kuruman said:Because you are looking for the minimum coefficient of static friction, i.e. the person is just on the verge of sliding.
No. There is a mathematical formulation based on a physical event that can be described in plain English. The event is that the person is about to start sliding in which case the force of static friction has reached its maximum value which is proportional to the normal force, the constant of proportionality being the coefficient of static friction. All that wording can be formulated in shorthand mathematical notation as ##f_s^{max}=\mu_sN##. It's a much more compact way of saying the same thing and that's why we use math when we do physics.bonbon1 said:ok thank you. Is there also a mathematical explanation for that?
and if there is a situation in which a person is in a rotor and the angular velocity changes (and then as a result, the normal force changes) and the person is still stucked to the wall, is it affect the fs or just the fsmax?kuruman said:No. There is a mathematical formulation based on a physical event that can be described in plain English. The event is that the person is about to start sliding in which case the force of static friction has reached its maximum value which is proportional to the normal force, the constant of proportionality being the coefficient of static friction. All that wording can be formulated in shorthand mathematical notation as ##f_s^{max}=\mu_sN##. It's a much more compact way of saying the same thing and that's why we use math when we do physics.
To be clear, we have the person in a rotor and they are just on the verge of sliding down. The force of static friction is exactly equal to the maximum force of static friction. But now the rotor speeds up. The normal force increases.bonbon1 said:and if there is a situation in which a person is in a rotor and the angular velocity changes (and then as a result, the normal force changes) and the person is still stucked to the wall, is it affect the fs or just the fsmax?
Thank you! Now I understandjbriggs444 said:To be clear, we have the person in a rotor and they are just on the verge of sliding down. The force of static friction is exactly equal to the maximum force of static friction. But now the rotor speeds up. The normal force increases.
1. Because the normal force has increased, the maximum possible force from static friction has increased.
2. If it only takes a frictional force of magnitude mg to support the person, it still only takes that much frictional force no matter how fast the rotor spins. The actual frictional force will be only as much as is required, not as much as could possibly be provided.
If, on the other hand the rotor slows down then the normal force decreases.
1. Because the normal force has decreased, the maximum possible force from static friction has decreased.
2. If it takes a frictional force of magnitude mg to support the person and the maximum force of static friction is less than that then the actual force from static friction will be equal to the maximum and the person is doomed to slip downward.