Three Blocks Attached by Strings

[Bashyboy]

Hello,

The problem is:

Three blocks are connected by two ropes as shown. They are on a surface wit ha coefficient of friction of 0.25. The masses of the blocks are $m_1=6~kg$,$m_2=9~kg$,$m_3=12~kg$. Block 1 is pulled with a $93~N$ force horizontally as shown. Find the tension in each rope.

Apparently I solved this with a rather difficult approach, which I did by making a free-body diagram for each block. I got the same answer, but I'd like to understand this easier method. This simpler method involves treating the three blocks as one system. I couldn't really figure out how to do this. Could someone show me how this method works?

 

[Doc Al]

If you treat the three blocks as one system, you can solve for the acceleration but not the rope tensions. (The ropes are internal to the system.) To solve for the tensions in the ropes you'll need to treat the blocks separately. But solving for the acceleration is a useful first step though--so it is an easier way.

 

[Bashyboy]

I am having a slight problem understanding why we can disregard the tension forces, by treating them as internal forces.

 

[Doc Al]

I am having a slight problem understanding why we can disregard the tension forces, by treating them as internal forces.

If you treat the three blocks as a single system, then how can you solve for those internal forces?

You choose how you define your system, depending on what you are trying to solve for. For some purposes, treating the three blocks together makes sense. For other purposes, it doesn't.

In order to solve for the tension you must have a system in which those tensions are external forces so you can apply Newton's 2nd law.

 

[Bashyboy]

Hmm, I think I understand. One other question I have is, why is the tension force between block one and two greater than the tension force between block two and three?

 

[Bashyboy]

Oh, wait! Internal forces don't produce an acceleration of a system, only external forces do. Yes, the tension forces do accelerate the blocks individually, but not the system as a whole.

 

[Doc Al]

One other question I have is why is the tension force between block one and two greater than the tension force between block two and three?

Think about it. The string between blocks one and two is pulling both block two and three, while the string between two and three is just pulling three.

 

[Bashyboy]

The way you describe makes it seem like the tension force between blocks one and two should be less than the tension force between blocks two and three.

 

[Doc Al]

The way you describe makes it seem like the tension force between blocks one and two should be less than the tension force between blocks two and three.

Why is that? You think it takes less force to accelerate two blocks than just one?

 

[Bashyboy]

Well, it depends. In this case, these two blocks combined have a greater mass than the third block, so it will take more force to accelerate to the two, at the same rate, than the third block.

 

[Doc Al]

Well, it depends. In this case, these two blocks combined have a greater mass than the third block, so it will take more force to accelerate to the two, at the same rate, than the third block.

String 1 is pulling blocks 2 & 3. String 2 is only pulling block 3.

 

[Bashyboy]

String one has a tension 72.3 N, and string two has a tension of 41.3. Why is T1 greater than T2?

 

[Doc Al]

String one has a tension 72.3 N, and string two has a tension of 41.3. Why is T1 greater than T2?

Read my last several posts! T1 has to pull two blocks. T2 only pulls one. (It's a little more complicated than that, since friction is involved, but that's the general idea.)