With some assumptions that I think you made, yes.MERuhl wrote:So are you saying that, by definition, if you get the CM in precisely the right spot, then the weight on the front wheels will always be 1 ounce?Stan Pope wrote:Actually, WW's numbers were 1.22 oz @ 7/8", so I wonder about his measurement.
If so, may I then conclude that one way (the best way?) to ensure the CM is placed accurately is to set the front wheels on scale as described above, and tweak the weight placement in the rear of the car until the front weight is 1 ounce?
I think this is what I was trying to ask in the first place...
You can consult your high school physics books to see the relationships.
Or, you can review the torques about the CM as the car sits quietly on the table (i.e. is stable or, as the physicists would say, in equilibrium). The torques about the CM must balance. If they didn't, the car would flip over. (Well, actually, one end or the other would raise up.)
Looking at the torques just about a horizontal axis perpendicular to the longitudinal axis and through the CM: the downward force by the front wheel(s) times the horizontal distance from CM to the front axle must just equal the downward force by the rear wheel(s) times the the horizontal distance from the CM to the rear axles. (Torque = moment arm length times perpendicular force)
You know the total forces down, the weight of the car. And you know the total of the moment arms, the wheelbase.
A little algebraic slight of hand and you see that things are exactly as you surmised.
Ya?
(Hope ai didn't make too many typos... the print is almost too small to proofread! I may have to borrow Great Aunt Millie's big magnifying glass!)
Now, why would someone measure the location of the CM rather than the weight on the front and rear wheels? Well, it is a practical decision. Not everyone has easy access to a sufficiently accurate scale, but almost everyone has a knife edge. (Actually, it is easier to use the narrow but flat edge of a yard stick, since balanced on a knife edge, the car is not stable.