Answer
41.7 N
Work Step by Step
The first thing we do for problems with a ramp is to set our coordinate axes so that the x axis is parallel to the plane and the y axis is perpendicular to it. We then need to resolve Fg (Force of the weight of the block) into its x and y components in the new coordinate system. Using the angle given and similar triangles, we find that Fg,x = Fgsin($\theta$) and that Fg,y = Fgcos($\theta$). To find the Tension, we see that it is in what we now call the x direction and so we list out all the forces acting in the x direction. These are T up the ramp and Fg,x down the ramp. since the block is not moving, the net Force must be 0 meaning that T - Fg,x = 0. Therefore, T = Fg,x = (8.5kg)(9.8$m/s^2)sin(30) = 41.7 N
