Finding Center of Mass on a Reaction Board Using Torque Principles

[leejos16]

Homework Statement

A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 3.0-m-long, 6.6kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 63kg woman lies on the reaction board with her feet over the pivot. The scale reads 23kg .

What is the distance from the woman's feet to her center of mass?

Homework Equations

T=F*d

The Attempt at a Solution

I know this is a problem that is related to torque, but I'm completely lost. Can someone help me..

 

[gomath]

Let's say the distance from the woman's feet to her center of mass is d. So now you have Tup=-T down, which tells you
l(board)*23kg*g=
-(0.5*l(board)*Fg(board)+d*Fg(woman)
And then the problem becomes much easier.

 

[ksj]

There is a simpler way of doing this without using torque! The formula for finding a center of mass using the reaction board method is:

x = (r2-r1)/W * d

where:
x is the centre of mass
r2 is the scale after the weight has been added (23kg)
r1 is the initial scale reading (assuming uniform density, r1 = mass of the board/2)
W is the weight of the person
d is the length of the board

Therefore, your answer is 0.94 m (from her feet)

The key concept here is that the center of mass is calculated by the formula: x(cm) = x1m1 + x2m2 + x3m3... / m(total)
Because your question requires you to separate the system (woman + reaction board), you simply subtract the weight of the board.
The center of mass of the board is exactly at the midpoint, which is why the woman's height is not needed.

 

[ksj]

Hope that helps!

 

[haruspex]

There is a simpler way of doing this without using torque...
x = (r2-r1)/W * d

Rearranging, xW = (r2-r1)d. Looks exactly like the torque equation to me.
I suggest that the object of the homework exercise is to use the principles of torque to solve it, not to look up some standard solution for reaction boards.