Читать книгу Physics I For Dummies - Steven Holzner - Страница 30

Want an inside trick that teachers and instructors often use to solve physics problems? Pay attention to the units you’re working with. Considering the thousands of one-on-one problem-solving sessions with students in which we worked on homework problems, this is a trick that instructors use all the time.

As a simple example, say you’re given a distance and a time, and you have to find a speed. You can cut through the wording of the problem immediately because you know that distance (for example, meters) divided by time (for example, seconds) gives you speed (meters/second). Multiplication and division are reflected in the units. So, for example, because a rate like speed is given as a distance divided by a time, the units (in MKS) are meters/second. As another example, a quantity called momentum is given by velocity (meters/second) multiplied by mass (kilograms); it has units of kg · m/s.

As the problems get more complex, however, more items are involved — say, for example, a mass, a distance, a time, and so on. You find yourself glancing over the words of a problem to pick out the numeric values and their units. Have to find an amount of energy? Energy is mass times distance squared over time squared, so if you can identify these items in the question, you know how they’re going to fit into the solution and you won’t get lost in the numbers.

The upshot is that units are your friends. They give you an easy way to make sure you’re headed toward the answer you want. So when you feel too wrapped up in the numbers, check the units to make sure you’re on the right path. But remember: You still need to make sure you’re using the right equations!

So your average speed is 65 miles per hour, which is pretty fast considering that this problem assumes you’ve been driving continuously for three days.

You don’t have to use a conversion factor; if you instinctively know that you need to divide by 24 to convert from miles per day to miles per hour, so much the better. But if you’re ever in doubt, use a conversion factor and write out the calculations, because taking the long road is far better than making a mistake. Far too many people get everything in a problem right except for this kind of simple conversion.