Question

A minimum force F is applied to a block of mass 102 kg to
prevent it from sliding on a plane with an inclination angle
30° with the horizontal. If the coefficients of static and
kinetic friction between the block and the plane are 0.4
and 0.3 respectively, then the force F is:
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Answer 1

Answer:

Explanation:

Given A minimum force F is applied to a block of mass 102 kg to  prevent it from sliding on a plane with an inclination angle  30° with the horizontal. If the coefficients of static and  kinetic friction between the block and the plane are 0.4  and 0.3 respectively, then the force F is:

We know that

F = f (applied) – f(gravity) – f(friction)

    = fa – fg + ff

So for equilibrium Fn = 0  and along the inclined plane we have mg sin θ

Fa = Fg – Ff

Fa = mg sin θ – μ s x N

             = mg sin θ – μs x mg cos θ

            = mg (sin θ – μs cos θ)

              = 102 x 10 (sin 30 – 0.4 cos 30)

            = 102 x 10 x 0.154

              = 157 N