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Compare r and l in the diagram to the left.
Any problem on the MCAT involving torque, will be a statics problem. Therefore, use the following three formulas in the order given to solve any MCAT torque problem:
Fupward = Fdownward
Frightward = Fleftward
tclockwise = tcounter-cIockwise
Let’s assume that I’m given the length of the board ‘L’, the distance from the left end of the board to the hanging string ‘x’, the mass of the object ‘m’, and my mass ‘ms’. First, I have confidence that since they asked me, I know that there is a way to answer the problem using only basic science. Second, I draw the board labeling all the force vectors that act directly on it and no others. Third, I choose my system. Since I want the board to be in static equilibrium, I choose the board as my system. Fourth, I choose a formula. Since this is a torque problem (I want to prevent the board from rotating.), I know that I must use the three equations given on the previous page, and use them in the order given. Since there are no horizontal forces, I can throw out the equation with horizontal forces. The equation for the vertical forces leaves me with two unknown variables: d and T.
Now I go to my third equation. But I need to know the torques on my system. In order to find the torques, I must choose a point of rotation. I can choose any point that I want, but, since I need all the forces to act at 90 degrees to their lever arms, I will choose a point on the board. Let’s say that I use the left end of the board as my point of rotation. Now I draw my clockwise and counter-clockwise torques.