Problem $\backslash$#$2$: $(35$ points$)$ A $3\mathrm{.}5-$lb ball of negligible size located at point $\backslash ($ A $\backslash )$ is released from rest and travels down a curved path as shown in Figure $2.$ The ball exerts a normal force of $5\mathrm{.}5$ lb on the path when it reaches point $\backslash ($ B $\backslash ).$

a$)$ Calculate the velocity $\backslash ($ v s $\backslash )$ of the ball at point $\backslash ($ B $\backslash ).$

b$)$ Calculate the radius of curvature $\backslash (\backslash$rho $\backslash )$ of the path.

c$)$ Calculate the angular momentum of the ball about the center of curvature $\backslash ($ O $\backslash ).$

Figure $2$

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