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Mechanics tensions problem

Hi! I have been doing cie mechanics m1 past papers and every now and then there are questions about tensions where a particle or ring is threaded on a rod. I thought that when you have two different light inextensible strings, the tensions in each one were going to be different and if there is only one string, the tensions are equal. To make myself clearer, i show here 2 questions that have thrown me.

For s12 qp 41 it is Q7. For w03 qp 4 it is Q6. If i have understood correctly, it seems that these questions are essentially the same, same situation but different numbers. Nevertheless in the s12 paper we have two different values of tensions and in the w 03 the tensions are equal. Can anyone please explain to me what is going on? Thanks! =D

9709_s12_qp_41.pdf106.6KB

9709_w03_qp_4.pdf91.4KB

Reply 1

ghostwalker

Original post by alex1114

Your general understanding is correct. If it's one string, and you have anything smoothly on it, the tension in the string will be the same in each part.

Both the questions you quote deal with, in effect, two strings, since the side string is fixed onto the main string.

In this case tensions can be, and usually are different, but then can be the same as well. In w03, notice that the triangle is isoscles, and the upper and lower parts make the same angle with the vertical. If you consider the point where they join, then resolving vertically, you can see that the tensions in the two parts must be the same.

If the angles were different, as in s12, then resolving vertically would give you different tensions. Have a go with the maths.

Reply 2

alex1114

Got it! How silly of me not realising that tension were the same because the angle was the same! Again, thank you for your help! This is helping me get through my M1 preparation! =D =D