Question

The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below.
If the block is at rest on section 1 of the incline, what is the magnitude of the force of static friction exerted on the block by the incline?

Answer 1

The static friction exerted on the block by the incline is $\mu _ s _1 Mgcos \ \theta$.

The given parameters;

• mass of the block, = M
• coefficient of static friction in section 1, = $\mu_s_1$
• angle of inclination of the plane, = θ

The normal force on the block is calculated as follows;

Fₙ = Mgcosθ

The static friction exerted on the block by the incline is calculated as follows;

$F_s = \mu_s F_n\\\\F_s = \mu _s_1(Mg cos\ \theta)\\\\F_s = \mu _s_1 Mgcos\ \theta$

Thus, the static friction exerted on the block by the incline is $\mu _ s _1 Mgcos \ \theta$

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