A bead of mass m , with a hole through its center, slides without friction along a vertical hoop of radius R. moves under the combined influence of gravity and a spring attached to the bottom of the hoop. For simplicity, we assume that the equilibrium length of the spring is zero, so that the force due to the spring is -kr, where r the instantaneous length of the spring, as shown. The bead hoop R nail (a) What is the intial energy of the system when the mass is at rest at the top of the hoop? (b) The bead is released at the top of the hoop with negligible speed. How fast is it moving when it reaches the bottom of the hoop? (c) Why would this problem be difficult to solve using a force approach?

A bead of mass m , with a hole through its center, slides without friction along a vertical hoop of radius R. moves under the combined influence of gravity and a spring attached to the bottom of the hoop. For simplicity, we assume that the equilibrium length of the spring is zero, so that the force due to the spring is -kr, where r the instantaneous length of the spring, as shown. The bead hoop R nail (a) What is the intial energy of the system when the mass is at rest at the top of the hoop? (b) The bead is released at the top of the hoop with negligible speed. How fast is it moving when it reaches the bottom of the hoop? (c) Why would this problem be difficult to solve using a force approach?