# 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?

Jul 2, 2017

13.22 N down the plane ; OR
58.32 N at an angle of 12.8 degrees from the ground perpendicular

#### Explanation:

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
AND
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 !