Torque

[MedPR]

A beam positioned on a fulcrum is 6m long. It has a weight of 300N attached to one end and a weight of 250N attached to the other. To establish mechanical equilibrium, the fulcrum must be placed:

A: 2.87m from the 250-N weight
B. 3.00m from the 250-N weight
C. 3.27m from the 250-N weight
D. 5.67m from the 250-N weight.

Intuitively the answer is obviously C, but I don't understand the reasoning behind some of the math.

For an object to be in equilibrium, net force = 0 and net torque = 0, so the sum of the torques must be 0. In this problem, the torques are (250N)(X) and (300N)(6-X).

TBR shows this:

SumT=T250N + T350N = 0

SumT=(250N)(X) - (300N)(6-X) = 0

After doing the math, you find that you need to subtract one of the torques in order for the X to come out as a positive value, but why do you automatically take the difference in the beginning?

I don't understand why your initial equation in solving this isn't 250NX+300N(6-X) = 0

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[Ssina]

I think they are doing Tsum= Tclockwise + T counter clockwise which has to equal to zero... idk I think just setting them equal, like you did, is just easier and faster