Can there be two normal forces acting on one body?

[flyingpig]

Homework Statement

A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is μ; therefore, the speed v of the block decreases. In terms of m, R. μ, and v, find expressions for each of the following.

[PLAIN]http://img202.imageshack.us/img202/8223/ropic.jpg

The Attempt at a Solution

The solution says

The frictional force f acting on the block is

f = µN

The normal force is the only radial force acting on the mass

N = ma_c = mv²/r

f = µm²/r

What I don't understand is how come it is the normal force that is counteracting the centripetal force? I thought there is friction

Here is a freebody diagram of what I THINK is happening.

[PLAIN]http://img42.imageshack.us/img42/5150/freebody.jpg

I used Paint...so lol

 

[rock.freak667]

The block is on the wall and not touching the ground, the natural tendency is for that block to move downwards due to gravity right? So in the vertical direction, there will be friction and the weight acting.

The block is in contact with the curved wall, so the normal force will point in the direction towards the center of rotation.

 

[flyingpig]

This is just out of blue, and is sort of related to the question

If I attach a hotwheel car to a rod and the rod is attached to a pivot and is free to rotate 360, will there be a normal force on the car? If I make it so that the car is in contact with the vertical wall.

 

[flyingpig]

The block is on the wall and not touching the ground, the natural tendency is for that block to move downwards due to gravity right? So in the vertical direction, there will be friction and the weight acting.

The block is in contact with the curved wall, so the normal force will point in the direction towards the center of rotation.

But it says it is sliding, doesn't that mean it is still in contact with the ground?

 

[rock.freak667]

But it says it is sliding, doesn't that mean it is still in contact with the ground?

Oh sorry, I misinterpreted the diagram for those spinning cylinder rides on a carnival.

But yes, it is contact with the ground so there is a normal force between the block and the ground.


It is also in contact with the wall, so there is another normal force between the wall and the block.

 

[flyingpig]

Oh sorry, I misinterpreted the diagram for those spinning cylinder rides on a carnival.

But yes, it is contact with the ground so there is a normal force between the block and the ground.


It is also in contact with the wall, so there is another normal force between the wall and the block.

[PLAIN]http://img217.imageshack.us/img217/5673/24449493.jpg

Here is what confuses me, why does it say the normal force is the only radial force? Isn't the centripetal acceleration is also pulling it inwards?

 

[rock.freak667]

[PLAIN]http://img217.imageshack.us/img217/5673/24449493.jpg

Here is what confuses me, why does it say the normal force is the only radial force? Isn't the centripetal acceleration is also pulling it inwards?

Remember, the centripetal force is a resultant of all the forces point towards the center of rotation.

Only the normal reaction between the block and the wall is pointing towards the center of rotation which means that the normal reaction = centripetal force.

In your free-body diagram, you should not have the centripetal force showing as an independent force.

 

[flyingpig]

Does that mean you can't model centripetal force with vectors? I am confused I thought F = ma and that Force is proportional to the changes in acceleration, that is the centripetal acceleration (which is a vector)?

 

[rock.freak667]

Does that mean you can't model centripetal force with vectors? I am confused I thought F = ma and that Force is proportional to the changes in acceleration, that is the centripetal acceleration (which is a vector)?

I mean that in your diagram, you have it as individual force such that the vector sum of F_c+N would give something when in fact, it is just N = F_c.


What I am saying is that in your FBD, is that you need to take out F_c as it a resultant force.

 

[flyingpig]

I mean that in your diagram, you have it as individual force such that the vector sum of F_c+N would give something when in fact, it is just N = F_c.


What I am saying is that in your FBD, is that you need to take out F_c as it a resultant force.

Yeah I had F_c + N because they are both acting in the same direction. That's why I asked if it can be a vector too.

 

[rock.freak667]

Yeah I had F_c + N because they are both acting in the same direction. That's why I asked if it can be a vector too.

They are both vectors, but you are treating F_c as if it does not depend on anything, when it depends on the normal force.

 

[Redbelly98]

A freebody diagram should only show forces that have some physical cause: gravity, friction, normal force, rope or string tension, etc.

Centripetal force is not a force that is physically caused by anything; it is simply equal to the net force, in the radial direction, for any object that moves in a circle.

We know that the centripetal force is equal to mv²/r, because we know that the centripetal acceleration is v²/r. Then we can equate mv²/r with ∑F (in radial direction) to set up an equation to (hopefully) help solve the problem.

Hope that helps!

 

[flyingpig]

If it is not real does that mean it is fictitious like centrifuge force? I am confused

 

[flyingpig]

A freebody diagram should only show forces that have some physical cause: gravity, friction, normal force, rope or string tension, etc.

Centripetal force is not a force that is physically caused by anything; it is simply equal to the net force, in the radial direction, for any object that moves in a circle.

We know that the centripetal force is equal to mv²/r, because we know that the centripetal acceleration is v²/r. Then we can equate mv²/r with ∑F (in radial direction) to set up an equation to (hopefully) help solve the problem.

Hope that helps!

But I thought centripetal acceleration is an acceleration that sucks an object inward for an acceleration. Which means centripetal force is also a force that sucks in the motion

 

[flyingpig]

Am I wrong?

 

[Redbelly98]

It's best to think of the centripetal force as the net result or vector sum of the forces (like gravity, normal force, rope tension). It's only called a centripetal force if the object happens to move in a circle. Again, we can't identify a physical cause for centripetal force the way we can for gravity, normal forces, or rope tension.

A simpler example is to imagine a ball attached to a rope, moving in a circle, in the absence of gravity. The only force acting on the ball is the rope tension. Since the rope tension makes the ball move in a circle, it is a centripetal force. That is, the centripetal force F_c is due to the rope tension T, so F_c=T.

 

[flyingpig]

It's best to think of the centripetal force as the net result or vector sum of the forces (like gravity, normal force, rope tension). It's only called a centripetal force if the object happens to move in a circle. Again, we can't identify a physical cause for centripetal force the way we can for gravity, normal forces, or rope tension.

A simpler example is to imagine a ball attached to a rope, moving in a circle, in the absence of gravity. The only force acting on the ball is the rope tension. Since the rope tension makes the ball move in a circle, it is a centripetal force. That is, the centripetal force F_c is due to the rope tension T, so F_c=T.

Do you mean

[PLAIN]http://img843.imageshack.us/img843/1692/70802958.jpg

Then this also brings me to another question, does the centripetal force always have to be perpendicular to the rotation axis?

 

[Redbelly98]

Do you mean

[PLAIN]http://img843.imageshack.us/img843/1692/70802958.jpg

Yes, that's the idea.

Then this also brings me to another question, does the centripetal force always have to be perpendicular to the rotation axis?

Yes, the centripetal force is directed towards the center of the circle.

 

[flyingpig]

OKay now that is out of the way, the nature of the thread still needs to be answered.

Why do you all still say centripetal force is not real? My book says centrifuge force is not real, but nothing on centripetal force.

You say it is non-physical, I don't understand. I came up with this idea on the blue, if a force cannot be measured with a spring scale, then it is not a force?

If it is indeed a fictitious force, then how can it have a mathematical model?

 

[Redbelly98]

The centripetal force is real, and it is due to things like gravity, normal force, or rope tension, etc.

When you do this:

Yeah I had F_c + N because they are both acting in the same direction.

You are counting the same force twice there, since F_c and N are one and the same in this example. The net force is just N, or equivalently F_c; it is not N + F_c.