# Tension in string, vertical plane

1. Aug 30, 2011

### phee

1. The problem statement, all variables and given/known data

Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

What is the tension in the string at the bottom of the circle?

Known:
Mass = 0.100 kg

2. Relevant equations

Fc = mv^2/r

3. The attempt at a solution

I know I need to find the velocity at the bottom to put it into the equation.

I just don't know how to figure out the velocity at the bottom, I know the velocity at the top of the circle is 1.56 m/s ^ 2

Any hints or tips on to what I should be doing?

2. Aug 30, 2011

### PeterO

If this is a very simple introductory question you might be expected to assume constant speed, but more likely, the keys have a lower Potential energy at the bottom of the circle, so will have the equivalent increase in kinetic energy - and thus speed.

Handy to note that Fc and Kinetic energy both have mv2 as part of their "formula"

3. Aug 30, 2011

### phee

How would I go about finding the velocity at the bottom, I don't think I assume constant velocity.

A FBD I drew up, the dot at the bottom is the keys.

4. Aug 30, 2011

### collinsmark

I'd do what PeterO suggests: Conservation of energy.

If you're not supposed to assume constant speed, then maybe you're supposed to assume constant energy in the system.

KEi + PEi = KEf + PEf

Sure, you could instead use kinematics, but conservation of energy is easier.

Btw, how do you know the velocity at the top of the circle is 1.56 m/s? That infomation wasn't in the problem statement. And is the square in the units (you typed 1.56 m/s ^2) a typo/mistake, or is that the acceleration?

5. Aug 30, 2011

### stallionx

The work done all the way from top to bottom is due to the Weight of keys, since Tension is centripetal and at every instant perpendicular to displacement.

6. Aug 30, 2011

### collinsmark

Okay, that's good. If there are no other forces or torques involved then you can use conservation of energy.

And btw, 1.56 m/s is ever so slightly not quite enough speed to keep the 0.25 m string from going slack. It's very close but not quite. Is this how you determined the "1.56" figure?

[Edit: I just realized that I wasn't replying to the original poster. (I'm doing this on a cell phone and it's tough to see everything.) But anyway, Phee, I pose the same statements/questions to you]

Last edited: Aug 30, 2011
7. Aug 30, 2011

### stallionx

m*g + T(top) = m v**2 /r

T(bottom)- m*g = m V**2 /r

we should keep speed but not velocity constant for circular motion.

Last edited: Aug 30, 2011
8. Aug 30, 2011

### PeterO

Speed does not have to be constant for circular motion!!

On a Ferris wheel, speed is approximately constant. for the "hot-wheels" toy set many children once used, the speed was certainly not constant as it did a vertical loop-the-loop.

9. Aug 30, 2011

### PeterO

I am not all that convinced by the diagram. I would prefer FT to appear much longer than Fg as a way of emphasising that you knew it was larger.

I would also never show it finishing close to the centre of the circle, lest someone thought you meant it to be the same length as the radius.

10. Aug 30, 2011

### stallionx

Should not the answer be : ( Taking g about 10 m/s**2 =

T( bottom ) = m *V**2/r + mg

which is :

0.97344 N

?

11. Aug 30, 2011

### stallionx

And I found it is about 4 N

if we vary the speed ?

12. Aug 31, 2011

### PeterO

Is this a problem posted by stallionx or Phee ?

13. Aug 31, 2011

### collinsmark

Please do not suggest answers to original poster's problem. It is against the forum rules. We're not here to do other people's homework for them.

That said, I will comment. No, that's not quite right. Conservation of energy, when involving gravity, generally implies that things speed up as they fall down. The keys' speed at the bottom is not the same as at the top.

Last edited: Aug 31, 2011
14. Aug 31, 2011

### PeterO

And the significance of that is ???

15. Aug 31, 2011

### PeterO

It is certainly going to be bigger than 1N. If the tension was less than 1N it would not even be stopped from going down - but it actually comes back up in a circular arc.

16. Aug 31, 2011

### stallionx

Ek(up) + m*g*L = Ek(down )

17. Aug 31, 2011

### PeterO

Firstly,

I assume that by (up) you mean when at the top, not while traveling up, and that by (down) you mean at the bottom, not while travelling down?

Secondly,

Where is Phee

18. Aug 31, 2011

### stallionx

Yes Sir,

19. Aug 31, 2011

### phee

Ok first off, I got the velocity at the top 1.56 m/s from part A of the question.

TO find the 1.56 m/s I did v = $\sqrt{}gr$

It doesnt say to assume speed is constant throughout, and I dont think it is as the keys travelling past the top point will end up going faster because of gravity.

Originally I had though to find the velocity at the bottom of the circle and plug the numbers into Fc=mv^2/r

I was stumped as to how to find the velocity in the first place at the bottom which led me to here.

This is my first unit of my course and I was not introduced to the conservation of energy. I will read up on it and see where it takes me, thank you.

Last edited: Aug 31, 2011