A block of mass m lies on a flat, frictionless plane against a spring with spring constant k compressed from its equilibrium position by a distance x. At the other end of the plane is a ramp inclined at an angle 0. The coefficients of friction (both kinetic and static) of the ramp vary with the distance along it as u () = Ay, where A is some constant , I the distance from the bottom of the ramp; and y the position in vertical direction. The system is sketched below. Spring Ramp Frictionless Plane The block is released and pushed along the frictionless plane by the spring and then moves up the ramp (the block is not attached to the spring). Write down an equation from which one calculate the maximum distance I traveled by the block along the ramp (do not solve for ).

A block of mass m lies on a flat, frictionless plane against a spring with spring constant k compressed from its equilibrium position by a distance x. At the other end of the plane is a ramp inclined at an angle 0. The coefficients of friction (both kinetic and static) of the ramp vary with the distance along it as u () = Ay, where A is some constant , I the distance from the bottom of the ramp; and y the position in vertical direction. The system is sketched below. Spring Ramp Frictionless Plane The block is released and pushed along the frictionless plane by the spring and then moves up the ramp (the block is not attached to the spring). Write down an equation from which one calculate the maximum distance I traveled by the block along the ramp (do not solve for ).