General Physics Question(s): attatched blocks with strings

[Blobikins]

Homework Statement

This is just a general question; but if there are two blocks attached with a string, how do you calculate acceleration and tension? Like, do you add the masses together and work with it, or do you do each separately?

Also; if you have one block on an incline, and another hanging over a ledge, how do you calculate acceleration there? Do you add the masses?

Homework Equations

F=ma
Fnet

The Attempt at a Solution

 

[Doc Al]

Sometimes you can add the masses, if you know what you're doing. But I recommend against that.

You can almost always solve these sort of problems by considering each mass separately and applying Newton's 2nd law to each. (You'll also need the constraint equations, which reflect the fact that the masses are connected by a string and thus their accelerations are related.) That's what I would recommend.

 

[Blobikins]

Sometimes you can add the masses, if you know what you're doing. But I recommend against that.

You can almost always solve these sort of problems by considering each mass separately and applying Newton's 2nd law to each. (You'll also need the constraint equations, which reflect the fact that the masses are connected by a string and thus their accelerations are related.) That's what I would recommend.

For the two blocks connected merely on a string on a flat plane, I've figured out how to do acceleration (masses all added up), but can you just calculate tension by isolating a single one of the bricks, and using the f = ma to find Ft?

Also, for the One mass hanging off an incline, I know you calculate fg for the hanging one, but what in the block on the incline do you need to calculate to work out the rest?Sorry!

 

[Doc Al]

For the two blocks connected merely on a string on a flat plane, I've figured out how to do acceleration (masses all added up), but can you just calculate tension by isolating a single one of the bricks, and using the f = ma to find Ft?

Absolutely.

Also, for the One mass hanging off an incline, I know you calculate fg for the hanging one, but what in the block on the incline do you need to calculate to work out the rest?

You need to calculate the component of its weight parallel to the incline.

 

[Blobikins]

What exactly do you mean by component of weight?

Like, fgcostheta?

 

[Doc Al]

What exactly do you mean by component of weight?

Like, fgcostheta?

Almost. For a mass on an incline of angle θ, its weight will have components mg sinθ parallel to the incline and mg cosθ perpendicular to the incline.

 

[Blobikins]

So, to calculate the acceleration of the mass hanging for force I use ma = fg(hanging) - fgsintheta, with the m for fnet being the total mass?

 

[Doc Al]

So, to calculate the acceleration of the mass hanging for force I use ma = fg(hanging) - fgsintheta, with the m for fnet being the total mass?

That will work. But I recommend that you apply Newton's 2nd law separately to each mass.

 

[Blobikins]

I know this must be getting annoying, I'm sorry, but why? What difference does it make?

(I'm not intending to be cocky, or snarky, I'm genuinely wondering.)

 

[Doc Al]

I know this must be getting annoying, I'm sorry, but why? What difference does it make?

Analyzing each mass separately allows you to solve for everything (tensions as well as acceleration) and will enable you to solve more complicated problems (multiple blocks interconnected, pulleys, friction -- all sorts of things).

For the simple cases you have mentioned, doing it your way is just fine. (But be sure you can do it my way as well.)

 

[Blobikins]

Thank you very much. I'm able to do any questions with ramps, and static friction in equilibrium, just combined masses were confusing me. Thank you.