I have a square table that used to be perfectly stable, back when it had a foot at the end of each leg. Now the feet are missing from legs B, C, and D There's only one left at leg A.
The table measures 50 cm x 50 cm with legs 99.5 cm long. The foot is flat and attached by a swivel so that the end of leg A is a constant 0.5 cm from the ground. (In other words, the total length of leg A plus the foot is 100cm, 0.5 cm longer than each of the other three.)
The table can now rock back and forth with the foot of A and its opposite leg C in constant contact with the floor.
If B is also in contact with the floor, how far is D from the floor?
Note: consider the tips of the legs to be singular points at the corners of a square.
Yes, the answer is 0.5 cm as Charlie says.
Imagine all legs are 0 cm in length and we're going to add 0.5 cm to one leg (A) while keeping one adjacent corner (B) and the opposite corner (C) still flat on the floor. The only way that can happen is for the axis of rotation be the line BC since neither B nor C moves.
Thus whatever A does, D also does.
Posted by Larry
on 2018-08-17 16:48:42