# A block weighing #14 kg# is on a plane with an incline of #pi/6# and friction coefficient of #1/5#. How much force, if any, is necessary to keep the block from sliding down?

##### 1 Answer

In order for the object to not slide down, a force of

#### Explanation:

Let us visualise the situation:

To analyze the motion of the block, we must know about the forces which act on it.

First of all, the gravity force

We ask: what force **Newton's Second Law**:

#F=ma#

Where

If the plane has an inclined

Now, on the parallel direction to the plane, we have:

#F_("parallel")=-F_0 + G_x - F_f=ma#

The sign of the force is determined by whether it acts for or against motion. In our case,

In order for the object to not move, the accerelation

#F_0=G_x - F_f#

Finding

#F_("perpendicular") = 0 = N-G_y=> N = G_y = mgcostheta#

If we take

#N = 140cos(pi/6) =70sqrt3~~121.24 " N"#

Finding

#G_x = mgsintheta=140sin(pi/6) = 70 " N"#

Therefore, for the block to not move, we must apply a force of: