Question

A bead of mass m slides without friction on a vertical hoop of radius R . The bead moves under the combined action of gravity and a spring, with spring constant k , attached to the bottom of the hoop. Assume that the equilibrium (relaxed) length of the spring is R. The bead is released from rest at θ = 0 with a non-zero but negligible speed to the right. The bead starts on the top of the circle opposing gravitational pull of the earth


(a) What is the speed v of the bead when θ = 90∘ ? Express your answer in terms of m, R, k, and g.

(b) What is the magnitude of the force the hoop exerts on the bead when θ = 90∘ ? Express your answer in terms of m, R, k, and g.

Answer 1

Use this link it shows the question you are solving , but it has slightly different parameters ie the equilibrium of the spring. It show that you need
GPE + EPE = KE + GPE + EPE
ie TOP=SIDE. You can then rearrange this to get everything on one side except v (your speed).

Answer 2

Use this link it shows the question you are solving , but it has slightly different parameters ie the equilibrium of the spring. It show that you need
GPE + EPE = KE + GPE + EPE
ie TOP=SIDE. You can then rearrange this to get everything on one side except v (your speed).
I cant post link so search on google for part b) What is the magnitude of the force the hoop exerts on the bead and look for the mit link

Answer 3

Part b) is working forces. So you have centripetal acceleration = N-kx where kx is the spring force.

cent acc = mv^2/r so us a)to derive this.

Answer 4

hey man can you tell the answer,, plzz help