Today Puzzle #578
Puzzle No. 578鈥� Monday 30 September
A father sits his two daughters on one side of a see-saw and plans to balance it with his weight on the other side. He places one daughter 2 meters from the pivot and the other 1 meter from the pivot. Knowing the father weighs 90 kg, each daughter weighs 20kg and turning moments are defined as ‘force times distance’, where should the father sit so as to balance the see-saw at the first attempt?
Today’s #PuzzleForToday has been set by Dr Geoff Evatt, Department of Mathematics, University of Manchester
Click here for the answer
66.7 centimetres from the pivot. One girls sits 2m one side of the pivot point of the see-saw. This gives a turning moment of 2m x 20kg x gravity. He places the other girl 1m from the pivot, giving a turning moment of 1m x 20kg x gravity. The combined turning moment on the girls side is thus (40 + 20) x gravity. If we label the balance position as y, which is distance from pivot towards the father, then his turning moment is ym x 90kg x gravity, which is 90y x gravity. And so, in balance, the turning moments on either side of the pivot must equal, meaning 60 x gravity = 90y x gravity. Cancelling gravity allows y to be found as 2/3 of a meter, or 66.7 cm, away from the pivot.
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