Determine the distance of the center of gravity from the end X of the plank?

[looi76]

Homework Statement

A non-uniform plank of wood XY is 2.50m long and weighs 950N. Force-meters (spring balances) A and B are attached to the plank at a distance of 0.40m from each end, as illustrated in the Figure below

http://img266.imageshack.us/img266/2377/physicsp23bgh5.png​

[/URL]
When the plank is horizontal, force-meter A records 570N

(i) Calculate the reading on force-meter B
(ii) Determine the distance of the center of gravity from the end X of the plank.

Homework Equations

Moment = Force x Perpendicular Distance

The Attempt at a Solution

(i) [tex]A + B = 950N[/tex]
[tex]B = 950 - 570 = 380N[/tex]

(ii) I don't know how to solve this question, need help!

 

[CompuChip]

In equilibrium, all the moments (A, B, gravity) cancel out.

 

[Moetasim]

To determine the distance of the center of gravity from the end X of the plank, we can use the principle of moments. The center of gravity is the point at which the weight of the object can be considered to act. In other words, if we were to balance the plank at this point, it would remain in equilibrium.

Let's label the distance from end X to the center of gravity as 'd'. We can then write the following equation:

570N x 0.40m = 380N x (2.50m - d)

This equation represents the principle of moments, where the moment on one side of the pivot (force-meter A) is equal to the moment on the other side (force-meter B).

Solving for 'd', we get:

d = 1.15m

Therefore, the center of gravity is located 1.15m from the end X of the plank. This makes sense intuitively, as the center of gravity would be closer to the heavier end of the plank.

Hope this helps!