A gravitron is an amusement park ride, in which people are inside a chamber.
The chamber begins spinning very fast,
and as it does, people stick to the wall!
In this pod, we will analyze the dynamics of the gravitron.
Review of Concepts
This pod is very heavy on dynamics!
You should review many of the previous pods on dynamics, especially
elevator problems 2, static friction problems
and vertical friction problems.
To recap some :
You do not actually feel the force of gravity. You feel the normal force of the ground
pressing on you. In an elevator, you feel lighter and heavier as the elevator moves,
not because the gravity acting on you is changing (it's not),
but because the normal force acting on you is changing.
The normal force is a constraint force. Unlike other forces, that match a particular value
a constraint force will match a value necessary to match a particular acceleration.
Typically, you need to find the net force acting on an object first, and then use this knowledge to find the normal force.
Static friction is also a constraint force. It is a maximum value equal to the normal force
times the coefficient of static friction.
If the force or forces opposing static friction exceed this maximum value, then an object will begin moving.
If they do not, then the object will not move and static friction will have whatever magnitude is
necessary to prevent motion.
Three forces, the normal force, friction, and gravity, act on someone in a gravitron.
In which direction does gravity act?
Which type of friction acts on people in the gravitron, static or kinetic friction? How can you tell?
Which force is the centripetal force? This is the force responsible for making people move in a circle? How can you tell?
Which force prevents people from falling down?
The maximum static friction is much stronger than it would typically be. People are not normally able to stick to walls due to friction alone!
Why is it so strong?
The people are not being pressed into the walls! They only feel like they are. Why?
This is the same concept we used the elevator problems.
According to this website on amusement park rides,
a gravitron spins at 24 rpm (24 revolutions per minute)
(The website also says that it uses "centrifugal force," which is incorrect. It uses centripetal force. See below.)
From the videos, the gravitron appears to have a radius of approximately 4 meters.
Assume a child with a mass of 40 kg is riding the gravtron!
Answer the quantitative questions below.
Whenever using a formula,
please write the formula out in its cannonical form
before plugging values into the formula.
Draw a free-body diagram of the person.
Three forces act on the person.
In a note next to your free-body diagram,
indicate the direction of each force in words.
Determine the angular speed in radians per second of the person.
Please use the conversion factor method.
Determine the linear speed of the person in meters per second.
Determine the person's centripetal acceleration and centripetal force.
Please make sure you refer to formulas appropriately while doing so.
Convert the centripetal acceleration to unit of free-fall acceleration.
(These are called "g"s).
Determine the magnitude of gravity acting on the person.
Determine the magnitude of the normal force acting on the person.
Explain your answer.
Determine the maximum value of static friction acting on the person.
Does the person move? Explain why or why not.
Determine the actual magnitude of friction acting on the person.
Explain how you determined your answer.
Centripetal Force and Centrifugal Force
There are two types of forces associated with circular motion: centripetal force and centrifugal force.
Centripetal force is the name for the force that causes something to move in a circle.
Centrifugal force is a "fictional force".
As explained above, when you are pulled in a circle by the gravitron, you are not being pressed into the walls,
in fact, the wall is pressing into you (this is the normal force).
But, this feels like you are being pressed into the wall by some other force.
That feeling of being pressed on is a "fictional force," called the centrifugal force.
For this class, that is all you need to know about centrifugal force.
If you take a class in Advanced Classical Mechanics in college, you will learn
to use Newton's Laws in a non-inertial reference frame (one that is accelerating)
and model the centrifugal force mathematically.
Many students believe that the reason you feel "pressed into" the wall has to do with Newton's Third Law.
They say that the wall presses you and the feeling of being pressed in is the reaction force.
This is incorrect.
The wall pressing on you creates a sensation that you are being pressed into the wall because
you are in a non-inertial reference frame.
The reaction force to this is you pressing on the wall, which you cannot feel because it is a force on the wall, not you.
This comic is from xkcd.com.
This is one of their most famous comics.
If you don't understand the reference, you should brush up on the classic James Bond movies.