I need help with a torque problem from my physics class. I attempted to do it, and my numbers, though reasonable, do not add up as they should. I'm hoping that if I describe the process step-by-step, someone could show me where I went wrong.
Here's the actual problem:
An 850.0N painter stands 1.2m from one end of a 3.00m scaffold supported at each end by a stepladder. The scaffold weighs 250.0N and there is a 40.0N can of paint 0.50m from the end opposite the painter. How much force is exerted by each stepladder?
I drew a picture to use as a reference. (Please forgive the sloppiness of the picture; it was done in Microsoft Paint, lol.)
This sort of problem is a bit trickier than the ones I'm used to because we're dealing with two supporting objects, and each exerts a different amount of force. My teacher suggested that we take out one of the stepladders in order to focus on calculating the force for one.
So, I placed my pivot point all the way at 0.0m (from the left of the scaffold). I ignored F1 so that I could focus on F2, which is on the opposite side of the pivot. (By the way, the red triangle represents the pivot point.)
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With that in mind, I wanted to find the total force exerted upward and downward because finding F2 and subtracting it from the total force (or Ft for the rest of this problem) should give me F1, no?
I then used this equation.
(850N)(1.2m) + (250N)(1.5m) + (40N)(2.5m) = Ft = F1 + F2.
My result was shockingly an even 1495N of Torque (which I just checked again as I typed this out).
As for F2, I assumed that its torque force x 3m should equal 1495. So, I divided 1495 by 3, and got approx. 498.33N. Subtracting that from the total force should get me F1, but I decided to check the answer by changing the pivot point to the other side and I set up the equation in favor of F1 instead.
So, I put into the calculator the following:
(40N)(.5m) + (250N)(1.5m) + (850N)(1.8m)
That comes out to be 1075, which is strange enough. 1075/3 is approx. 358.33, and that obviously doesn't make 1475 or 1075 when combined with 498.33.
I just realized that this drawing is not very proportional, unless the painter is the size of an infant, lol.
Sorry for the lengthy explanation, but I'd really appreciate if someone could tell me where I went wrong. Thanks in advance!