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Physics $101$

A simple pendulum consists of a small ball of mass $m=200g$ swinging on a massless, inextensible string of length $R=7m.$ At time $t=0$ the pendulum is released from the horizontal position, as shown below. A short time later, the pendulum reaches the bottom of its swing and encounters a nail sticking out of the page a distance $L=6m$ below the pivot point. The pendulum begins to wrap around the nail, and at time $t=t_{\text{t}\text{o}\text{p}}$ it is at the top of its first rotation.

$t=0$

A$.$ Is mechanical energy of the earth$-$ball system conserved during the interval from $t=0$ to $t=t_{\text{t}\text{o}\text{p}}?$ Explain your reasoning.

B$.$ Find the speed of the ball at time $t=t_{\text{t}\text{o}\text{p}\text{.}}.$ Show your work.

C$.$ Find the magnitude and direction of the acceleration of the ball at $t=t_{\text{t}\text{o}\text{p}\text{.}}.$ Show your work.