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.


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


unanswered
(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

Got the first one:

sqrt((0.83*k*R^2)/m+2*g*R)

Can't seem to find the second (b)

Answer 2

me 2,,unable to get the second! but trying!! plzz help someone

Answer 3

(2*(sqrt(2)-1)*k*R)+(2*m*g)-((sqrt(2)-1)*(k*R)*(1/sqrt(2)))

Answer 4

a) Fx(x)= -8*x*(x^2-1)

b). x=1

c) v(x=0)= 1.5

d) v(x=-1)= sqrt(6)