Question on problem solving and Newton's 3rd law

[FancyNut]

When there are two objects interacting, like a block on another one, when do you write your equations/draw free body diagram for both objects as a single system? And when should you write eq/draw diagrams for each block separately?

For example there was a question where there was an inclined block with another square on top of it... there was a force on the inclined block and the Q wanted me to find out the force needed to keep the top block from sliding... all surfaces are frictionless...

The teacher solved it as a single system (though I still don't know how it doesn't slide even though there's either a normal force or weight component adding to the force... =\ ).. There are other problems, like a block on another block but with friction between them and the bottom block and floor. Do I also model those as single system or write free body diagrams for each block? And what if the force was pulling on both from the top block? or pulling both but from the bottom block? Does it make a difference?

I know if both blocks have the same acceleration, it helps to think of everything as a single system but I can't apply it to other problems...

Much thanks in advance for any help. :)

 

[boaz]

hey, i also study mechanics in college. from experience, do free body diagrams everytime you have a question on static systems. it really helps and makes it easier to understand the question. in addition, the way your teacher solved the problems is an alternative way to get the answer of the problem. however, it's neither recommended nor useful.

 

[Duarh]

Yeah, I found back when I was doing the exact same problems you're working on (I suspect - Giancoli?) that it was hard to solve the problems without involving artificial forces and whatnot else if I did a single system diagram. Free body diagrams worked out better; they're also easier not to make a mess out of.

You might want to go out for a walk at some point and just think about what's going on, though. I always find that rewarding, even if it takes me hours to figure out what's going on in a straightforward mechanics problem.

By the way, there's a lot of insight to be gained from this very sliding block problem if you just take your time thinking about it. There are things going on there on the small scale that make it all work that are worth a lot of attention.

 

[FancyNut]

Duarh: our text is by Randal Knight-- my school dropped Giancoli thank god. :)

Anyway yeah I know there are several ways to solving a problem... what gets to me is that, in that problem with the small box on an inclined bigger box, there is NO FRICTION... and all the forces like normal (or weight x-comp depending on x-y coordinates you choose) AND the forces on the inclined box are to the right.. there is nothing keeping the box still on the incline.

The only way I can imagine this is if you push the bottom inclined box really hard and the air resistance keeps the smaller box on the same position relative to the bottom inclined box... but there is also no air resistence in the problem.

 

[Duarh]

This is a tricky one to get intuitive about, yes. What's holding the small box up is the contact force from the big block - by pusing the big block to the right, you're also exerting a force on the smaller block (which is conveyed through the perpendicular normal force). Maybe thinking about it this way helps: the only way the big block can exert a force on the small block is through the normal force (which is just saying the force is perpendicular to the inclined surface) - so, the harder you push on the big block, the more of a normal force will be exerted on the small block. Now you want to calculate a normal force such that its vertical component would effectively cancel out the force of gravity. This leaves you with a substantial horizontal component of the normal force that's uncompensated for. That's okay, though: whenever you push on an object in the horizontal direction and keep pushing, you accelerate with the same acceleration (since you're sticking together) - so this horizontal component of the acceleration is just the acceleration experienced by the big block in order to supply the necessary normal force. Mathematically, you can calculate the net force on the big block in the horizontal direction (pushing force minus horizontal component of -normal force, by Newton's third law), set it equal to m*a, where a is the acceleration on the small block due to the horizontal component of the normal force, and solve for the pushing force.

This is probably a bit confusing; I know I always am a bit confused myself when I come back to the problem after a long while; it's well worth thinking about, though.

Edit: ah, why don't you like Giancoli, btw? I think it's a very good introductory text, even if it doesn't go too deep.

 

[FancyNut]

That was a very good explanation!

As for Giancoli, I've only seen a bit of it and you're right it doesn’t look that bad but when you compare it to Knight's text it just doesn't hold up. Giancoli goes into math immediately after each topic is introduced but Knight spends a LOT of time trying to make you understand the concepts, and explaining the physics of each problem. I also like the emphasis on problem solving-- it really helps a lot.

Another great thing about Knight's text is www.masteringphysics.com which is where the Homework is posted. Now it's not exactly a good thing to spend hours on one problem getting "try again" replies and since there is no professor corrrecting, you don’t know what you're doing wrong, but overall it's a better learning experience then solving homework from end-of-chapter problems.

My only complaint is that the solutions for the study guide are only with the professor. =\ He doesn’t assign any HW for the study guide and now it’s useless since there is no way for me to get the solutions (I checked their site—you have to be a professor).