March 29, 2017

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Here’s how two different students approached part A.

Elizabeth: Since the little brother is half as heavy as her sister, he must sit twice as far from the pivot in order to “compensate” for his lower weight—6 feet instead of 3 feet.

Jill: I used the formula for torque, Torque = Fr, where F is force and r is distance from the pivot. Here, the
relevant forces acting on the see-saw are gravitational, the weights of the children: F1 = 60 pounds and
F2 = 30 pounds. The big sister sits r1 = 3 feet from the pivot, and we’re solving for r2. The torques
must balance: F1r1 = F2r2. I plugged in the numbers to get (60 pounds)*(3 feet) = (30 pounds) * r2, and
solved for r2 to get 6 feet.

1. The two students got the same answer. Did one (or both) of them get lucky, or are both kinds of
reasoning valid? Explain.

2. Are Jill and Elizabeth’s reasoning fundamentally the same, fundamentally different, or a mix of those two extremes? Explain

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