# Speed of a Wave on a string

## Homework Statement

The drawing shows a 16.9 kg ball being whirled in a circular path on the end of a string. The motion occurs on a frictionless, horizontal table. The angular speed of the ball is ω = 12 rad/s. The string has a mass of 0.013 kg. How much time does it take a wave on the string to travel from the center of the circle to the ball?

## The Attempt at a Solution

I have attempted this but Im just stuck I thought it has something to do with finding the tension but I dont know how to since there is no radii given.

Dick
Homework Helper
I'm going to have to agree with you there. I don't see how you can get anywhere without knowing the radius. It's the only length scale in the problem and the velocity definitely needs something with dimension length. No hidden clues in the diagram?

Nope nothing ot indicate length

Although a similar one in my book has the answer as 3.36X10^-3]

Edit: ITs in second the answer is that in second but I do not see how it doesnt explain

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Dick
Homework Helper
m/sec, I would assume. Then are you supposed to carry some knowledge of a previous problem over into this one? You DEFINITELY need a radius. Otherwise, you just have to write the answer as radius*something.

Dick
Homework Helper
Nope nothing ot indicate length

Although a similar one in my book has the answer as 3.36X10^-3]

Edit: ITs in second the answer is that in second but I do not see how it doesnt explain

Oh, my fault. I was thinking you needed a velocity, and you don't. You need a TIME. Sorry again. Put the radius equal to r and work everything out. In the end, the r will cancel.

ok so what equations? do i set w=v/r to v=sqrt (f/(m/l))

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Dick
Homework Helper
Use F=Ma to get the tension T, use rho=m/r to get the density. Velocity=sqrt(T/rho), right? You have to know some these formulas. Just put them all together and put the unknown radius equal to r.

It wants us to use the formula v=√(F/(M⁄L))

Dick
Homework Helper
It's not just about formulas, it's about understanding. F is the string tension, M is the string mass and L is the string length. How is F related to the mass at the end of the string, the angular speed and the length of the string? You have to do this. I can't do it for you.

Yes I get that, I am not familiar with the Rho=m/r part havent seen that in my 3 years of physics.
I also cant figure out how to change angular velocity to centripetal acceleration

Dick
Homework Helper
rho is linear density. You haven't seen that? kg/m. The main issue here is what is F, the tension. You've got have have seen that in three years of physics. What tension is required in the string? It's uniform circular motion.

Dick
Homework Helper
I also cant figure out how to change angular velocity to centripetal acceleration

You have to put in the unknown radius to do that. Does rw^2 ring a bell?

Im sorry Im just not getting it. This was not really for homework point I was just trying to get it for a final in a few days. Can you tell me your answer so I can back track it possibly

Dick
Homework Helper
A number isn't going to tell you anything. What's the tension in the string using the given mass at the end of the string, the angular velocity and a radius r? Yes, use the centripetal acceleration.

Ok my answer I got was 0.00231 seconds.
In fact I used the answer from the previous problem I posted. I back tracked from that answer and I figured it out. I appreciate you attempts to steer me but I must also inform you that telling me the answer would have helped me much more. I understood the problem and you did helped me. I thank you for that. However I would have more quickly understood it had you given me the answer I requested. In other cases I may not have had a chance to make use of a similar problem and answer and may not have been able to work through it.

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Dick
Homework Helper
Judging by the amount of work and effort you showed in this thread, I'm going to have to guess somebody else gave you that answer until I'm proved wrong. Or can you post your work and show you actually know how to get it? Giving the answer simply isn't the way things are supposed to work here. You're welcome.

Hey Dick quit being one. I genuinely came to here for help and you really wrote me off early. I dont understand what you stood to loose by giving me the answer or a detailed solution. Very few of us in the world want to become a Physicist and thanks to pompous people like you it discourages many young people for affirming that wish. Its this kind of behavior that encourages a self castration of our field, preventing future generations from even attempting the profession. This is a small community that should be close-knit I take every opportunity to help people in lower classes and when I ask for help because a very specific problem was giving me difficulty I am met with adversity and even worse on my first post. I am far from lazy so you can dismiss that belief and soon I will be posting my solution after I scan it into my computer. You have true soured my first impression of this forum.
-Anthony

Edit:
Hey Dick quit being one. I genuinely came to here for help and you really wrote me off early. I dont understand what you stood to loose by giving me the answer or a detailed solution. Very few of us in the world want to become a Physicist and thanks to pompous people like you it discourages many young people for affirming that wish. Its this kind of behavior that encourages a self castration of our field, preventing future generations from even attempting the profession. This is a small community that should be close-knit I take every opportunity to help people in lower classes and when I ask for help because a very specific problem was giving me difficulty I am met with adversity, and even worse it was on my first post. I am far from lazy so you can dismiss that belief and soon I will be posting my solution after I scan it into my computer. You have true soured my first impression of this forum.
-Anthony

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Dick
Homework Helper
"adversity and even worse"???. Oh come on, Mugen Prospec. Look back on the thread and try to figure out when and where you actually tried to work out the problem using the advice I was trying to give you. If you are going to get all ripped because I wouldn't give you the numerical answer, then that's your problem.

I see you have all these awards for being a great help and you did help me on the canceling the radius part. However for someone to go from helpful to antagonistic is unnecesary. If you look at my original post I knew I need the tension and I knew the angular velocity caused the tension on the rope. All of this was already know. I reached an impasse and you showed me the hidden path then it was late so I had to sleep on it. Im not all "ripped up" but look what you did, you exhibited the worst traits in teaching: you became frustrated early and became scathing.

Mugen Prospec, here are your options: you can say thank you to the person trying to help you (regardless of actual help given) or you can pray on getting help the next time around.

Dick