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Unformatted text preview: Plausibility again When you check a result to see whether it makes any sense, one way of doing it is to look at the units and to see if they match. This is such an easy step it has to become automatic — you should look at the units during the process of solving a problem, not just at the end. There are however, other ways to check on the validity of a result. The most important is to see what happens when you vary some of the parameters that the result depends on. There are usually several such variables, masses, angles, distances, speeds, etc. If there is an angle specified in the problem, see what happens as that angle increases or decreases, perhaps as it goes to 0 or 90 degrees, or as it becomes negative. θ m m 1 2 Example: A car is towing a trailer down a hill when suddenly the engine, clutch, and brakes all fail. (The road also becomes covered with ice.) The masses of the car and trailer are m 1 and m 2 respectively, and the road makes an angle θ with the horizontal. Find the acceleration down the hill, a x . Don’t solve it. I’m not interested in the solution for the moment, I just want to look at some proposed answers to see whether they make any sense. (1) a x = ( m 1- m 2 ) g/ ( m 1 + m 2 ). (a) If m 1 = m 2 , this is zero and the car and trailer don’t accelerate downhill. I think you’ll agree that this is implausible; the forces pulling downhill are still there even if the masses are equal. (b) It doesn’t depend on the angle θ . The steeper the road, the bigger the acceleration should be. (c) If m 2 > m 1 this is negative, meaning that the acceleration is back up the hill. You don’t even need brakes. (2) a x = g tan θ . (a) When θ = 0, this is zero, which is all right. On a level surface it should move with constant velocity. It passes this test....
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- Fall '11