A train traveling at a constant speed of $26\mathrm{.}8\frac{m}{s}$ rounds a curve of radius $255m.$ A chandelier suspended from the ceiling swings out an angle $$ from the vertical throughout the turn.

a$.$ Draw the free body diagram for the chandelier. Break any vectors that do not lie on axis' into their components.

b$.$ Write a sum of forces equation for the vertical direction. Explain why you have chosen to apply either the $1^{st}$ or $2^{nd}$ law.

c$.$ Write a sum of forces equation for the horizontal direction. Explain why you have chosen to apply either the $1^{st}$ or $2^{nd}$ law.

d$.$ Combine the equations to establish an equation that can be used to calculate the angle the chandelier swings.

e$.$ Calculate $$

The second hand on a wall clock is $11\mathrm{.}5cm$ long.

a$.$ What is the period of motion in seconds?

b$.$ What is the velocity of the tip of the second hand in $\frac{m}{s}?$

c$.$ What is the acceleration of the tip of the second hand in $\frac{m}{s^2}?$