A uniform beam of length L and mass mB is supported by two pillars located L/3 from either end, as shown in the figure. A duck of mass mD stands on one end. A scale is placed under each pillar. The entire system is in equilibrium.

a) Draw a free body diagram.

b) Enter an expression, in terms of defined quantities and g, for the force (FR) that the scale under the right pillar shows.

c) Enter an expression, in terms of defined quantities and g, for the force (FL) that the scale under the left pillar shows.

d) Enter an expression, in terms of defined quantities and g, for the sum or the scale readings.