A mass of $100$ grams is tied to a $50 cm$ long string(secured to the ceiling). The mass swings around in an horizontal circle with a constant speed and it performs a quarter of circle every second. What's the tension of the string and its angle with respect to the horizontal axis?

Mass swinging

So the problem gives me this data:

  • mass : 0,1 kg
  • string length : 0.5 m
  • angular speed : $\frac{\pi}{2}rads^{-1}$

I can find the weight($g = 9.8 ms^{-2}$):

  • weight : 0.98 N

Now I don't know how to find the tension and angle using only this data. I've seen similar problem and they usually give you already the tension or the angle of the string.

  • $\begingroup$ Draw the free body diagram at first ... Identify which forces are working ... $\endgroup$ – Nehal Samee Apr 16 '18 at 10:09
  • $\begingroup$ If you are in doubt of where to start, always try to think of some equation/formula were what you are looking for is included. And then start from there. Here, you are looking for the force of string tension - this only appears in Newton's laws. So set up one of Newton's laws either vertically or horizontally (you will need to make a force diagram in order to have the correct forces plugged into Newton's law). Then look at what more is needed (what else is unknown), and think of new equations/formulae where they are included. Step by step you will get closer and closer until you are done. $\endgroup$ – Steeven Apr 16 '18 at 11:06

Let the tension in the string be T. Then clearly for the horizontal plane, the component of T along the radius provides the required inward (centripetal) force.

If you assume the angle marked in the figure to be $\theta$, then

T$ cos\theta = m*\omega ^2 * r$

Here, $r = $ (string length)*$cos\theta$

Hence, $$T = m*\omega^2*l$$where $l$ is the string length. I hope you can take it from here.


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