A painter (mass 67 kg) is walking along a trestle, consisting of a uniform plank (mass 19.0 kg, length 6.660 m) balanced on two sawhorses. Each sawhorse is placed 1.13 m from an end of the plank. A paint bucket (mass 3.67 kg, diameter 24 cm) is placed as close as possible to the right-hand edge of the plank while still having the whole bucket in contact with the plank.
(a) How close to the right-hand edge of the plank can the painter walk before tipping the plank and spilling the paint?
(b) How close to the left-hand edge can the same painter walk before causing the plank to tip?