A uniform horizontal beam $5\mathrm{.}00$ m long and weighing $3\mathrm{.}00$x $102$ N is attached to a wall by a pin

connection that allows the beam to rotate. Its far end is supported by a cable that makes an

angle of $53\mathrm{.}0$o with the horizontal. If a person weighing $6\mathrm{.}00$x $102$ N stands $1\mathrm{.}50$ m from the wall,

find the magnitude of the tension T in the cable and the force R exerted by the wall on the

beam.

Example $5$

A solid frictionless cylindrical reel of mass M $=3\mathrm{.}00-$kg and radius R $=0\mathrm{.}400$ m is used to draw

water from a well. A bucket of mass m $=2\mathrm{.}00$ kg is attached to a cord that is wrapped around

the cylinder.

$($a$)$ Find the tension T in the cord and acceleration of the bucket.

$($b$)$ If the bucket starts from rest at the top of the well and falls for $3\mathrm{.}00$s before hitting the

water, how far does it fall?