Can Static Friction Keep a Child Safe on a Rotating Cone Ride?

[nate9519]

Why is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, he slips out of his seat and climbs to the top of the ride's structure which is shaped like a cone with its axis vertical and its sloped sides making an angle of 20 degrees with the horizontal. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point 5.32 m down the sloped side from the center of the cone. The coefficient of static friction between the boy and the cone is .7. The ride operater does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the boy rotates in a circular path at a speed of 3.75 m/s.

I have no idea where to start here. My teacher doesn't even go over this . How do I solve this and with what equations

 

[Matterwave]

I am having some trouble picturing this in my mind. Have you drawn out what the situation looks like? Hopefully the problem came with an illustration of some sort to describe the situation?

 

[nate9519]

There is a picture in my book. The child is sitting on the surface of a cone. he is 5.32 m from the center and the angle he is sitting at is 20 degrees. I think they want me to prove that given these conditions the child would actually fall off. kinda like the type problem where they ask how fast of car can negotiate a banked curve without sliding. but I have no idea how to work those kinds of problems because my teacher sucks

 

[phinds]

It still is completely unclear just what this looks like, YOU may be clear on it but your words are not making it clear to us. Present a sketch.

Also, your teacher may well suck but if you go through life not learning anything because of your teachers ...

 

[nate9519]

heres the picture.

http://books.google.com/books?id=FR...=onepage&q=serway jewett figure p6.46&f=false

 

[Matterwave]

Oh ok, that makes thing a lot clearer. Your inclination is correct. You should show that the force of friction is not enough to keep the child on top of the cone.

To do that, balance forces. If you are in the frame of the rotating child, there are several forces you need to look at:

1. Frictional force
2. Gravitational force
3. Normal force
4. Centrifugal force (due to the frame not being inertial)

Show that the forces do not balance.

If you want to work in the inertial, non-rotating frame, then you must consider the following 3 forces:

1. Frictional force
2. Gravitational force
3. Normal force

And then you must show that these forces do not combine to give you a sufficient centripetal force to keep the child in a circular trajectory at that speed.

 

[nate9519]

Ok. I know how to calculate the forces but I don't know what you mean by showing the forces don't balance

 

[nate9519]

Im guessing I should show that the centrifugal force is greater than the friction force. is that right?

 

[nate9519]

Im confused now. how can I find any force because the problem didn't give me the childs mass

 

[Matterwave]

You shouldn't need the mass to look at the relative sizes of the forces, just keep it as "m" for now.

What I mean by "show that the forces don't balance" is that if you can show that the forces can't all add up to 0, then the child will not be able to stay put where he is on the cone.