$**27.$ Bob and Will are at it again, working at a lumberyard holding a heavy uniform board

in place so that it can be cut. The board is $2$ m long and has a mass of $90$ kg$.$ It is perched on

a frictionless roller $50$ cm from Will$$s end. Will thinks he is helping by pushing horizontally

on the board with a force of $400$ N$.$

$1\mathrm{.}5$ m

WillBob

$0\mathrm{.}5$ m

a$)$ Draw the beam and add an arrow to it indicating the approximate direction of the

force that Bob must exert on the board to keep it from moving.

b$)$ Find the magnitude of the force that Bob must exert to keep the board from moving.

c$)$ Suppose Bob finally gets fed up and walks away from the job. What force