An object slides down an inclined plane at a constant velocity. Find the coefficient of sliding friction if the plane is inclined at an angle of α degrees to the horizontal.

###### Solution.

There are three forces acting on the object: the force of gravity – mg, the normal force – N and the frictional force – f_{k}.

According to the Newton’s First Law of motion, if the object moves at constant velocity then net force on an object is zero.

Therefore, the sum of the projections of the forces along each axis is zero and the Newton’s equations of motion are

Y – axis : N – m*g*cos(α) = 0

X – axis : – f_{k} + m*g*sin(α) = 0

Let’s use the fact that f_{k} = μ_{k}*N

Hence,

– μ_{k}*m*g*cos(α) + m*g*sin(α) = 0

Finally,

μ_{k} = tan(α)

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