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Old Aug 16th 2008, 09:30 PM   #1
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Normal reaction

In which of the following situations is the
magnitude of the normal reaction of the
supporting surface always equal to the
weight of the body?

(2) An astronaut in a spacecraft which
performs circular motion around the
earth.

how is that statement (2) wrong?
Is that because there doesn't exist any normal reaction in circular motion?(circular motion round the earth means an
orbital?)
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Old Aug 16th 2008, 10:38 PM   #2
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In orbit around a planet, the centripetal force is provided entirely by gravity. That is,

$\displaystyle \frac{mv^2}{r} = G\frac{M_E m}{r^2}$

The centripetal force acting on the astronaut is therefore NOT provided by the normal reaction force with the spacecraft.

If you draw a diagram with the astronaut inside the spacecraft, the only force on the astronaut is $\displaystyle mg$... because that is all that is required.
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Old Aug 17th 2008, 05:14 PM   #3
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Originally Posted by DivideBy0 View Post
In orbit around a planet, the centripetal force is provided entirely by gravity. That is,

$\displaystyle \frac{mv^2}{r} = G\frac{M_E m}{r^2}$

The centripetal force acting on the astronaut is therefore NOT provided by the normal reaction force with the spacecraft.

If you draw a diagram with the astronaut inside the spacecraft, the only force on the astronaut is $\displaystyle mg$... because that is all that is required.
I'll add what I think was implied here: there will be no normal force on the astronaut because the gravitational force does not press him/her onto one of the surfaces, for the reason given above. This is why it is called "free-fall." The acceleration of the object is the same as the acceleration due to gravity.

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