Calculate Centripital Force for Circular Motion

[pb23me]

How do you calculate how much frictional force is required or centripetal force to keep an object in circular motion.

 

[einsteinoid]

Centripetal force is calculated with the following formula:

[PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP13719ch7a8fegb1ibfe0000305fb7476a23789e?MSPStoreType=image/gif&s=40&w=168&h=181

 

[einsteinoid]

I should also mention, "centripetal" simply means "center seeking" and applies to the force or acceleration directed towards the center of a circle or arc as an object moves around it in uniform circular motion.

The centripetal force could be actualized in many ways, such as in the form of friction (between the tires/road of a car bending a turn), tension (on the string of a yo-yo being spun in a circle), gravity (between a satellite/planet during orbit), etc.

 

[pb23me]

Thanx. But how do I know if it is enough to keep it in a circle. I've worked a problem out have all the values but don't know how much force is enough. The problem I have is asking if the frictional force is enough to keep going in circular motion. I've calculated all tha values just not sure how much force is enough...

 

[einsteinoid]

Well, if the angle between the normal force and the surface upon which the body is traveling is 90 degrees, then I think all you would need to do is make sure that the magnitude of centripetal force doesn't exceed the magnitude of maximum static force between the body/surface. If it does, that means that the static friction would break, turning into kinetic friction, and send the object out of orbit.

Recall that in this scenario,

Max Static Friction Force = (coefficient of static friction)*(Normal Force)

Anybody want to check my logic?

 

[pb23me]

That sounds right however I get confused as to which direction the forces are in? It seems as though friction and centripetal frce are in the same direction?

 

[pb23me]

If that's so than how does one oppose the other?

 

[einsteinoid]

Well, in the scenario you're describing, the frictional force is the centripetal force.

This may help:

 

[einsteinoid]

If that's so than how does one oppose the other?

They aren't opposing one another. Let's stick to this car example:

You would first find the car's maximum static frictional force (the normal force * the static friction coefficient). This value will tell you the maximum amount of frictional force between the tires and the road that can be applied toward the center of the circle before the tires begin to slip.

To find out if this is enough centripetal force to in fact keep the car from falling out of orbit at speed V, plug V into the centripetal force formula (m(V^2/r)) and see if the maximum frictional force value is >= to amount of centripetal force needed.

If max_static_friction >= required_centripetal_force, the car will remain in uniform circular motion. Otherwise, the car will fall out of orbit.

I hope I'm explaining this correctly.

 

[pb23me]

Thanx that sounds good...:)

 

[2rashmi1993]

hey guys m a bit confused!
maximum static friction means limiting friction...right?

 

[einsteinoid]

My peers and I don't generally use the phrase "limiting friction" so I can't be 100% sure that I know what you mean, but if by "limiting friction" you mean the maximum amount of frictional force that a body/surface allows before they begin to slip, then yes, "maximum static friction means limiting friction."

There are really only two types of friction:

Static Friction: The frictional force between an object and its surface when they are both at rest relative to one another--this is the friction that allows you to stand on a shingled roof without sliding down it even though it is at a steep angle. It exists between the coarse shingles and the rubber soles of your shoes.

Kinetic Friction: This is the friction that exists between an object and its surface when they are moving relative to one another. This would be the friction at work if the aforementioned roof was wet and you began to slip. The cold-welding taking place between the object/surface is more or less the same phenomenon at an atomic level as that which is taking place under static friction but we call it kinetic[i/] because in this case it isn't strong enough to keep the body motionless relative to the surface. Rather the cold-weld between the objects is being repeatedly broken and rewelded, which will resist your sliding (slow you down) but it isn't strong enough to stop you.

So don't horse around on wet shingled rooftops.

Sometimes you hear the phrase "rolling friction" as in the resistance on a ball as it rolls across the floor, but as I understand it, rolling friction is more or less a special case of the above two phenomenas.