FRICTIONAL FORCE

An object weighing 30 units (don't worry about the g part) lies on an inclined plane and a rope attached to the object goes over a pulley. In the coordinate system chosen, the object is at (1,2,1), the pulley is at ( -4,6,2), and is a vector normal to the plane. The positive z-axis points straight up and the coefficient of friction between the object and the plane is 1/10.

1. What is the minimum force which must be applied through the rope to drag the object up the plane? In which direction (i.e. vector) will the object start moving up the plane if this minimum force is applied?
2. What is the minimum force which must be applied through the rope to stop the object from sliding down?

Your answer must be accurate to 6 digits. Include a sketch for a clearer presentation, and be sure to explain the meaning of any symbols you introduce. Spend a few minutes interpreting your solution. Be sure your solution makes sense. Poorly presented solutions will lead to loss of credit.

 
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