# How to find tension in a rope with mass and length

The mass of 6 kgs is supported by a uniform rope which has a mass of 1. What is the tension in the rope at its lower, upper and mid-point? Please explain how to work out as I thought the tension in the lower, upper and mid-point was the same? The first thing i will start with is the general equation you will need to use to find the forces. I am sure you have seen it before:. The main trick to this is that the rope has a mass itself. Usually we assume that the rope does not weigh very much in comparison to the mass it is holding.

In that case you are right, the tension would be the same everywhere in the rope. In this case though the rope has a mass, this means that each little section of rope will have to support the mass, as well as the rest of the rope that is below it.

Think about your arm hanging down. You hand has to hold up your fingers, your forearm has to hold up your fingers and your hand, your upper arm has to hold up your forearm, hand and fingers.

Just like this the rope has to hold all the pieces of rope that are below it. So now what you want to do is draw out the problem, and try to understand what is happening with the forces:.

So at the top we have the attachment point and hanging from that we have the mass at the end of the rope. Now look at the lower end of the rope and what it is holding up. You can see that the only weight it has to support is the weight of the mass. For the end of the rope we can write:. Now for the midpoint of the rope, you can imagine cutting it in the middle and trying to support the weight below it.

This will include the mass as well as half of the rope. This is a total of:. Use the same concept for the top of the rope. You can see that you need to support the weight of the mass, as well as the entire weight of the rope. This means that you will have a total mass of 7kg. Answer Save.

## Tension on a rope with mass

Brain V. So now what you want to do is draw out the problem, and try to understand what is happening with the forces: [ m ] So at the top we have the attachment point and hanging from that we have the mass at the end of the rope. Let me know if you have any other questions. Still have questions? Get your answers by asking now.Hot Threads. Featured Threads. Log in Register. Search titles only. Search Advanced search….

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Tension on a rope with mass.

Thread starter Solidmozza Start date Mar 17, Homework Statement A block with mass 'M' is attached to the lower end of a vertical, uniform rope with mass 'm' and length 'L'. A constant upward force 'F' is applied to the top of the rope, causing the rope and block to accelerate upward. Find the tension in the rope at a dstance 'x' from the top end of the rope, where 'x' can have any value from 0 to 'L'. The Attempt at a Solution I'm a bit confused on this question.

I've tried breaking the problem up into three parts - one for the block mass 'M', one for the top of the rope and one for a point 'x' on the rope - but I can't seem to get it to work. Thanks in advance. Try to apply Newton's 2nd law to the whole system in order to find the acceleration.

Then try to look at an element of the rope at a distance x from the top end of the rope, and try to express the mass of that element somehow. Then apply Newton's 2nd law again. I don't have the time to write it down and check if it's right, though. Ah sweet! That seems so obvious now - Silly me! There are only 2 forces acting here: the combined weight force of the rope and the block, and the upward force. Since the whole thing is accelerating, we use newtons second equation of motion Now we take the point 'x' on the rope.

Am I right in saying that there are only two forces here - the tension force due to action-reaction pairs which acts upwards, and the weight force? It seems to work mathematically Thanks for your help :D. You must log in or register to reply here. Related Threads on Tension on a rope with mass Tension on a rope with significant mass. Last Post Oct 10, Replies 1 Views 12K. Tension on a massive rope. Last Post Oct 14, By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. A mass m hangs on 3 ropes symmetrically with equal base angles. The base angles are 45 degrees. So the middle rope Tension is vertical to the load mg.

How can one find the delta l of the middle and the side rope? I did the sum of vertical forces and now end up staring at the question on how to move further to solve for tensions s1 and s2 also the change in lengths. The remainder of the analysis is straightforward, and just involves doing the equilibrium force balance. It also holds from horizontal equilibrium:.

### How to measure stress/tension on a rope?

You can express the change in lengths by using elementary trigonometric relations; you can express the length change of the side ropes in dependence on the length change of the middle rope; it holds:. Sign up to join this community. The best answers are voted up and rise to the top.

Home Questions Tags Users Unanswered. Rope Tension and change in length of rope Ask Question. Asked 2 years, 11 months ago. Active 2 years, 11 months ago. Viewed 1k times. Also E and A are given for the calculation of delta l.

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Post as a guest Name. Email Required, but never shown. The Overflow Blog. Featured on Meta. Feedback on Q2 Community Roadmap. Related 1. Hot Network Questions. Question feed.During these challenging times, we guarantee we will work tirelessly to support you. We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission — to help everyone in the world learn how to do anything — no matter what.

Thank you to our community and to all of our readers who are working to aid others in this time of crisis, and to all of those who are making personal sacrifices for the good of their communities. We will get through this together. In physics, tension is the force exerted by a rope, string, cable, or similar object on one or more objects. Anything pulled, hung, supported, or swung from a rope, string, cable, etc.

Being able to calculate tension is an important skill not just for physics students but also for engineers and architects, who, to build safe buildings, must know whether the tension on a given rope or cable can withstand the strain caused by the weight of the object before yielding and breaking. See Step 1 to learn how to calculate tension in several physical systems. To calculate the tension on a rope holding 1 object, multiply the mass and gravitational acceleration of the object.

If the object is experiencing any other acceleration, multiply that acceleration by the mass and add it to your first total.

