Question

A child sits on one side of a teeter totter of length 7.60 m, a distance of 49.7 cm away from the end of the beam. The child has a mass of 21.6 kg. Her mother has a mass of 43.6 kg. How far away from her end does she have to sit in order for the teeter tooter to be exactly balanced?

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Answer 1

I suppose we assume that the beam is balanced around its center, 3.80 meters from each end.
Then figure out how far from the center the child is. Do everything in meters:
3.80 - .497 = 3.303 meters
Then how much moment (torque) does the child exert around the center?
Weight = 21.6 kg so 21.6 g Newtons times 3.303 meters = 71.34 g Newton meters
Now
How far must the mother sit from the center (remember they asked for fromthe end so we have to do that at the end of this) to balance the child?
call it x from the center
So the moment is
43.6 g x Newton meters
so
43.6 g x = 71.34 g
Notice that g, the acceleration of gravity, cancels out and we could have done this in kilograms but best to do it in force units, Newtons
x = 71.34/43.6 meters from the center
x = 1.64 meters from the center
which is 3.80 - 1.64 = 2.16 meters (or 216 cm) from her end

Answer 2

Thanks!