- #1

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- Homework Statement
- Two particles of mass 3kg and 5kg are connected via a light inextensible string which slides over a massless frictionless pulley. Calculate the tension in the rope the instant the system is released from rest and the instantaneous acceleration of each particle.

- Relevant Equations
- F=ma

I'm not really struggling with the question but the coordinate systems involved more so. So due to the modelling assumptions we know that the tension will be equal throughout the rope so we can use f = ma on each particle respectively and solve the resulting equation (as acceleration will be equal for both particles). If we take the upwards direction as positive for both particles we get the following:

$T - 3g = 3a$ and $T - 5g = -5a$

Which is perfectly fine. However my textbook does something else which is quite weird, in the textbook they take the positive direction to be different for each particle, they take the positive direction to be the direction of each particles acceleration. So they get;

$T - 3g = 3a$ and $5g - T = 5a$

Now I've noticed that regardless of which way you define positive for each particle, the equations generated are always correct.

Here comes my question.

1. Is it perfectly fine to define the positive direction different for each part of a system?

2. If not, why does it work in this situation?

Thanks for your help and time

$T - 3g = 3a$ and $T - 5g = -5a$

Which is perfectly fine. However my textbook does something else which is quite weird, in the textbook they take the positive direction to be different for each particle, they take the positive direction to be the direction of each particles acceleration. So they get;

$T - 3g = 3a$ and $5g - T = 5a$

Now I've noticed that regardless of which way you define positive for each particle, the equations generated are always correct.

Here comes my question.

1. Is it perfectly fine to define the positive direction different for each part of a system?

2. If not, why does it work in this situation?

Thanks for your help and time