Another physics question, please help?

Question

A uniform plank of length 5.0m and weight 225N rests horizontally on two supports, with 1.1m of the plank hanging over the right support. To what distance (x) can a person who weights 450N walk on the overhanging part of the plank before it just begins to tip?

The answer is .70m.
My friend and I tried to do this one yet we could never come up with the answer. We thought it would be pretty simple but it ended up not being. Any help anyone can give will be seriously appreciated

Answer 1

Assume the center of the mass of the plank is located at 2.5 m.

Let the fulcrum (point of rotation) be the right support ---- and we will make all of our measurements off of that point.

The left support can be ignored b/c it does not affect the moment.

Draw it out --- you should have a 1.1 m overhang on the right side, a 225N force acting down in the center of the board (which is 1.4 m from the point, to the left). Now, the only other force in this case is the 450N person and they will be to the right of the point, so set up your eqn of known moments:

225N * 1.4 m = 450 N * X m --- where we are looking for x.

solving the eqn, x = .7 m

So, just after .7 m, the plank will rotate about the point.

Answer 2

Ignore the left support. The right support divides the 5.0 m plank into a 3.9 m segment and a 1.1 m segment. Each one can be viewed as having its own mass (proportional to length) and a center of mass, with the two centers of mass acting independently to cause a moment. The person is an independent mass at a point location.

For example, the 3.9 m segment of plank has a mass of (3.9 m / 5.0 m)*(225 N) = 175.5 N and a center of mass at (3.9 m) / 2 = 1.95 m to the left of the support. The 1.1 m segment has its center on the right side of the support. The only unknown is the position of the person to the right of the support.

Select a positive direction for moment (usually counter-clockwise) and do a moment balance about the right support, where you now know the mass and center of mass of the left and right portions of the plank and the mass of the person. The only unknown is x, the position of the person, and the furthest the person can walk along the plank would be the position x where the sum of the moments is zero. (Any further, and the person's side tips down.) Remember that moment is equal to the product of the force (weight) and the lever arm (distance from the fulcrum or support), and that the moments on opposite sides of the support act in opposite directions.

I get 0.7 m when I solve for x.