Tension in a rope with mass

1. The problem statement, all variables and given/known data

Two blocks shown in figure are connected by heavy uniform rope of mass 4kg. An upward force of 200N is applied as shown.

(a)What is the acceleration of the system?

(b)What is the tension at the top of heavy rope?

(c)What is the tension at the mid-point of the rope?





2. Relevant equations

I Took g=10m/s^2.





3. The attempt at a solution

See the attachment. I drew FBD.

The first question is easy.

Net gravity force=(7+4+5)g=160N downwards

Net Force in the system=200-160=40N upwards.

Acceleration of the system=40N/16kg=2.5m/s/s upwards.

This answer coincides with the Answer Key.



For third question, I should break the rope into 2 identical rope and find the tension. Right?



First I tried second question. I get stuck in the second question due to the nonm-zero net force(40N).



In the diagram, F1-70=Net force=40N. Then F1=110N upwards. Right?

F2-F1+40=40. Right?

Then F2 should be 110N downwards right?



But the answer is 137.5N

Attached Images

Untitled.png (20.3 KB)