1. The problem statement, all variables and given/known data A box of weight W is pushed by a force F on a horizontal floor (the diagram below shows the force on the box is at an angle theta to the horizontal) If the coefficient of static friction is mu, show that the minimum value of F that will move the crate is given by: F=(mu*W*sec theta)/(1-mu*tan theta) 2. Relevant equations The only maths needed i think is trig functions such as sec=1/cos, 1=sin^2+cos^2 etc. For physics, I have called the frictional force acting against the box fr and the reaction against the horizontal plane R. fr=mu*R is the only equation I could find with the exception of the equations that are results of Newton's thid law (which are listed in my attempted solution) 3. The attempt at a solution Horizontally I worked out F*cos theta=fr=mu*R Vertically, F*sin theta=W=n (not sure which values to use so I plugged them all in there) 1st attempt: R is rective force and W=mg so R=W. fr=mu*W F*cos theta=mu*W F=(mu*W)/cos theta But obviously the result is more complicated than that so I then tried: fr=R*tan theta (taken from previous class notes but I don't know if this value is suitable for this problem...) F*sin theta=W=n F*sin theta*tan theta=mu*W=(F*sin^2 theta)/cos theta F=(mu*W*cos theta)/sin^2 theta (from rearranging the above line) F=(mu*W*cos theta)/(1-cos^2 theta) then I just trailed off... I have made many more attempts but have rubbed them out as they were yet more unsuccessful... Please help!