A ladder of length L = 2.7 m and mass m = 21 kg rests on a floor with coefficien

Question

A ladder of length L = 2.7 m and mass m = 21 kg rests on a floor with coefficient of static friction ?s = 0.54. Assume the wall is frictionless.

1) What is the normal force the floor exerts on the ladder?

2) What is the minimum angle the ladder must make with the floor to not slip?

A ladder of length L = 2.7 m and mass m = 21 kg rests on a floor with coefficient of static friction ?s = 0.54. Assume the wall is frictionless. 1) What is the normal force the floor exerts on the ladder? 2) What is the minimum angle the ladder must make with the floor to not slip?

Explanation / Answer

1) the normal force the floor exerts on the ladder is,

Ny = mg = 21 x 9.8 = 205.8 N

2) the minimum angle the ladder must make with the floor to not slip:

f = 0.54 x Ny =0.54*205.8 = 111.132 N

so force by wall Nw = f = 111.132 N

mgcos(theta)(L/2) = (111.132)sin(theta) L

            tan(theta) = 2(111.132)/ mg = 2(111.132)/ 21*9.8

                   theta = tan-1 [1.08] = 47.2o

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