Help Joanne Solve Cable System Tension Issues

[bradycat]

I am trying to solve the tension in the cable system and I can not get to the answer.
See attached file for question 4-4 and 4-6.

I have no clue as to what to do with the 100 kg weight on the 4-4 problem.

As for 4-6. I came up with 7 T at the p arrow, and when I multiply that to 3 for finding T I do not get 222 N. I get a much larger number. I am not calculating them properly. I have followed my book, but it's not working.

Any help would be great, or to explain it to me. My teacher showed me to do FBD of each pulley, but where do you start, that is what I don't get also.
Thanks
Joanne

 

[osnarf]

draw a FBD of each of the pulleys, and of the small weight, and of the large weight at the bottom. Start with the bottom weight if you want, it doesn't matter.

If you do, you will have one downward force on it (due to the gravity of the bottom wieght), and several upward forces (the tension from the cords).

Next, say you want to draw the FBD of the small weight. How many upward-directed and downward directed forces will you have? The key is to think of it as it's own entity. It's own gravity will obviously be pulling down on it. Will anything else be? What will be keeping it from falling?

If you do this for all components, you will have a linear system of equations which should give you all the information you need.

 

[bradycat]

I am trying 4-4 and still not getting it. T1&T3 are 981 N and T2 is 1960 N.
Can you explain it more in detail perhaps, thank you
Joanne

 

[osnarf]

The 100kg weight will have one upward force - the tension from the cord above. It will have two downward forces - the gravity from the 100kg weight and tension from the cord below. Then the tension above T₂ equals the force of gravity of the 100kg weight and the tension below T₃.

Now look at the pulley above the 100kg weight. It has one downward force, T₂. it has two upward forces, the tension from each side of the cord. Since it's the same cord, running through a pulley, these tensions are equal.