Question

A bead of mass $150g$ constrained to move along a vertical smooth and fixed circular track of radius $3m$, as shown in the figure, is released at $B$. The spring in the plane of the track has natural length of $1m$ and spring constant of $\frac{3}{16}N/m$. What is the normal force (in $N$ ) exerted by the track on the bead when it passes through $A$?

Answer 1

Find the value of velocity.
Given,
Mass of the bead, $m=150g$
Radius, $R=3m$
Natural length, $L=1m$
Spring constant, $k=\frac{3}{16}N/m$
Applying work-energy theorem between $A$ and $B$,
$W_g+W_{\text{s}tring}=\Delta K$
$mgh+\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$
$\frac{150\times 10\times 3}{1000}+\frac{1}{2}\times \frac{3}{16}\times 4^2=\frac{m{v}^2}{2}$
$12=m{v}^2$
Find the value of normal.
$N=\frac{m{v}^2}{r}$
$N=\frac{12}{3}=4N$
Final answer: $4$