Explaining How a Rotating Cylindrical Spaceship Simulates Gravity

[Calpalned]

Homework Statement

One way to simulate gravity is to shape a spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface. Explain how this simulates gravity.

Homework Equations

$F = m/v^2$

The Attempt at a Solution

My textbook's solution guide says that "For objects (including astronauts) on the inner surface of the cylinder, the normal force provides a centripetal force which points inward toward the center of the cylinder. This normal force simulates the normal force we feel when on the surface of Earth." On the Earth's surface, I know that the normal force push up from the ground (and counter acts gravity so that we don't fall through the Earth). In the spaceship's artificial gravity, the normal force has no gravitational force to counteract, so why doesn't the normal force push the astronauts up and away from the surface (and towards the center of rotation). Thank you so much.

 

[Fyj]

The thing is, your tangential velocity is continuously pushing you against the side of the wall. So the normal force is what is preventing you from going through the wall. However, unlike gravity, the normal force doesn't give you kinetic energy, it exists only when you are against the wall and its only big enough to stop you going through (ie to counter the force that you are applying on it.) As soon as you are off the wall, it isn't there.

It doesn't do any 'work' on you. The reason it feels like gravity is because you are used to having a force against your feet all the time. Your brain has been accustomed to that feeling and it knows that feeling only exists because gravity is pushing on you. However when you are not on earth, and you still have the feeling of something pushing your feet, even if there isn't anything to push you down, your brain will tell you otherwise. (I guess)
-Hope this helps.

 

[Phynos]

Imagine taking a sharp turn in a car. The car seat and door exert a force on you that causes you to change direction with the car. If you were to continue turning and drive in circles, you would experience a continuous force from the car seat and door. This force is preventing you from following a strait path through space.

it exists only when you are against the wall and its only big enough to stop you going through (ie to counter the force that you are applying on it.) As soon as you are off the wall, it isn't there.

If you were standing on that wall, and you were to jump, you would 'fall' towards the wall similar to how you do on here on Earth. To float there freely you would have to cancel out the velocity you have with respect to the axis of rotation on which the ship is spinning.

 

[tms]

Homework Equations

$F = m/v^2$

This equation is not correct. You can see that by checking the dimensions, which should be $M L / T^2$.