How Does Tension Vary Along a Heavy Rope with Applied Force?

[spacecadette]

The two blocks in the figure (Intro 1 figure) are connected by a heavy uniform rope with a mass of 4.00 kg . An upward force of 200N is applied as shown.
(See attachment)

I figured out the acceleration to be 3.53m/s^2
The tension at the top of the heavy rope is 120N.

How would I find the tension at the midpoint of the rope?

 

[Carid]

At the midpoint what are the forces pulling down?

 

[tiny-tim]

good ol' Newton's second law

Hi spacecadette!

I figured out the acceleration to be 3.53m/s^2
…
How would I find the tension at the midpoint of the rope?

You mean the rope between the two blocks?

You have the acceleration, so just use good ol' Newton's second law on the lower block.

 

[Carid]

You have the acceleration, so just use good ol' Newton's second law on the lower block.

The rope has mass too...

 

[tiny-tim]

oops!

The rope has mass too...

oops … didn't spot that …

in that case, it's Newton's second law on the lower block and half the lower rope!

Thanks, Carid!

 

[batmankid]

Can someone please help me with this problem. I don't understand how to get the tension at different points in the rope. I got the acceleration easily. But I don't know how to do the other 2 parts of the problem.

 

[tiny-tim]

I don't understand how to get the tension at different points in the rope.

Hi batmankid!

Are you the same person as spacecadette?

To get the tension part-way along a rope, just spit the rope into two ropes, each with its own mass, and use Newton's second law (or a force-diagram) on one bit of the rope.

 

[batmankid]

No, I'm not the same person as spacecadette. He was able to figure out that the tension at the top of the rope is 120N. I wasn't able to get that far. Hopefully once i know how to get that, I'll know how to get the tension mid-way along the rope.

 

[tiny-tim]

He was able to figure out that the tension at the top of the rope is 120N. I wasn't able to get that far.

ok then … to get the acceleration, treat the two blocks and the rope between them as one body, and apply Newton's second law to it.

then to get the tension at the top of the rope, treat the lower block and the rope as one body, and apply Newton's second law to that.

 

[batmankid]

I got the weight of both the lower block and the entire heavy rope, but that did not give me the tension. (4kg + 5kg)(9.8)=88.2N but that's not the 120N I'm supposed to get. What am I doing wrong?

 

[batmankid]

Nevermind thanks. I figured it out!