Chair Pads Seat
A look at what is currently available on eBay
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A child who rocked back and forward on his chair while sitting at the table.?
Now, assuming the thin legs of the chair are in the form of a square each side of which is 40 centimeters and the thick padded chair seat is 50 centimeters from the floor, at what angle form the vertical will the chair fall over backwards?
The mass of the chair is 12 Kilograms, and the mass of the child is 30 Kilograms. When the child is sitting down, his center of mass is 18 centimeters from the seat of the chair.
Any help at all would be great I don't even know if I fully comprehend the question or how to set it up.
You need to compute the rock angle theta at which the combined CG is directly over the line on the floor between the two rear legs (if he's rocking back). Since the CG is always at or directly over the center of the seat, it must move 0.2 m backward to tip.
With the kid, the CG rises by 0.18*30/42 = 0.12857 m from its initial height of 0.5 m for a total height of 0.62857 m.
Thus theta must = arctan(0.20/0.62857) = 30.805 deg.
EDIT: Bill R's comments are well taken. I have assumed that simplicity rules, and the "thin" legs are to be considered massless, and the kid's CG is 18 cm above the center of the seat, allowing a one-dimensional calculation. If I'm wrong, mea (and to some extent, asker's) culpa.
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