dpy:
That is ubelievably cool of you to share that. I'm going to add a slightly different perspective on the answers, which may or may not help.
75.) The projectile is being propelled by force due to the magnetic field strength, which ultimately depends on current. The question involves maintianing the same kinetic energy (exit speed) without spending the same amount of input energy. To solve this, we can focus on the areas where energy is lost. In this case, friction and electrical resistance are the two prime candidates. From here I agree with dpy's reply (with a slight adaptation of choice (c)):
For (a), lowering the current would lower power consumption, but it would also lower exit speed, so that can't be it.
For (b), lowering the rail resistivity means that it would take less energy (which translates to power) to achieve the same amount of current. With the same amount of current, you have the same exit speed. so the answer is (b).
For (c), lowering cross sectional area is equivalent to increasing resistivity (think of a hallway becoming more narrow), which is opposite to choice B and can't be the answer based on the above logic.
For (d), reducing mag. field strength would again lower power consumption like (a), but it would also lower exit speed, so that can't be it.
76.) given F=ma, force = 3.0, mass = 0.06. you find that a=50m/sec2. plug that into the formula: x= 0.5at2. solve for t
77.) while lengthening the rails increases its electrical resistance and the time over which the projectile is being exposed to friction, the more important concept here is time during which an acceleration is applied. Longer rails allow the projectile to be accelrated over a greater distance, and thus to a greater speed. While choice (a) may be a true statement in and of itself, it would explain a slower speed, so choice (a) is eliminated. Choices (b) and (c) both would explain and increase in speed, if they were true. Neither is applicable in this case, because increasing the rail length would not increase the magnetic field strength, which in turn would not increase the force applied to the projectile.
78.) from the chart based on the first 2 experiments, you see 1.5x the currrent is equivalent to 1.5x the speed. this indicates that the relationship between current and speed is directly proportional. so decreasing current by 2x will decrease speed by 2 times EXCELLENT EXPLANATION Let me add the units/equation approach too. It is given in the passage that the force is proportional to current squared. It is also true that the kinetic energy is equal to force x distance, so ultimately, the force is proportional to the exit speed squared. Because for is proportional to both current squared and velocity squared, the current and velocity must be directly proportional. Choices (c) and (d) should have been eliminated immediately, because increasing current is going to increase the speed. The question is simply whether it is directly or whether it has a square root relationship. Table or equation, both get you the answer.
79.) this requires the same formula as #76. h = 0.5at2. a is 9.8, so 0.5 x 9.8 yields 4.9. This eliminates choices (c) and (d). Squaring the time yields 10-4, so choice A is best.
