Question

A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 404 N walk on the overhanging part of the plank before it just begins to tip?

(225)(5.0) = (1.1)(400x) = 2.55m

Is this correct? Thank you!

Answer 1

When the person reaches the maximum distance x along the overhanging
part, the plank is just about to rotate about the right support.
At that instant, the plank loses contact with the left support, which consequently exerts no force on it. This leaves only three vertical forces acting on the plank: the weight W of the plank, the force FR due to the right support, and the force P due to the person. The force FR acts at the right support, which we take as the axis, so its lever arm is zero.

225•(3.9-2.5) = 404•x
x=225•1.4/404=0.78 m

Answer 2

A 15 ft plank of mass 50 kg is laid across two ladders. The ladders are 5 ft apart, and the plank is laid such that 5 ft of it hang off at each end. You have a mass of 90 kg.

(a) How far out past the ladder can you walk before it gets dangerous?


You have a friend of mass 50 kg who is standing on the plank between the ladders, 2.2 ft from the left ladder.

(b) How far out past the rightmost ladder can you safely walk now?