Solving F = MA Problem: Confirm Solution & Extend Problem

[Knight526806]

So the Problem is with the picture which is attached.

Attempted Solution:
for m2: F = m2a = T - m2g
T = m2g
then for m1: F = m1a = T
a = T/m1
Then plug in: a = m2g/m1

then for all three blocks: F = (M = m1 = m2)a
so: F= (M +m1 +m2) (M2g/m1)

Now I'm pretty sure that's the right answer, but i need to know if my work is done correctly, every single part because I have to do this problem in front of the class . Moreover, how could I extend this problem. Like what would be a very related problem but make it a little more complicated and if you could provide a solution for the extension that would be awsome.
Thanks for all responses in advance.

 

[collinsmark]

Hello Knight526806,

Welcome to Physics Forums!

then for all three blocks: F = (M = m1 = m2)a

I think you made a typo where you typed a couple of "=" signs instead of "+" signs. But...

so: F= (M +m1 +m2) (M2g/m1)

That sounds about right to me (Although I think you meant to type "m2" instead of "M2", but I'm just getting nitpicky now.)

If you want to be really clear, then you might want to break up respective forces into components. For example, when you started with m₂, you might want to temporarily restrict your discussion of F to F_z to find the tension on the string. Similarly, if you wanted to, you could break up the x-direction force into the individual forces on the individual blocks and pulley. This includes the normal force of Block M to block m₂, and the normal force from the pulley (the pulley is attached block M) to the string, which accelerates block m₁ and the force needed to accelerate block M by itself. Then add up everything at the end (which will give the same answer that your already worked out above). You'll use Newton's third law a lot. This might seem like overkill, and in my opinion, it is sort of is overkill. But if you really want to be explicit, doing it this way should hold up better to questions.

Have phun presenting!

 

[collinsmark]

Let me elaborate a little bit about what I meant with my last post.

The way you solved the problem is fine in my opinion. So there's nothing wrong with that. I'm not criticizing the way you solved the problem. But if you want to be completely prepared to answer any and all questions about the problem, there is a more detailed way to go about it. http://www.websmileys.com/sm/happy/535.gif

When you present your analysis, you might want to be at least prepared with some details in case somebody asks you about the forces on any individual block. Even it means just keeping this more detailed solution in your back pocket.

The way to go about doing this in explicit detail is to draw a free-body diagram of each individual block (you already know how they fit together, but you might want do also treat everything individually in case you get asked about it).

For example, consider block m₂ on its own. Draw all the individual forces acting on block m₂. You know that force m₂g points down. There is a force T which points up. And you know that since block m₂ does not accelerate in the z-direction, T = m₂g (which you've already calculated). But wait, what other forces are on block m₂? You know that it's accelerating at the rate a in the x-direction. So it is getting pushed by something. It's getting pushed by block M! And since you know the mass and acceleration of block m₂, you can calculate the force on block m₂ from block M.

And since block M is exerting a force on block m₂, you also know that block m₂ is exerting a equal and opposite force on block M (in the negative x-direction), due to Newton's third law of motion. So now you know two forces acting on block M, the force F (shown in the diagram) and the force that block m₂ exerts on it (discussed above). (There may be other forces on block M too, that I haven't discussed above.)

What other forces are involved? Do the same procedure for block m₁ and the pulley, eventually finding all the forces acting on block M. Once you have that, you can sum together all the forces acting on block M, and calculate what is the magnitude of force F (shown in the figure) that will cause block M to accelerate at a.

This is a more detailed way to work the problem (perhaps more detailed then really necessary), but it leaves no questions unanswered. Using this method, you should be able to handle any question that gets asked about the problem.