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hanggingou4315
Joined: 21 Feb 2010
Posts: 4
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 Posted: Fri May 28, 2010 9:19 pm Post subject: question 46 |
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| why are we using this equation (g=v2/r) for weightlessness? are we assuming that the only acceleration that acts on the plane is the one that pulls it inward? |
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mcat_premed3832
Joined: 19 Oct 2006
Posts: 428
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| Posted: Fri May 28, 2010 11:28 pm Post subject: |
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| Quote: | | are we assuming that the only acceleration that acts on the plane is the one that pulls it inward? |
No, that is not the assumption. In fact, there are 2 forces of acceleration counterbalancing each other.
| Quote: | | why are we using this equation (g=v2/r) for weightlessness? |
Because the 2 forces are: (1) the weight of the plane Mg directed downwards and (2) the centrifugal force Mv2/r directed upwards (away from the center of the earth).
Thus the forces equate for weightlessness in circular motion:
Mg = Mv2/r
g = v2/r
Here is some general information on the topic of weightlessness adapted from http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html
As you know, the weight of a person is given by mg. One's "perceived weight" or "effective weight" comes from the fact that you are supported by the floor, a chair, etc. If all support is removed suddenly and you begin to fall freely, you would suddenly feel "weightless" - so weightlessness refers to a state of being in free fall in which there is no perceived support. The state of weightlessness can be achieved in many ways:
Going over the top of a roller coaster
Being in an elevator and the cable breaks (here force normal N = 0)
Having an airplane accelerate upward quickly and then suddenly make a dive (approximated by flying a plane in a circular arc as in this problem)
Being in orbit around a planet (i.e. Earth) |
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