A mass M of 5.60E-1 kg slides inside a hoop of radius R=1.50 m with negligible friction. When M is at the top, it has a speed of 4.31 m/s. Calculate the size of the force with which the M pushes on the hoop when M is at an angle of 44.0°.

Conservation of energy. Calculate the difference in height for the mass from when it's at the top of the hoop to its position at 44 degrees. That change in height equates to a loss of potential energy, and hence a gain of kinetic energy. From that you can determine the mass's increase in speed. And from there you can determine its centripedal acceleration, and hence the force it applies against the hoop due to its acceleration. Finallty, subtract out the componenet of force due to gravity acting on the mass.