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

In summary: 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.
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?

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At the midpoint what are the forces pulling down?

good ol' Newton's second law

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.

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

The rope has mass too...

oops!

Carid said:
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!

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.

batmankid said:
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.

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.

batmankid said:
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.

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?

Nevermind thanks. I figured it out!

## 1. What causes tension between 2 blocks?

Tension between 2 blocks is caused by an external force pulling in opposite directions on each block. This creates a force that attempts to stretch or elongate the materials in the blocks, causing tension.

## 2. How is tension measured between 2 blocks?

Tension between 2 blocks is typically measured in units of force, such as newtons or pounds. It can also be measured in terms of the amount of elongation or deformation that occurs in the materials of the blocks.

## 3. Can tension between 2 blocks be negative?

No, tension between 2 blocks cannot be negative. Tension is always a positive force that acts in the opposite direction of compression. If the force pulling on the blocks is reversed, it would create compression instead of tension.

## 4. What is the difference between tension and friction between 2 blocks?

Tension and friction are two different types of forces that can act between 2 blocks. Tension is a pulling force that attempts to elongate the materials, while friction is a resistance force that acts to prevent sliding between the surfaces of the blocks.

## 5. How can tension between 2 blocks be reduced?

Tension between 2 blocks can be reduced by decreasing the external force pulling on the blocks, increasing the strength or elasticity of the materials in the blocks, or by introducing a counteracting force to balance out the tension force.

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