To calculate the tension when a pulley is lifting 2 loads vertically, multiply gravity time 2, then multiply it by both masses. Divide that by the combined mass of both objects. For examples and formulas for different situations, read on! Did this summary help you? Yes No. Log in Facebook Loading Google Loading Civic Loading No account yet?

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There are 9 references cited in this article, which can be found at the bottom of the page. Calculating Tensions On Multiple Strands. Related Articles. Article Summary. Method 1 of Define the forces on either end of the strand. The tension in a given strand of string or rope is a result of the forces pulling on the rope from either end.

Assuming the rope is stretched tightly, any change in acceleration or mass in objects the rope is supporting will cause a change in tension in the rope. Don't forget the constant acceleration due to gravity - even if a system is at rest, its components are subject to this force.Hot Threads.

Featured Threads. Log in Register. Search titles only. Search Advanced search…. Log in. Contact us. Close Menu. Support PF! Buy your school textbooks, materials and every day products Here! JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Tension of a massed String. Thread starter Knightycloud Start date Feb 21, Homework Statement How to find the tension in a string with a weight.

The string is not a light one it has a we say 1kg weight. How to find the tension at the both ends and the middle if it is equally pulled at both sides horizontally??? PeterO Homework Helper. Knightycloud said:. OH thanks, That really made it clear. So, if we say that a heavy string is freely hanged in a roof, how is the tension??? Just make the hanging mass 0 At bottom no tension and at top the weight of rope.

I thought the 12N force will be the same as the beginning of the string. Now I got it. I really appreciate this knowledge you've given.

I never expected such a vast explanation. I'll never forget the theory now!!! Mainak Gupta. Mainak Gupta said:. You must log in or register to reply here. Related Threads on Tension of a massed String Tension in a string of mass. Last Post Apr 26, Replies 7 Views 10K. Last Post Nov 8, Replies 3 Views 5K. Tension at the middle of a string of known mass. Last Post Oct 10, Replies 2 Views 2K.

Work Done by Tension of Mass on a string.What Is Tension? Every physical object that's in contact with another one exerts forces. Depending on the objects that are making contact, the contact force has a different name. For rope, as with cable and chain, the force is called tension. Any object that rope is used to pull, hang, swing or support is subject to tension. As ropes are not usually used to push an object, tension in this respect is a pulling force.

This pulling force can be exerted over a certain distance, which equates to the length of the rope. If you attach a rope to an object and pull it, the rope begins to stretch and eventually goes taut. This is because it is under tension. If you release the tension on the rope by stop pulling on it, it goes slack.

**Module 7 1 Calculate tension in a rope given sag**

If the tension becomes too great so that the rope cannot stretch any further, it will eventually break. In practical terms, this means you need to check the rope's tension limit when attempting to lift or pull an object with it.

The formula for tension remains the same regardless of the body acting on the rope or the body that is being acted upon. For the equation of tension in a rope, weight W is equal to the mass of the object m multiplied by the acceleration of gravity g.

### Tension of a massed String

As tension is a force, the results given through the formula are expressed in newtons and noted with the symbol N. Tension on a Single Length of Rope For a single length of rope, its tension is determined by the forces acting at either end of it. Any changes in the mass of the object the rope is attached to or the level of acceleration instantly changes the tension in the rope. There are various factors that affect the tension. Gravity is a source of constant acceleration, even when the rope is still.

When an object is being suspended by a rope, the object's weight counts as a type of acceleration. Rotational acceleration is another consideration. When an object is hanging from a rope and being swung around in a circular motion, centripetal force occurs. The faster the object rotates, the higher the centripetal force is exerted by the rope to keep the object moving.

## Tension Formula

Also, friction has to be taken into account. When a rope is used to pull an object along another surface, such as the ground, friction occurs between the surface and the object. This is transferred to the rope's tension.

Tension on Multiple Lengths of Rope A rope used in a pulley system is configured so two lengths of rope are created with just the one piece. Used to lift parallel loads, both lengths have the same amount of tension. When non-parallel loads are being lifted via a pulley system, the rope's tension is changed as the gravity force on the weight has changed, as has the pulling force on the second length of the piece of rope.

Home Science. What Are the Types of Acceleration? What Is the Definition of Constant Acceleration?All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.

Hottest Questions. Previously Viewed. Unanswered Questions. Machinery and Tools. Does the tension of the rope depend on the length of the rope? Wiki User A one foot long rope holding 10kg has the same tension as a rope 30 feet long holding 10kg.

The weight has not changed so why would the tension change. Disregarding the weight of the rope of course. The speed of the wave would depend on the tension, the length of the rope, and the mass per length unit.

This doesn't help in this particular case - you need more data. By the way, Hz. Wavelength would be measured in meters. Asked in Physics, Machinery and Tools What is the direction of tension in a rope? The direction of tension in a rope always runs both ways and parallel to the rope. Asked in Physics If two equal forces pull on opposite ends of a massless rope what is the tension in the rope?

Asked in Physics, Kinematics What will be the tension in a rope that is pulled from its ends by to opposite forces N each? Assuming you meant two forces, the tension will be N. The answer will depend of Without that information, the question cannot be answered. Asked in Physics What will be the tension in a rope that is pulled from its ends by two opposite forces n each?

Neglecting the weight of the rope itself, the tension will be newton in any part of the rope.

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