Finding Tension in Multibody Systems in AP Physics II

[z-component]

We're now studying classical mechanics in AP Physics II (forces specifically) and I have a very broad question. When I'm given a multibody system and am asked to find specific forces, such as tension between two objects, I sometimes use the wrong value for mass. How do I know if I am supposed to add two masses or just use the one object's mass depending on what's asked?

For example, if I am to find the tension in a rope between two objects, do I use the mass of the two objects or of the whole system?

 

[Doc Al]

How do I know if I am supposed to add two masses or just use the one object's mass depending on what's asked?

It depends on what you are trying to find. If you are trying to find a property of the entire system (say the acceleration of the center of mass), then you'd use the mass of the entire system.

For example, if I am to find the tension in a rope between two objects, do I use the mass of the two objects or of the whole system?

In this case, the only way to find the tension is by analyzing the masses separately. (If you treat them as a single system, the tension will be an unknown internal force.)

 

[z-component]

So if I'm finding tension or normal forces between two objects I analyze separately as in two different equations? Is there any general rule of thumb for these situations?

 

[Doc Al]

Don't think of this as an additional "rule of thumb" that you have to memorize. It's just the way Newton's laws work. If you want to study the forces acting on a given object (like the tension or normal forces you mentioned), then apply Newton's 2nd law to that object.

Realize that if you take both objects together as a single system, you won't be able to learn anything about the forces between them, since they will be internal forces (and, per Newton's 3rd law, they will cancel out). This will all become obvious after you've solved a few hundred problems.

But, as I said earlier, often it will prove useful to analyze the problem both ways: As a composite system and as separate objects.

 

[z-component]

Thank you, that helps. I am looking forward to the 100th time I solve a mechanics problem... ;)