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
#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: