Physics problem, please help im really stuck!?

Question

I've tried the following problem and I keep getting the wrong answer. I'm just hoping someone can help me figure this one out.

In exercise physiology studies, it is sometimes important to determine the location of a person's center of gravity. This can be done with the arrangement shown in Figure P8.67. A light plank rests on two scales that read Fg1 = 450 N and Fg2 = 310 N. The scales are separated by a distance of 2.00 m. How far from the woman's feet is her center of gravity?

Thanks a lot guys!

Answer 1

The CG is between the two scales. let us say it is at a distance of x1 from scale 1 and x2 from scale 2. (assume the plank remains horizontal)

Then, x1*Fg1 = x2*Fg2 (the moments must be equal)

>> x1/x2 = Fg2/Fg1
and x1 + x2 = 2
>>
x1 = 2 * (310/(450+310)) ~ 0.816 m

Now tell me where the feet of the woman are.

Answer 2

Assume that Fg1 is at the left side and Fg2 at the right side, then take imaginary point M say 1 m on the left side of Fg1 and on a extended straight line from Fg2 and Fg1.
The resultant of Fg1 and Fg2 say Fgr=Fg1+Fg2 at a distance of x to the right of Fg1,
Then moment produce by Fgr at point M equals : (1+x)*Fgr=(1+x)*(450+310)=
(1+x)*760 Nm
This moment must equals total moment of Fg1 and Fg2 at point M too that is 1 * Fg1 + (1+2) * Fg2 = 1*450+3*310 =1380 Nm.
Hence (1+x)*760=1380
1+x = 1380/760 =1.816
x=0.816 m to the right of Fg1
If the woman's feet lies exactly at Fg2,
then the c.g. of woman is 2-0.816= 1.184 m from woman's feet.
Hope this help you

Answer 3

Exercise Physiology Studies

Answer 4

Learn Human Anatomy & Physiology Now!

Answer 5

I wish you had given me what you said is Figure P8.67. Without it, I'm afraid I'm unable to be of help to you. Sorry.