Answer:
The speed at point B is 5.33 m/s
The normal force at point B is 694 N
Explanation:
The length of the spring when the collar is in point A is equal to:
![lA=\sqrt{0.2^{2}+0.2^{2} }=0.2\sqrt{2}m](https://tex.z-dn.net/?f=lA%3D%5Csqrt%7B0.2%5E%7B2%7D%2B0.2%5E%7B2%7D%20%20%7D%3D0.2%5Csqrt%7B2%7Dm)
The length in point B is:
lB=0.2+0.2=0.4 m
The equation of conservation of energy is:
(eq. 1)
Where in point A: Tc = 1/2 mcVA^2, Ts=0, Vc=mcghA, Vs=1/2k(lA-lul)^2
in point B: Ts=0, Vc=0, Tc = 1/2 mcVB^2, Vs=1/2k(lB-lul)^2
Replacing in eq. 1:
![\frac{1}{2}m_{c}v_{A}^{2}+0+m_{c}gh_{A}+ \frac{1}{2}k(l_{A}-l_{ul}) ^{2}=\frac{1}{2}m_{c}v_{B}^{2}+0+0+\frac{1}{2}k(l_{B}-l_{ul}) ^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm_%7Bc%7Dv_%7BA%7D%5E%7B2%7D%2B0%2Bm_%7Bc%7Dgh_%7BA%7D%2B%20%20%20%20%20%20%5Cfrac%7B1%7D%7B2%7Dk%28l_%7BA%7D-l_%7Bul%7D%29%20%20%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7Dm_%7Bc%7Dv_%7BB%7D%5E%7B2%7D%2B0%2B0%2B%5Cfrac%7B1%7D%7B2%7Dk%28l_%7BB%7D-l_%7Bul%7D%29%20%20%5E%7B2%7D)
Replacing values and clearing vB:
vB = 5.33 m/s
The balance forces acting in point B is:
Fc-NB-Fs=0
![\frac{m_{C}v_{B}^{2} }{R}-N_{B}-k(l_{B}-l_{ul})=0](https://tex.z-dn.net/?f=%5Cfrac%7Bm_%7BC%7Dv_%7BB%7D%5E%7B2%7D%20%20%20%7D%7BR%7D-N_%7BB%7D-k%28l_%7BB%7D-l_%7Bul%7D%29%3D0)
Replacing values and clearing NB:
NB = 694 N