When an object is placed on an incline which is not
frictionless, there are two forces acting on it. One is the force due to the
gravitational pull of the Earth, in the downward direction and the other is an opposing
force due to friction.
In the problem, the object does not
have any acceleration. This means that the two forces acting on it are
equal.
The gravitational force downwards can be expressed
as a sum of two vectors, one normal to the inclined plane and the other parallel to the
plane.
The magnitude of the component normal to the plane
is m*g*cos 47.9, where m is the mass and g is the acceleration due to
gravity.
The magnitude of the component parallel to the
plane and acting in a downwards direction is m*g*sin
47.9.
The force of kinetic friction opposing any
acceleration due to the the force of gravitation is N*Kf, where N is the normal force
and Kf is the coefficient of kinetic friction.
N*Kf =
m*g*sin 47.9
=> m*g*cos 47.9*Kf = m*g*sin
47.9
=> Kf = sin 47.9 / cos
47.9
=> Kf = tan
47.9
=> Kf =
1.106
The required coefficient of kinetic
friction is 1.106
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