Problem : Two blocks of masses 10 kg and 20 kg are connected by a string that passes over a pulley as shown in the figure. Neglecting friction between surfaces, find acceleration of the blocks and tension in the string (consider g=10m/s2 ).

 

Solution : The blocks are connected by a taut string. Hence, their accelerations are same. Let us assume directions of accelerations as shown in the figure. Also, let the magnitude of accelerations be “a”.

According to Newton's Law.F=ma

∑Fy=T−10g=10ay

The problem is that.

in above equation why we took T as positive and mg as negative?

On the other hand in ∑Fy=20g−T=20ay i.e for "20Kg" we took T negative and mg positive.

I will be thankful to you if you solve my problem of signs.

The + or - signs are a coordinate convention. Within each equation you have to be consistent. You know the direction of a, and assign it a sign, and that dictates what sign you apply to T or g.

 

In case #1, a and T are in the same direction, so they have the same sign. In case #2, g and a are in the same direction, so they have the same sign.

 

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There are many problems where it is not obvious what direction of a particular resultant vector will be. In those cases you need to use a consistent sign convention throughout all of the problem.

I understand it thank you but I want more explanation of sign convension in coordinate system.

Pick one, and be consistent. One direction is positive and the opposite direction is negative. There really isn't much more to it than that. Most of the time there is nothing in the problem that forces you to choose a particular convention or coordinate system, though many times the right choice of coordinate system makes the solution easier; that recognition comes with experience of solving problems.

One acceleration should be positive since one block will go in the positive direction (i.e. up). That means the other block will go in the opposite direction hence negative. (i.e. down). Makes sense?

So if a block moves upwards at 5m/s then upwards is positive.

 

So acceleration due to gravity would be -10 (note the negative) (often a more accurate 9.81 is used), because gravity acts downwards, and you've just define up as positive, therefore down is negative.

 

Of course you could work the other way round too. You could say that the block moves upwards at -5m/s and therefore acceleration due to gravity would be 10. It doesn't make a difference as long as you keep the signs the same throught the question.

Thank you of all very very much.I am very grateful to you.