# This is way easy if you are smart!

1. Oct 28, 2006

### emerica86

circle question its easy (still need help)

Suppose you tie a rock to the end of a 1.5 m long string and spin it in a vertical circle. What is the minimum speed it can travel and "just" get around the top? (Hint: The rope will just start to go "slack" and the only force acting on the rock, downward, is gravity.)

-------m/s

:yuck:

here is my work:
so i thought it would be 9.9 since 9.8 is gravity or something i am completely lost. if someone could help that would be great

Last edited: Oct 28, 2006
2. Oct 28, 2006

### Hootenanny

Staff Emeritus
Okay, at the top of the circle what forces are acting on the rock?

3. Oct 28, 2006

### emerica86

gravity ....?

4. Oct 28, 2006

### Hootenanny

Staff Emeritus
Yes (assuming the string is slack as the hint suggests), so since the rock is travelling in a circle what must the weight of the rock be equal to?

5. Oct 28, 2006

### emerica86

gravity i think but i tried 9.8m/s and it was wrong.....

6. Oct 28, 2006

9.81 [m/s^2] is gravitational acceleration, and Hootenanny asked you about a force.

7. Oct 28, 2006

### Hootenanny

Staff Emeritus
Any object undergoing circular motion must experience a C## Force.

8. Oct 28, 2006

### emerica86

i dont know what forces are acting on it i am so confused

9. Oct 28, 2006

### emerica86

oh a centriipugal force?

10. Oct 28, 2006

### JSBeckton

Draw a free body diagram, 2 forces, centrifigal force and gravity, they are equal at the critical point. f=ma for gravity, i can't remember the centrifigal force eqn off the top of my head but mass should cancel and you can solve for velocity.

Its been awhile since intro physics so I'm a bit rusty.

11. Oct 28, 2006

### Hootenanny

Staff Emeritus
No, centrifugal forces only arise when we consider the circular motion from an non-inertial reference frame (i.e. the rocks), the correct term would be centripetal force. Now, what equations do you know that deal with the centripetal force?

12. Oct 28, 2006

### emerica86

f=mv^2/r ?

13. Oct 28, 2006

### Hootenanny

Staff Emeritus
That's the one , so since weight is the only force acting when the rock is at the minimum velocity, it follows that the weight of the rock must be providing all the required centripetal force at this point. Do you follow?

14. Oct 28, 2006

### emerica86

yes i follow i just dont get what the weight is because the problem says nothign to do with weight.

15. Oct 28, 2006

### Hootenanny

Staff Emeritus
I'm sure you know that the weight of an object is the product of it's mass and the gravitational field strength ($W=m\cdot g$)

16. Oct 28, 2006

### emerica86

yes i know that equation im just saying the origional problem dosent tell you the mass of the rock. so how do you get it?

17. Oct 28, 2006

### Hootenanny

Staff Emeritus
The question is do you really need it? Equate the weight of the rock with your equation for the centripetal force and see what happens to the mass...

18. Oct 28, 2006

### emerica86

omg i give up unless someone just gives me the answer lol

19. Oct 28, 2006

### Hootenanny

Staff Emeritus
Okay, I'll give you a hint (but don't be too quick to abandon hope). If we equate the weight of the rock with the centripetal force we obtain;

$$mg = \frac{mv^2}{r}$$

Can you go from here?

20. Oct 28, 2006

### emerica86

oh duhh
ok thank you very much