Why does tension equal weight plus centripetal force?

[Osaid]

I can't seem to post pictures, but I will give the link to the question along with the link to the answer given in the mark scheme. Here goes:

Question: http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Physics%20(9702)/9702_w07_qp_4.pdf

Answer link (mark scheme): http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Physics%20(9702)/9702_w07_ms_4.pdf

The part I am having a problem with is the last part of the question. The mark scheme states that the force in cord = weight + centripetal force. I don't get why and how this is so because aren't the directions of the weight and the centripetal force opposite?

Thanks in advance, guys !

 

[CWatters]

The part I am having a problem with is the last part of the question. The mark scheme states that the force in cord = weight + centripetal force. I don't get why and how this is so because aren't the directions of the weight and the centripetal force opposite?

They are indeed acting in opposite directions...

If we take up as positive and draw a FBD for the mass then the net force acting on the mass would be T-mg. Where T is the tension and mg is the weight. Ok with that so far?

In order to make the mass rotate the net force acting on the mass must provide the required centripetal force F_cp. So..

T - mg = F_cp

rearrange that to give

T = F_cp + mg

 

[Osaid]

They are indeed acting in opposite directions...

If we take up as positive and draw a FBD for the mass then the net force acting on the mass would be T-mg. Where T is the tension and mg is the weight. Ok with that so far?

In order to make the mass rotate the net force acting on the mass must provide the required centripetal force F_cp. So..

T - mg = F_cp

rearrange that to give

T = F_cp + mg

Thanks bro ! I get it now !