Afixed hoop of radius R stands vertically.Aspring with spring constant k and rel

ID: 1367178 • Letter: A

Question

Afixed hoop of radius R stands vertically.Aspring with spring constant

k and relaxed length of zero is attached to the top of the hoop.

(a) A block of mass m is attached to the unstretched spring and

dropped from the top of the hoop. If the resulting motion of the

mass is a linear vertical oscillation between the top and bottom

points on the hoop, what is k ?

(b) The block is now removed from the spring, and the spring is

stretched and connected to a bead, also of mass m , at the bottom

of the hoop, as shown in Fig. 5.34 . The bead is constrained to

move along the hoop. It is given a rightward kick and acquires an

initial speed v0 . Assuming that it moves frictionlessly, how does

its speed depend on its position along the hoop?

Afixed hoop of radius R stands vertically.Aspring with spring constant k and rel