A $21\mathrm{.}0-$kg child on a $4\mathrm{.}00-$m$-$long swing is released from rest when the ropes of the swing make an angle of $29\mathrm{.}0$ with the vertical.

$($a$)$ Neglecting friction, find the child's speed at the lowest position.

m$/$s

$($b$)$ If the actual speed of the child at the lowest position is $2\mathrm{.}70$ m$/$s$,$ what is the mechanical energy lost due to friction?

J