How Does a Student's Position Affect Scale Readings and Center of Gravity?

[Soojin]

Homework Statement

For some reason I can't get my picture to show up, but here is the link to it:
http://img.photobucket.com/albums/v302/Robi41035/Picture1.jpg

"The plank is uniform and 2.2 m long. Initially the scales each read 100 N. A 1.60 m tall student then lies on top of the plank, with the soles of his feet directly above scale B. Now scale A reads 394.0 N and scale B reads 541 N.

a) What is the student's weight?

b) How far is his center of gravity from the soles of his feet?

c) When standing, how far above the floor is his center of gravity, expressed as a fraction of his height?"

Homework Equations

a) w = mg
Possibly L₁W₁=L₂W₂.

b)center of gravity = mr²/sum of masses

c) I think this one is just the answer for b/1.60.

The Attempt at a Solution

a) I know that weight = mg. I also thought I might have to use the equation L₁W₁=L₂W₂, but I'm not sure how to set this up.

b) I know that the center of gravity = mr²/sum of masses, but I'm not sure what I should be using as "m" and "r".

I know this is simple, but I'm having a hard time grasping the concepts. If anyone can help me out, I would appreciate it a lot. Thanks!

 

[D H]

b)center of gravity = mr²/sum of masses

That is not the equation for the center of mass. One way to check: Look at the units. The center of mass is a position vector: It should have units of length. Your equation has units of length squared. The correct equation is
M_{tot}\boldsymbol{x}_{cm} = \sum_i m_i \boldsymbol{x}_i

a) I know that weight = mg. I also thought I might have to use the equation L₁W₁=L₂W₂, but I'm not sure how to set this up.

You are missing that L₁+L₂=L=2.2 meters. What this will give you is the center of mass of the plank+person. You will need to use some additional information to get the location of the center of mass of the person.