1)        A 50 kg crate is dragged across a floor by pulling on a rope inclined 37 above the horizontal.
            (g = 10 m/s² ,  cos(37) = 4/5)

     (a)  If the coefficient of static friction is (1/3), what minimum tension in the rope is required to start
            the crate moving ? (12)

           Forces acting on the crate are as indicated in the diagram.

           Apply Newton's 2^nd law along x and y, just as crate begins to move,

          
From the y equation we obtain

          
Substitute this in the x equation with the law of friction gives,

     (b)  If the coefficient of kinetic friction is (1/4), what is the magnitude of the initial acceleration
           of the crate ? (13)

           When crate moves the diagram above is unchanged. Newton's 2^nd law equations are slightly
           altered, due to the acceleration of the crate.

          
From y equation,

          
Substituting into frictional force law and x equation,

           
Assuming a fixed value of T we find