2 questions (weightlessness and SHM)

[KatieKangaroo]

the acceleration of free fall of a satellite has a finite value so that an object at this position certainly has weight. making reference to the perception of weight by an observer, explain how astronauts inside this satellite arppear to be weightless. i thought weightlessness was when the gravitational force on a body from two masses 'canceled out' so there was no overall force acting of the body, but don't think this is true in this situation. can anyone explain this to me?

also, find an expression in terms of Xo (amplitude) for the displacement of a particle when its velocity is half its maximum velocity.
i have wXo/2 (w is angular velocity), however i don't know if 'w' should be in the expression if it says in terms of 'Xo'. can anyone suggest another expression?

thanks in advance for your help.

 

[nazgjunk]

As for your weightless astronauts, that is fairly basic. The sattelite (or space station, or whatever) is falling continuously. The astronauts are falling at an equal rate, so that cancels all gravitational forces out. Sort of.

 

[Doc Al]

the acceleration of free fall of a satellite has a finite value so that an object at this position certainly has weight. making reference to the perception of weight by an observer, explain how astronauts inside this satellite arppear to be weightless. i thought weightlessness was when the gravitational force on a body from two masses 'canceled out' so there was no overall force acting of the body, but don't think this is true in this situation. can anyone explain this to me?

The term "weightlessness" can be confusing. You need to distinguish real weight (the gravitational attraction) from apparent weight. The apparent weight of a supported body is the force that the body exerts on its support. "Weightlessness" means that the apparent weight is zero, not the real weight. (So your thought that weightlessness means that the net gravitational force is zero is not correct.)

This makes sense when you think about what causes us to feel that we have weight. We can't sense gravity directly; instead we feel the forces exerted on us by whatever is supported us: the floor, the chair, etc. The reason why astronauts in orbit feel weightless is that the satellite and the astronauts are both falling together--the satellite doesn't have to support the astronaut, since both are falling about the earth. Another easy way to feel weightless (at least briefly) is to jump out the window! Take away the supporting floor and your apparent weight goes to zero. (Obviously your real weight--the gravitational pull of the earth--hasn't gone to zero!)

also, find an expression in terms of Xo (amplitude) for the displacement of a particle when its velocity is half its maximum velocity.
i have wXo/2 (w is angular velocity), however i don't know if 'w' should be in the expression if it says in terms of 'Xo'. can anyone suggest another expression?

Write the expressions for displacement and velocity and compare them. (Hint: The expressions will have some trig function.)

 

[daniel_i_l]

They could also appear to be weightless if the are orbiting around the earth. This would happen when the centripetal force equaled the gravitational force.

 

[KatieKangaroo]

thank you, so is it that the satellite is exerting no reaction force on the astronaut as they are both falling at the same rate about earth?

and for my 2nd question, there are no equations in my notes on SHM involving trigonometric quantities I am pretty sure my teacher would have told us if we needed to know them.
the only equations we have are the ones for velocity and acceleration, none for displacement. so is my expression the only one i can get?

 

[Doc Al]

thank you, so is it that the satellite is exerting no reaction force on the astronaut as they are both falling at the same rate about earth?

Right. They exert no contact force on each other.

Just like in a elevator if the cable breaks--both you and the elevator would fall together, so you would exert no force on the floor of the elevator (and vice versa) and thus you would be "weightless".

and for my 2nd question, there are no equations in my notes on SHM involving trigonometric quantities I am pretty sure my teacher would have told us if we needed to know them.

I don't see how you can solve this problem without such equations. Here they are: http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html#c2