Using Acceleration to find Tension

[Peter G.]

So, my teacher drew on the board my attachment. The mass, lower case m, is accelerating both itself, and mass, Upper case M. The lowercase m mass is 10 g and the uppercase M mass is 90g

He then did the following to calculate the acceleration:

a = F / m
a = 0.1 N / 0.1 kg = 1 m/s

Ok, but then he wants to calculate the Tension on the string, the red arrows in the diagram. Now, if there's any tension in the string, how could he have used the weight of the lowercase m block as the resultant force in the acceleration calculation? The resultant force should be the W - T, I thought we couldn't calculate the acceleration without the tension!

Anyone can help me with this?

Thanks!

 

[Doc Al]

Now, if there's any tension in the string, how could he have used the weight of the lowercase m block as the resultant force in the acceleration calculation?

If there's no tension in the string, how is the small mass pulling the larger one? You (or your teacher) took a shortcut--the weight of the small mass can be considered as the net external force on the system, not the net force on the small mass.

It may be less confusing if you wrote separate force equations for each mass, then combined them.

The resultant force should be the W - T, I thought we couldn't calculate the acceleration without the tension!

Yes, that's the net force on the small mass. (But your earlier equation looks at the entire system.)

You can use Newton's 2nd law to find the tension.

 

[Peter G.]

So if I want to calculate acceleration I use the resultant force on the system I only use the weight of the small mass? The tension does not interfere?

 

[Doc Al]

So if I want to calculate acceleration I use the resultant force on the system I only use the weight of the small mass? The tension does not interfere?

Considering the two mass system as a whole, the tension is an internal force--it acts equally and oppositely on each mass, so it cancels.

But if you want to figure out the tension, you'll have to look at one of the masses by itself. In that case tension is an external force and must be considered.

 

[Peter G.]

Oh! I got it! So, considering the whole system the tension force cancels, leaving the weight as the net force, hence, the weight of the small mass can be used to calculate the acceleration of both blocks.

And to calculate the tension itself we have to look at one block independently, and the acceleration for the small block was calculated in the whole system.

Thanks for the patience and for shedding some light into this!