Question

A crate of weight Fg is pushed by a force on a horizontal floor. (a) If the coefficient of static friction is ?_s, and is directed at angle?

Answer 1

A) F is at angle theta below the horizontal

so F horiz = P cos (theta)

normal force = Fg

Force to get crate moving = Fg*us

Also you have to overcome the force of the weight itself

P cos theta = us*Fg + P *us*sin (theta)

P cos theta - P *us*sin (theta) = us*Fg

Divide through by cos (theta)

P - P*us*tan(theta) = ( us*Fg*sec(theta))

P(1 - us*tan(theta)) = ( us*Fg*sec(theta))

P = ( us*Fg*sec(theta)) / (1 - us*tan(theta))

b)by differentiating P wrt theta for minimum value of P you will get a theta put this value of in given equation you can get minimum value of P

Thank