ETS2017 Problem 1

[GeorgesOatesLarsen]

Inspiration:

A net force F_A acts on object A, and a net force F_B acts on object B. The mass of object B is twice the mass of object A, and the acceleration of object B is twice that of object A. Which of the following is true of the forces F_A and F_B?

A: F_B = 1/4 F_A B: F_B = 1/2 F_A C: F_B = F_A D: F_B = 2F_A E: F_B = 4F_B

[GeorgesOatesLarsen]

Proposed implementation:

Stick with two objects, two forces, F_A, F_B, A, B. Pick different integer values for the ratio of masses and ratio of accelerations. For generating problems: randomize F_B = or F_A = order. Always include F_B = F_A. Pick random ratio R such that the correct ratio (C) satisfies C = R^n such that n = -3, -2, - 1, 0, 1, 2, or 3. Pick an assortment of different powers of this ratio as possible false answers. Guarantee that the correct answer is among them.

[GeorgesOatesLarsen]

Well, I ended up going absolutely berserk on this. The order of all variables, and which of the three variables in F=ma we are solving for are all randomized completely. Answers are randomly generated from the prime factorizations of the ratios given in the problem. (This ended up being more elegant than the least root idea above). The ratio 1 is guaranteed to be included, and both fake and real answers are generated in inverse pairs.

[GeorgesOatesLarsen]

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