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
Elizabeth used correct logic and was able to do the problem "in her head" by reducing the problem to its essentials. Zero net torque requires equal and opposite torques on opposote sides.
The reasoning of both is fundamentally the same.
how
both are the same
What is answers for this question.
1. Both Elizabeth and Jill's reasoning are valid. They arrived at the same answer, which suggests that their approaches were correct. However, they utilized different reasoning methods to solve the problem.
Elizabeth used a logical deduction by considering the weight difference between the sister and the little brother. She assumed that the little brother's lighter weight had to be compensated for by sitting twice as far from the pivot. This approach makes intuitive sense and provides the correct answer in this specific scenario.
On the other hand, Jill used the formula for torque, which is a mathematical approach to solving the problem. She considered the gravitational forces acting on the see-saw due to the weights of the children and utilized the equation F1r1 = F2r2 to set up the balance of torques. By plugging in the given values, she derived the equation to solve for r2 and obtained the same answer as Elizabeth.
Both reasoning methods yielded the same result, indicating that they are both valid approaches. Elizabeth's reasoning appeals to common sense and intuitive understanding of the situation, while Jill's reasoning utilizes mathematical principles and equations.
2. Elizabeth and Jill's reasoning can be considered fundamentally different. Elizabeth relied on logical deduction and intuitive understanding of the weight and balance concepts involved. She formulated a relationship between the little brother's weight and his sitting position to maintain balance. This reasoning does not involve numerical calculations or the application of formulas.
On the other hand, Jill's reasoning was based on the application of a specific formula for torque and the use of mathematical equations. She utilized the given values of force and distance to set up an equation and solved for the unknown variable. Her reasoning involved mathematical manipulation and the application of a physics formula.
While both approaches led to the same answer, the methods used were distinct. Elizabeth's reasoning can be considered more qualitative and conceptual, while Jill's reasoning is quantitative and formula-based. Therefore, their reasoning can be categorized as a mix of fundamentally different approaches.