9M) R = stand stand (m + 94 ) Rx - 6*9mJgtang usiong eper and can f = (sm + 9 g fare "f=MR, [uring en 0] © (5mt 9 g fand = uki R = font Mg 5m tam gtang = M fmt Mg 10 IM 2 (5m 49 M) fand 10 (mm)