An object with a mass of #6 kg# is on a plane with an incline of #pi/12 #. If the object is being pushed up the plane with # 2N # of force, what is the net force on the object?
13.22 N down the plane ; OR
58.32 N at an angle of 12.8 degrees from the ground perpendicular
Since there is no coefficient of friction given, the only opposing force is gravity's compnent in the plane
= 6kg 9.8 m/s^2 sin pi/12 = 15.22 N
thus F(net plane) = 15.22 - 2 = 13.22 N down the plane
The other component of gravity is
6kg 9.8 m/s^2 cos pi/12 = 56.8 N perpendicular to the plane
So the net Force is the combination of
56.8 N perpendicular to the plane
13.22 N down the plane
The magnitude of this combination is found with the Sqrt
of the sum of the squares of 56.8 and 13.22 = 58.32
The angle is arctan 13.22/58.32 = 12.8 deg from the perpendicular
Hope someone can check my work here !