A uniform plank AB AB\,AB of length 2L metres and mass m m\,m kilograms rests on a horizontal platform, with the end B B\,B projecting over the edge of the platform. The edge of the platform is at the point C C\,C of the plank, where AC=1.6LAC = 1.6LAC=1.6L metres.
A child of mass 34m\displaystyle \frac{3}{4}m43m kilograms stands on the plank at BBB.
Show that the plank does not tilt.
Find, in terms of mmm, the greatest mass of a child who could stand at B B\,B without the plank tilting.
State one modelling assumption you have made about the child.