Weightlessness

December 23, 2007 | By admin In Mcat Exam | Comments(0)
Shrike: Weight is defined as the force of gravity on an object, and always equals mg. In popular parlance, an object is "weightless" when its apparent weight is zero. Apparent weight is just what a scale would read if the object were sitting on it; i.e., it’s the force exterted on it, in an upward direction, by what it’s resting on (or, occasionally, hanging from). An object is therefore weightless when the floor et al is not pushing it up; in other words, when it’s in free fall.

Another example of apperent weight being zero is a neutrally buoyant object submerged in a fluid, or any object floating in equilibrium on the surface of the fluid. Because the buoyant force balances the force of gravity, no more force is needed to support it and a scale under the object would read zero.

Xanthines: Weight is the force due to gravity, which on earth is mg. An object has no weight when there is no acceleration due to gravity. Alternatively, I guess an object could be considered weightless if something cancels out mg, like objects with densities identical to water that are submerged in water. This is why NASA conducts some of its training underwater and why senior citizens excercise in water. They don’t have to deal with the forces being exerted by that pesky gravity.

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What are the kinds of waves, and in what materials do they appear?

December 22, 2007 | By admin In Mcat Exam | Comments(0)

There are two kinds of waves, longitudinal and transverse. Longitudinal waves are waves that vibrate in the same direction that they travel (propagate). Transverse waves vibrate across their direction of travel.

Every physical material — solid, liquid, and gas — can conduct a longitudinal wave — that’s a compression wave, also known as sound (though often we call it sound only if it’s of a frequency near the range of human hearing) — in any direction. There are no longitudinal waves other than compression, i.e., sound, waves that matter on the MCAT.

Compression waves propagate in all directions through their media (i.e., sound diffuses).

Every physical material with a surface (i.e., every solid object, and every liquid/gas and liquid/liquid interface) can conduct a transverse wave in any direction along the surface, with displacement normal to the surface. Note that a thin wire is a special case, essentially a surface with normals pointing out of the wire in all directions, so it can vibrate in any direction perpendicular to it.

Though there have been MCAT passages with waves traveling in multiple directions on surfaces, these were unusual; in almost all problems, there is only one wave. Waves on surfaces, and especially liquid surfaces, can be very complex to model, so they don’t appear very often.

Other waves are possible, including transverse waves far from the surface of objects. Though these waves might appear, their precise properties shouldn’t matter on the MCAT.

In addition to waves in substances, light can be modeled as a transverse wave. Never mind what it’s a wave of.

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What are the conservation laws, and when do they apply?

December 21, 2007 | By admin In Mcat Exam | Comments(0)
  • In theory, momentum is always conserved, regardless of what happens. On MCAT problems, momentum is conserved if the system, i.e., all the objects that are mentioned, includes everything that exerts force on anything else. The most common trouble here is the Earth — if gravity causes objects to fall, but the Earth is not mentioned in the problem, then AAMC would claim, confusingly, that momentum is not conserved.

    Momentum and its conservation is usually mentioned in collision problems.

  • Everything listed above for momentum is also true of angular momentum: it’s always conserved in theory, but might not be according to AAMC if something is missing from the system. Angular momentum appears infrequently on the MCAT.
  • Energy is not conserved, except in special cases: it is conserved during perfectly elastic collisions (you know that it’s perfectly elastic because they tell you so), and when the only forces involved in a problem are "conservative."

    Conservative forces on the MCAT are: gravity, electrostatic, springs; also, any physical pushing or pulling that doesn’t involve dynamic friction. Dynamic friction, electrical resistance, radioactive decay, and any collision that is not perfectly elastic, are not conservative. If in doubt, it’s not.

  • Mass is conserved on the MCAT, except possibly in radioactive decay. If anyone has seen an exception to this principle in AAMC materials or tests, please advise.
  • Net charge is conserved, always.
  • The number of baryons (for us, protons and neutrons) is conserved, always. On the MCAT, we can just add them because we don’t encounter antiprotons.

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How do I solve MCAT optics problems?

December 20, 2007 | By admin In Mcat Exam | Comments(0)

The easiest way to solve MCAT optics problems — all of them — is to know three equations (which must be memorized):

  • 1/o + 1/i = 1/f
  • m = -i/o
  • p = 1/f

… nine easy definitions (try them; you already know most of them):

  • o = distance (from the lens/mirror) to the object
  • i = distance to the image
  • f = focal length (sometimes hiding in the problem, as Radius of Curvature/2)
  • m = magnification (which, oddly, includes being right side up and upside down)
  • p = power
  • converging = bringing together
  • diverging = spreading apart
  • real = light goes there
  • virtual = light does not go there

… three things you already know about the world, for translating MCAT problems and figures into the proper form:

  • magnifying glasses, which are convex, make light come together
  • mirrors are different from lenses (they have the opposite effect on light)
  • concave is different from convex (it has the opposite effect on light)

… four easy, but perhaps novel, principles for setting up and interpreting the equations, based on the idea that positive is good:

  • object o –> always + (because it’s always real, and real is good)
  • image i –> real is + (because real is good)
  • focal length f –> converging is + (because it’s good to come together)
  • magnification m –> upright is + (because it’s good to be upright)

… and one sensible method:

  • to find the effect of mutiple lenses or mirrors, add their powers to get the power of the combination.

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