A uniform steel beam of mass M M\,M kilograms and length 2a 2a\,2a metres is held in a horizontal position of equilibrium by two supports at the points A A\,A and BBB.
A A\,A is a distance y y\,y metres from the left-hand end of the beam, and B B\,B is a distance (y+0.24)(y + 0.24)(y+0.24) metres from the right-hand end.
The magnitude of the normal reaction on the beam at B B\,B is four times the magnitude of the normal reaction on the beam at AAA.
Show that a−y=ca - y = ca−y=c, where c c\,c is a constant to be determined.