Force question netwon law?

Question

IP A block with a mass of 3.1 kg is placed at rest on a surface inclined at an angle of 45° above the horizontal. The coefficient of static friction between the block and the surface is 0.50, and a force of magnitude F pushes upward on the block, parallel to the inclined surface. (a) The block will remain at rest only if F is greater than a minimum value Fmin, and less than a maximum value Fmax, Explain the reasons for this behavior. (b) Calculate Fmin (c) Calculate Fmax

Answer 1

3.1 kg mass has the weight of 30N (=3.1*9.8), which has the normal force of 21N (=30*sqrt(2)/2) against the slope, and a sliding force (parappel to the slope) of the same 21N. The static friction between the block and the slope is directed parallel to and upward on the slope, with the magnitude 11N proportional to the normal force (=0.5*21N). If there is no extra force acting on the block, the block would slide down since the total down-ward force is: 10N (=21N-11N). Hence the extra force pushing on the block must be equal or greater than 10N, to avoid the block sliding down. On the other hand, if the extra force is greater than the sum of the sliding force (21N) and the friction force (11N), the block would move upwards. Hence, the Fmin = 10N, and Fmax = 32N.