A scaffold (a uniform horizontal board of mass 50 kg and length 4 m) is supported by a rope at each end. A 100 kg painter stands on the scaffold at a location such that the tension is one rope is four times that in the other. Where is the painter standing (specify clearly the distance from one or the other end)?

Question

A scaffold (a uniform horizontal board of mass 50 kg and length 4 m) is supported by a rope at each end.  A 100 kg painter stands on the scaffold at a location such that the tension is one rope is four times that in the other.  Where is the painter standing (specify clearly the distance from one or the other end)?

Damon · Answer

4 F up at one end, F up at the other
so
100 + 50 = 5 F
F = 30
4 F = 120
take moments around end close to the 100 kg painter. x is from that end (the 4F=120 end) to the painter)

100 x + 2(50) = 4(30)

100 x = 20
x = .2 meters