# Caluclating tension in string that is moving in horizontal circles.

Hi all,

First of all I'd like to say thank you to you all for providing a great forum which has been a great help to me working through my ics home learning course.

As i have learnt on here and other places on the internet the information I have in my course materials is not always correct and can be very confusing causing hours of unnecessary extra work.

The question I am very stuck on is: Calculate the tension in a 3m string attached to a 3kg bob that is moving in horizontal circles of 0.6m radius.

All the information I have on working this out shows that tan should be used to work out the angle, I have questioned this with my tutor and he doesn’t seem to have an answer for me. (What chance have I got?)

I have always been very interested in physics and have enjoyed learning throughout the course. I just can’t seem to find a simple clear formula for working this question out?

Any help greatly appreciated
Many thanks,Dave.

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Which forces do you think are acting on the bob?

That would just be gravity?

The pull of gravity is not the only force.

Imagine you are the bob. Which pulls or pushes would you feel?

I guess a force would be created with the momentum?

There are only two forces:

the pull of gravity mg and the tension in the string.

Ok so I think I have got it:

mg=f
3x9.81=29.43N (force acting down on the bob)

So now I need to work out the angle and get the force acting on the string?

What kind of force does a particle need so that it can move in a circle?

I think I finally have the answer.

angle = tan-1 0.6/3
angle = 11.30993247

t=3x9.81/cos11.30993247
t=29.43/0.9805806757
t=30.01282886

So the tension on the string will be 30N?

The main thing that has confused me is that i read on here that tan shouldent be used also there is a mistake in my learning material.

centrifugal

'...angle = tan-1 0.6/3...'

note that tan(angle) is NOT 0.6/3

0.6/3 = sin(angle)

Ok i'm very confused now, thats the way a simular problem just different mass and string lengh is worked out in my learning material - is that wrong then?

It all depends on which angle one takes.
A diagram of the forces is very important in a problem like this.

I have drawn a diagram that definitely helps.

I have attached an example of the same question with different figures (notice the mistake cos14 is not 0.25?) I have also used this example to work out my problem and have written it to the side.

Would you mind taking a look at this?

Many Thanks
Dave.

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I always start with a diagram of the forces acting so that I try to understand how the equations are obtained.

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Thats great.

So I now have

$\theta$ = sin-1 06/3

$\theta$ = 11.53695903

t = mg/cos$\theta$

t = 3x9.81/0.9797958971

t = 30.03686797N

That definitely clears up everything, Thankyou very much for your help.