Now we have the centripetal force acting towards the centre of the planet and the gravitational force of attraction that the planet exerts on the mass... again towards the centre of the planet.
Thus, shouldn't it be the sum of the centripetal force on the mass and the gravitational force and not the difference ?
Now we have the centripetal force acting towards the centre of the planet and the gravitational force of attraction that the planet exerts on the mass... again towards the centre of the planet.
Thus, shouldn't it be the sum of the centripetal force on the mass and the gravitational force and not the difference ?
No. For 2 reasons. If your argument was correct, then as the Earth spins faster the acceleration of free fall would get greater. The opposite is the case. If the Earth span fast enough such that the centripetal acceleration was equal to g, then objects on the surface would not appear to fall at all, giving a measured value of zero for g. So clearly from a common sense perspective, it cannot be the sum of the two, but rather the difference. Why? There is only one real physical force acting on the object, that is the gravitational attraction of the Earth. F. This is constant. When the Earth is not spinning, letting the object fall produces an acceleration towards the centre g, due to gravity where F = mg If the object is also moving in a circle it has a centripetal acceleration (towards the centre) a. This acceleration also has to be provided by the force F (This is the only place it can come from). Both accelerations are towards the centre and add. So now F = m(g' +a) where g' is the new acceleration measured due to gravity. F=mg' + ma So mg' = F - ma
Also, apparent weightlessness would be when Gravitational force = centripetal force, right ?
Yes. "Weightlessness" can be a problem because of the different definitions people have of it. In particular how they define "weight" in space. Weightlessness is certainly a "feeling". (Or lack of!) If you are in circular orbit around the Earth you will certainly feel "weightless" and the centripetal force on you will be equal to the gravitational force.
Yes if by g here you mean the "measured" value of g. (What I called g')
Yes. "Weightlessness" can be a problem because of the different definitions people have of it. In particular how they define "weight" in space. Weightlessness is certainly a "feeling". (Or lack of!) If you are in circular orbit around the Earth you will certainly feel "weightless" and the centripetal force on you will be equal to the gravitational force.
So basically the cosmonauts/astronauts in the ISS are experiencing weightlessness because they are at a particular distance from the earth such the gravitational force = centripetal force.....
So basically the cosmonauts/astronauts in the ISS are experiencing weightlessness because they are at a particular distance from the earth such the gravitational force = centripetal force.....
Yes. They are in orbit and the centripetal force on them is equal to the gravitational force on them.