Question

a beam positioned on a fulcrum is 6 m long. it has a weight of 300 n attached to one end and a weight of 250 n attached to the other end. to establish mechanical equilibrium, the fulcrum must be placed how far away from the 250 n weight? (answer in m)

Answer 1

To establish mechanical equilibrium, the fulcrum must be placed 3.27 m away from the 250 N weight.

What is the position of the fulcrum?

The position of the fulcrum from the 250 N weight is determined by applying the principle of moment as shown below.

let the position of the fulcrum = d

The position of the 250 N from the fulcrum must be greater than the center of the beam since 300 N is heavier than 250 N.

----------------------------------Δ--------------------------------

↓                                     d                                      ↓

250 N                                                                    300 N    

the position of the 250 N weight from the fulcrum = d

the position of the 300 N weight from the fulcrum = 6 m - d

take moment about the pivot;

sum of the antic lock wise moment = sum of the clockwise moment

250 ( d ) = 300 ( 6 - d )

250d = 1,800 - 300d

550d = 1,800

d = 1,800 / 550

d = 3.27 m                              

Thus, the position of the fulcrum from 250 N depends on the length of the beam and the weight hanging at the other end.

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