Units
You need to know how to convert miles per hour (mi/hr) to furlongs per fortnight (fur/for), for example. To accomplish this, multiply by 1. (Huh? 1 times a number is that same number. So what good is that?) Well, not just any version of 1. Here are a few useful forms of the number 1: (8 fur/1 mi), (24 hr/1 day), (14 days/1 for). In each of these, the numerator equals the denominator, so these fractions really are equal to the number 1. Try using these to show that 60 mi/hr is 1.6 x 105 fur/for. Do it yourself; don’t click on ????????
You know that a light-year (ly) is a unit of length, don't you? Well, in that spirit here is another unit of length: the beard-second (bs): the change of length of a beard in a second. (If you were the size of a hydrogen atom, a hair would look like a freight train coming out of a tunnel.) Say a beard grows 6 inches per year. Divide by the number of seconds in a year and we get the bs distance in inches, about 2 x 10-7 in.
Force and mass units:
A can of corn is labeled "net wt 11 oz. (311g)." Thus the Jolly Green Giant is saying that ounces and grams are both units of weight. This might drive your physics instructor up the wall, for reasons which you will understand later. In physics, a gram is a mass unit. Weight is a force; mass is not a force, it is a measure of the inertial property of matter. Your physics instructor will probably say that the Jolly G.G. is wrong. Don’t argue. Physics people are usually quite adamant about this.
Here's the deal: Much of physics deals with motion, and the fundamental
principle is Newton's 2nd law, which is that the acceleration of a body is
proportional to the net force acting on it divided by its mass. If we always
worked with this law by proportions, any units would be ok. But we don't. We
rig up these designer units such that a = f/m: the acceleration is equal to the
net force divided by mass. Having done that, we get all messed up if force
units are used for mass or mass units for force. In these motion problems, we
always use kilograms, grams, or slugs for mass. The corresponding force units
are
Gravitational force (weight) is mg, (by applying f=ma) where g is the acceleration of a freely falling body, and experimentally we find that gravity does not care if the body is falling or not- the force is the same. Be sure to put m in kg, g, or slug, and put g = 9.8m/s2 or 980 cm/s2 or 32 ft/s2. Then the force automatically comes out in N, dyne or lb.
You need the gravitational acceleration in the appropriate units: g = 9.8 m/s2 = 980 cm/s2 = 32 ft/s2 = 22 mph/s. Now the solution to the above problem: 2 ton car means that in free fall, the only force acting on it is the 2 tons and its acceleration in free fall is 9.8 m/s2. Now set up a proportion. The ratio of the accelerations is the same as the ratio of forces-- a/g = 0.25/2........so a = 1.2 m/s2 (rounded to 2 digits) when the 0.25 ton is the net force.
The method above works with any units, but the net force must be in the same units as the weight or mass (but do not ever tell your physics instructor that you used a mass unit for force). Suppose a 5 kg wagon has a net force of 2 kgf acting on it. (Force of 2 kgf means a force equal to the weight of a 2 kg mass at sea level. Mention kgf to a physics instructor, and you will be tarred and feathered.) Let us find the acceleration in mph/s: a/g = 2/5....... hence a = 8.8 mph/s.
Incidentally, I hardly ever use this method, because I am a physics text animal. Physics text problems are geared to the conventional method.
I warned you; now your mind is poisoned and your only hope is to go back to my main physics page and study hard. Or if
you came from the
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