How to Calculate Tension

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Understanding tension definition, force could be a key to understand; however, ropes and cables expeditiously transfer force over a big distance. Knowing how to calculate tension is vital, not only for physics students but also for engineers and designers.  

A sledge pulled by a team of Siberian Huskies could be an excellent example to validate this truth. Behind using the normal force, the ropes attached to the sledge, passes the force from running huskies to the sledge. Tension is a type of force on the length of a medium, particularly a force carried by a versatile medium, like a rope or cable. Tensions are often outlined as associate degree action-reaction types of forces.  

To construct safe buildings, Most Engineers assume that strain on an object will be resisted by the strain due to the object’s weight before yielding. Anything stretched or hung, supported or swung from a rope is subject to the force of tension. Like all forces, tension will accelerate objects or cause them to deform. 

This article will stress the tension definition, its formula and calculate it effectively in different practical situations. Moreover, it will also give examples of its practical implications.

Tension Formula

The tension on an object can be calculated by multiplying the mass of the selected object and the force of gravitation which is then added to the product of acceleration and the mass which that object is carrying. Mathematically, it is represented as follows:

T= mg ma 


T = tension, N, kg-m/s2

m = mass, kg

g = gravitational force, 9.8 m/s2

a’ = acceleration, m/s2

Tension Definition

Tension force is the associated axial force that passes through an associated object that pulls, sort of a rope, string, or chain. We can also observe tension force in alternative materials, like rods and bars, providing they’re subjected to external pull or tensile masses. As tension is a type of force, thus its unit is also Newton (N). Any flexible or elastic instrumentation, like a string, rope, chain, wire, or cable, will exert pulls solely parallel to its length. Thus, a force carried by an elastic material could be tensioned with a direction parallel to that under observation material.

Tension force is additionally a good example of Newton’s Third Law of Motion. That states if a body exerts a force on another body, the other body will exerts an equal force but opposite force towards the first/original body. Tension force is also termed as a reactive force that counteracts associate external pull force. This characteristic of tension force is the reason why it’s, in a way, quite just like normal/simple force.                                                               

What is Tension

Well, what is tension? All physical objects that are in reality will exert forces on one another. Forces are given several names such as push, pull, thrust, lift, weight, friction, and tension. Normally, these forces are sorted into many classes and given names according to their application or source, like however they’re transmitted or their effects. If one in every of the objects exerting the force happens to be a rope, string, chain, or cable, the point is termed tension. At the atomic level, once atoms and molecules are forced with the exception of one another and gain P.E. (potential energy) with a restoring force existing, the restoring force would possibly produce tension. 

Each ending portion of the string or rod beneath such tension might pull on the thing it’s connected to revive the string/rod to its relaxed length. Whereas considering a rope, the stress force (tension) is felt by each section of the rope in each of the directions, except the endpoints. The endpoints undergo tension on one portion and, therefore, the force from the weight/load connected. Tension may be a propulsion force, and it’s not a pushing force as ropes cannot push effectively. Trying to push the rope can cause the rope to travel slack, losing the stress (tension) it possesses.  

How to Calculate Tension

Namely, we tend to use Newton’s second law to relate the thing’s motion to the forces concerned. Following Newton’s Second Law of Motion, we demonstrate the summation of forces by using the free-body diagram of the under observation object. Gravity isn’t the only force that may affect the stress (tension) in any rope/rod. Any force associated with the acceleration of an associated object the rope is connected to.

Calculation Step by Step

  • The tension force is often calculated by calculating the force of gravity from the load. Multiply the weight’s mass in kilograms by 10 (9.81 to be precise) m/s2.The result is a force acting in the downward direction in Newton.
  • Determine the result of any acceleration and alternative forces functioning on the rope. Account for forces like angular acceleration and friction.
  • Use free-body diagrams to point out the various directions and magnitudes of the forces that act on a body. Counting on the direction, either add the forces or cipher them from gravity to reach the total stress (tension) on the rope.
  • Determine the tension force using the Newton’s second law of motion equation

Example 1

  1. If the mass suspended is in equilibrium, then the stress (tension T) is analogous to the weight (W) of body T = W.

If you take a rope to suspend a piano that weighs two hundred metric weight (200 kgs) units, calculate tension within the rope.

  1. However, if the body is traveling downward, then the stresses will be T = W – ma.

You pull with a lot of force on a rope to raise a 200-kg piano. However, it hasn’t changed its position. If the piano still exerts a force of five hundred Newton N) on the floor, subtract it from the total energy, 18,600 N.

  1.  If the body is traveling upward, then the stresses will be T = W + ma.

You may use an electric winch to raise a 200-kg piano to the fifth floor of a building; the piano accelerates upward at a rate of one meter per second square (m/s2). If the piano accelerates, the piano’s mass resists being elevated, making a downward force just like gravity.

The spreadsheet solution is given below;

Case 1). a=0 T = mg = 200*9.81 (=E3) in N

Case 2). T = mg-ma (=I3-J3) in N

Case 3). T = mg+ma (=M3+N3) in Newton (N)

Tips for Calculating Tension

  • For most physics’ issues, assume ideal strings – in alternative words, our rope, cable, etc. is thin, massless, and cannot be stretched or broken.
  • Draw the forces exerted on the mass in question to substitute the signs within the equation.
  • Write down Newton’s second law for a direction within which the tension force is directed.

Calculating Tension in Pulleys

Pulleys are simple devices that use a suspended disc to adjust the direction of a rope’s tension force. In a straightforward machine pulley configuration, the rope or cable runs from a suspended weight up to the machine pulley, then right down to another, making two lengths of rope or cable strands. However, tension force in each of the rope sections is equal when forces of various magnitudes are stretching each end of the rope.

Example 2

Let’s say we’ve two weights hanging vertically from a machine in parallel strands. Weight one features a mass of ten kilos, whereas weight two features a mass of five kilos. 

during this case, we’d determine tension as follows:

· T = 2g(m1)(m2)/(m2+m1)

  T = 2(10)(9.81(5)/(5 + 10)

  T = 50(19.6)/(15)

  T = 980/15

  T = 65.34 Newtons


1What is the difference between tension and stress?Tension is a type of force that acts axially when an object is being stretched from its ends, whereas stress results from a force being applied to an object.
2Is it true that tension always acts in the opposite direction of a force applied?This is one of three of Newton’s laws of motion. It applies to any force on an object; there’s an equal force but in the opposite direction.
3If the multiple strands of rope are not perpendicular, how will the measurement be done?Solve the horizontal and vertical elements on an individual basis.
4How does gravity affect the force of tension?Tension acts in the opposite way of gravity. If the mass is hanging, it should be balanced by tension. Otherwise, it’ll accelerate down because of gravity.

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