# Centripetal Force and a Word Problem

1. Nov 6, 2005

### briguy2188

One question says "It has been said that centripetal force is is not a unique force. Outline what a centripetal force is as well as three (explained) examples of what is meant by this statement.(5 marks)" Here is my theory:
Newtons first law states that an object in motion stays in motion unless an unbalanced net force acts upon this object, casuing it to change direction. Centripetal force is that force. Examples of CP include friction, tension, and gravity. I was also thinking normal force?? Anyway, that is all ive come up with so far...i dont know how exactly to explain those examples but does anyone have any suggestions as to what it means by saying "is not a unique force?"

And here is a word problem that i cant crack:

A skier skiing downhill reaches the bottom of a hollow with a velocity of 23.4 m/s and then coasts up a hill with a 31.5 degree slope. How far up the hill will she travel before she stops if the coefficient of friction is 0.14? (10 marks)

Ok, so far all i have done is drawn a FBD, and found out the X and Y components of the skier. Dont know if that is right, but i ended up with a weird equation: Fnet = Ff = Fg sin(theta) and Fn = Fg cos(theta)
therefore Ff = u(Fgcostheta)
*the small case letters in front of the F's are subscripts for friction, gravity, and normal force, and the u is coefficient of friction

Thanks for the help.

2. Nov 6, 2005

### bijanv

from what I know... a centripetal force is not a force by itself (and therefore it is not recognized as a force in FBD diagrams) ... Its more like a behaviour that we call it centripetal but it is actually caused by the forces u mentioned (friction, tension, etc.) normal force can also be a centripetal force

3. Nov 6, 2005

### kp

are you sure about those Cp examples?

for the skier girl, thing about conservation of energy equations, you know...P.E. = K.E. just don't forget about friction.

4. Nov 6, 2005

### whozum

Your definition of centripetal force is incorrect. A NET force can be centripetal, and what it means is basically that the force always points towards to a center of some kind of ellipse. The particle therefore travels in elliptic motion.

For your word problem, use an energy method and realize that any change in the energy of the system will be lost to friction. Set up an equation that gives the total change of energy (at the final and initial points) and then set it equal to the change in energy (which is lsot to friction).

$$\Delta E = E_f - Ei = W_{friction}$$

You can find E_i and W_f from the given information.

5. Nov 6, 2005

### lightgrav

centripetal is a direction perpendicular to the velocity.
Centripetal acceleration is that component of the acceleration vector.
Of course, the sum of Force vector components cause that m a_centrip.

Do you know Energy approach? too bad...

Otherwise, (1) fix this : Fnet = Ff + Fg sin(theta) .
Now, compute the expected acceleration, and use it to find time_stop.
How far to go with average speed = 1/2 starting speed, for this duration?

6. Nov 6, 2005

### briguy2188

is CF the centre seeking force of an object, causing it to change its direction?

7. Nov 6, 2005

### whozum

Any force can change an objects direction. A centripetal force is a specific case where the force changes the objects direction so that it has an elliptic motion.

8. Nov 6, 2005

### Cyrus

Any force can change an objects direction. A centripetal force is a specific case where the force changes the objects direction so that it has an elliptic motion.

well, any time there is a curved motion there is a component of centripital acceleration, thus centripital force, that is in the direction of the radius of curvature along the curve at that point in time. Not an ellipse, any GENERAL curvilinear motion. (although a circle is a special case of an ellipse, its clearer to talk about a circle).

Last edited: Nov 6, 2005
9. Nov 6, 2005

### lightgrav

No, whozum, a Force parallel the velocity does NOT change object's momentum or velocity direction. That's why we use components parallel and perpendicular to the velocity.
The parallel component increases the object's speed,
the perp component changes its direction.
It is called centripetal component because at that instant,
the trajectory describes a curve with radius r = v^2/a .

(Don't confuse a temporary curve in a trajectory with a central Force.)

10. Nov 6, 2005

### briguy2188

I think i undersand what you are saying whozum. is that why CF is not unique? since any other force can serve the same purpose as CF?

Ok then, il try again.

An object undergoing circular motion is constantly changing its direction. Therefore, that object is accelerating and according to Newtons Second Law, that acceleration is caused by an unbalanced force acting upon the object. The net force and the subsequent acceleration is directed inwards, which is the CF.

am i on the right track?

11. Nov 6, 2005

### Cyrus

briguy2188, its quite simple. You must draw a picture to get your anwser. Draw the velocity vector at any instant along the curve. Now draw it a little time increment later. Now translate them so that one tip and one head are lined up. Do you see the small change in direction? Thats where your acceleration is coming from. Its not the SPEED change that causes acceleration, its the DIRECTION change of the velocity vector thats causing it.

12. Nov 6, 2005

### lightgrav

yea, you were on-target with first post too.
flesh out those examples from post 1

13. Nov 6, 2005

### briguy2188

i see....still doesnt answer my question as to why centripetal force is not unique. still trying to piece it all together :D:D

14. Nov 6, 2005

### briguy2188

i think i can explain the examples...
CF can be in the form of friction when a car turns. The friction from the tires causes the car to change its direction, therefore inducing CF??

When a ball is being swung in a circular motion, tension in the string causes the ball to swing in circles

Hmmmm....gravity?? Ummmm not too sure but would the moon orbiting the earth be an example??

15. Nov 6, 2005

### lightgrav

it is a direction, not a source.
Real Forces are labeled according to what the source of it was ... each real force has a unique source. Your examples show that.

16. Nov 7, 2005

### briguy2188

lightgrav, what do you mean? can you give some examples please?

17. Nov 7, 2005

### Cyrus

i see....still doesnt answer my question as to why centripetal force is not unique. still trying to piece it all together :D:D

That question makes no sense. It is the result of curvilinear motion, ANYTHING that causes motion to change direction will cause a centripital acceleration.

18. Nov 7, 2005

### briguy2188

so CF is a direction, not a force correct?

19. Nov 7, 2005

### Cyrus

Centripital Force is a FORCE, but it results when a body is forced to change its direction, because there is a centripital ACCELERATION.

Your examples have just been justifying what causes it to moving in a circular motion. That is the CAUSE, the centripital acceleration --> centripital force is the EFFECT.

20. Nov 7, 2005

### briguy2188

ohhh i see i see. thanks a lot guys!