# Tension+ centripetal force

1. Oct 19, 2007

### klm

Two wires are tied to the 400 g sphere shown in figure. The sphere revolves in a horizontal circle at a constant speed of 8.30 m/s

1) What is the tension in the upper wire?
2) What is the tension in the lower wire?

okay i know that m=.4 and v=8.3
i dont know r, which i thought that maybe i could find by doing the square root (1^2-.5^2) =.866
and then Force= m V^2 / R sooo.. (.4)(8.3^2)/(.866) = 31.819 . but i dont know where to go from there?

2. Oct 19, 2007

### klm

okay i also think..
Fnetx= -T1 cos 26 + -T2 cos 26 = mv^2/ r
Fnety= Tsin 26 + -T2 sin 26 -Fg= mv^2/ r

3. Oct 19, 2007

### klm

so my free body diagram looks like 1 wire pulling in the 2nd quad, one in the 3 quad, and Fg going straight down on the y axis

4. Oct 19, 2007

### Sourabh N

yep. No motion in y-dir., so forces sum up to zero. In X- dir. they will contribute to centripetal force.

Last edited: Oct 19, 2007
5. Oct 19, 2007

### klm

but i dont understand how the tension in the 2 wires are going to be different

6. Oct 19, 2007

### klm

Fnety= Tsin 26 + -T2 sin 26 -Fg= 0
T1 sin 26 - T2 sin 26 = Fg
T1 sin 26 - T2 sin 26 = 3.92

Fnetx= -T1 cos 26 + -T2 cos 26 = mv^2/ r
-T1 cos 26 + -T2 cos 26 = 31.82

7. Oct 19, 2007

### klm

^ i am not sure how to solve for T1 or T2 . can you please help me with that

8. Oct 19, 2007

### klm

9. Oct 19, 2007

### klm

i figured out the T2, but now i cant figure out T1. shouldnt it just be plug T2 into one of the equations and it should give you T1??

10. Oct 19, 2007

### Staff: Mentor

Where does the 26 degrees come from?

Which way does the centripetal acceleration act?

Once you correct your equations, isolate the T1 term in each, like this:

$$T_1 \sin\theta = mg + T_2 \sin\theta$$

11. Oct 19, 2007

### klm

26 came from inverse tan (.5/1)

12. Oct 19, 2007

### klm

does centripetal acc act on the Horizontal force?

13. Oct 19, 2007

### Staff: Mentor

But the 1 m side is the hypotenuse. That should be inverse sin (.5/1).

14. Oct 19, 2007

### Staff: Mentor

My question is: What's the direction of the centripetal acceleration?

15. Oct 19, 2007

### klm

umm this may be wrong, but i thought centripetal acc just means that the direction is toward the center

16. Oct 19, 2007

### klm

ohh wait i know what i did. it is just the angle that is messing me up! thank you for pointing that out. i dont know why, but the angle i used still let me get the tension of the first string??!

17. Oct 19, 2007

### Staff: Mentor

That's exactly right. So, what direction is that? Should it be positive or negative?

18. Oct 19, 2007

### klm

negative

19. Oct 19, 2007

### klm

would that be right?

20. Oct 19, 2007

### Staff: Mentor

Good. So fix your equation for horizontal forces.