μSomeone is pushing a packing case of mass 30 kg up an inclined slope of angle 11.3deg. as shown in the diagram below. The coefficient of kinetic friction between the case and the slope is µk = 0.100 and the coefficient of static friction is µ = 0.200. 1. The minimum force the person must apply parallel the slope to keep the case from sliding down the slope (i.e., just to keep it in equilibrium, at rest) is: A) 59 N B) 120 N C) 152 N D) 32 N E) Zero 2. The maximum force that the person can apply parallel to the slope without causing the crate to move is: A) 59 N B) 118 N C) 29 N D) 136 N E) 88 N My prof discussed this in class a bit, but he went through it so fast, I'm not sure I have this right. 1. The F applied plus F static friction must equal the F parallel to keep it from slipping. I think then: Fapplied + μ(mg cos theta)= (mg sin theta) So, Fapplied min. = (mg sin theta) - μ(mg cos theta)= Zero???? because: 30 x 10 (sin 11.3) - .2(30 x 10 cos 11.3) = -.05 I feel like conceptually I'm missing something. I don't really understand what the minimum applied force to keep the box stationary means vs. the max applied force to keep the box stationary. 2. For the max applied force to keep box stationary, then would this be Fapp = (mg sin theta) + μ(mg cos theta)= 30 x 10 (sin 11.3) + .2(30 x 10 cos 11.3) = 118N?? At first I thought the answer to this was just the coeff of static friction x FN(mg cos theta), which I thought gives the max static frictional force which would be 59N, but now I just don't really know because they are asking for the max force applied by the person which I think is certainly different then just the max Fstatic. There is another component to the question also asking what the min and max force to keep the box moving at constant velocity is and I assume to figure these out I would use the same formulas above but substitute μ for kinetic friction. I'm getting really confused though about this conceptually. Can someone please help explain the "why" behind this? For one, I don't quite understand the min. and max forces to apply to keep a box stationary or moving. Do I even have the formulas above correct? Thanks so much! It seems the more I look at this the less I get it! I seemed to "get it" in class, but now I feel like my understanding went out the window!