A block of mass m rests on a plane inclined at an angle with the horizontal see the figure. A spring with force constant k is attached to the block. The coefficient of static friction between the block and plane is μS. The spring is pulled upward along the plane very slowly. 

A block of mass m rests on a plane inclined at θ with thehorizontal. The block is attached to a spring of constant k asshown in the figure. The coefficients of static and kineticfriction between the block and plane are μs and μk, respectively.Very slowly, the spring is pulled upward along the plane until theblock starts to move. (a) Obtain an expression for the extension dof the spring the instant the block moves. (b) Determine the valueof μk such that the block comes to rest just as the spring is inits unstressed condition, that is, neither extended nor compressed.(You stretch the spring a distance d, and the block begins to move.The block moves a distance d until the spring is no longerstretched, and then the block stops. This is a hardproblem!).

A 2.0 kg box rests on a plank that is inclined at an angle of 65 degrees above the horizontal. The upper end of the box is attached to a spring with a force constant of 360 N/m, as shown in the figure .If the coefficient of static friction between the box and the plank is 0.26, what is the maximum amount the spring can be stretched and the box remain at rest?