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 450 n walk on the overhanging part of the plank before it just begins to tip

Answer 1

0.7 meters from the support, or 0.4 meters from the end of the board. Another way of describing the problem is to have the 450 N person move so that the center of mass of the plank and person system is on the second support. So let's first determine how far from that support the center of mass of the plank is. We can model the plank as a point mass source that's 2.5 meters from either end. So that point mass is 2.5-1.1 = 1.4 meters from the pivot. So let's multiply that radius by the mass, getting: 1.4 m * 225 N = 315 Nm Now the person will be at just the tipping point when their mass multiplied by the distance equal 315. So let's do the division. 315 Nm / 450 N = 0.7 m So the person will be at the tipping point when he's 0.7 meter from the support, or 1.1 - 0.7 = 0.4 meters from the end of the board.