美国高考SATII物理专题分析--SAT II Physics Test-Taking Strategies(4)
Slightly Underhanded Way #1: Elimination through Logic
By scanning the possible answer choices, you can see that the answer will begin either with a 4 or a 2.5. There are three options beginning with 4 and only two beginning with 2.5. Odds are, the correct answer begins with 4. The test makers want to give you answer choices that are close to the correct answer so that, even if you’re on the right track, you might still get caught in a miscalculation.
Second, make a rough estimate. At what sorts of distances might a satellite orbit? We can eliminate A immediately: that answer has our satellite orbiting at 4 cm from the center of the Earth! That leaves us with a choice between B and C. Those aren’t bad odds for guessing.
Slightly Underhanded Way #2: Work with the Letters
This is a method for those of you who like manipulating equations. From looking at the answer choices, you know the answer will be in meters. You’ve been given three quantities, one expressed in m/s, one expressed in kg, and one expressed in N·m2/kg2. These are the only three quantities you’ll be asked to draw upon in order to get your answer. Because F = ma, you know you can substitute kg·m/s2 for N. So a quantity expressed in N·m2/kg2 can equally be expressed in m3/kg·s2.
The trick, then, is to combine a quantity expressed in these terms with a quantity expressed in meters per second and a quantity expressed in kilograms, and wind up with a quantity expressed solely in meters. To do that, you need to get rid of the “kg” and the “s” by canceling them out. Start by canceling out the “kg”:
Now you need to cancel out the “s2” in the denominator. Let’s divide by the square of our “m/s” quantity:
There you have it. You didn’t need to use a single formula to get the answer. You just had to be aware of the terms in which your answer needed to be expressed, and manipulate the quantities you were given in the question.
Word to the wise: don’t use this method unless you’re absolutely stumped. It can backfire, and is of course no substitute for careful reasoning.