How to Apply the Tension Formula in Physics Problems
When does force take place? If two bodies are in physical contact, then we notice that they apply forces on each other. Well, what’s in it for tension? Have you ever pulled something up or toward you using a rope? If you do, you are putting the rope in tension.
This article will explain how all of these processes are executed? When a body is in contact with a rope, string, cable, or spring, all of these objects are going through tension. We can also calculate the tension in string formula with ease.
Dimensional Formula of Tension
Tension is a type of force that acts along the length of the medium such as rope or string. A force is necessary to put these objects under tension. Tension is also named something exciting, i.e. action-reaction pair.
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The Tension Dimensional Formula = [M1 L1 T-2]
Tension is nothing, but it’s a force that has got another improved name. Tension acts at both the end of the string (from the above picture). The tension force is available on each point of the string.
Tension Force Formula
You can calculate the tension formula on a body by the summation of the product of mass and gravitational force along with the product of mass and acceleration.
So, the tension equation is equal to T = mg + ma
Tension Force Examples
Let’s solve a question.
Q. Find the tension on a string if it is dangled with a brick of 10 kg. Acceleration is 3 m/s2 in the upward direction.
Ans: Data are given, m = mass of the brick = 10 Kg
When the brick is getting an upward acceleration, the Tension Formula Physics is expressed as
T (Tension in A String Formula) = mg + ma
= 10 × 9.8 + 10 × 3 = 128 N
Surface Tension Equation
Surface tension is defined as a phenomenon that happens when a phase has made the interaction with the surface of a liquid. The other phase can also be a liquid. Liquids tend to occupy the least surface area. They behave like elastic sheets.
The formula for the surface tension is:
ℽ = ½ . F/L
Here, T = Surface Tension of the liquid
L = length on which the force exerts
F = force per unit length
Tension Formula Pulley
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If the wedge of mass (m) is heaved upwards by two forces of F and T, then the mg will be alike the sum of F and T. So,
2F = mg
or F = mg / 2
FAQs on Tension Formula Explained with Examples
1. What is tension force in Physics, and how is it generated?
In physics, tension is a pulling force transmitted axially by means of a string, cable, chain, or similar one-dimensional continuous object. It is generated when forces pull on opposite ends of an object, causing it to stretch or become taut. Tension always acts along the length of the string or cable, pulling the objects it is connected to inwards towards the center of the string.
2. What is the standard formula used to calculate tension?
The formula for tension (T) depends on the motion of the object it supports. The main variations are:
For a stationary object (at equilibrium): The tension equals the force of gravity. The formula is T = mg.
For an object accelerating upwards: The tension must overcome gravity and provide for the acceleration. The formula is T = mg + ma.
For an object accelerating downwards: Gravity is assisted by the downward acceleration, reducing the tension. The formula is T = mg - ma.
Here, 'm' is the mass, 'g' is the acceleration due to gravity (approx. 9.8 m/s²), and 'a' is the acceleration of the object.
3. How does the tension in a string change when the object it supports accelerates?
The tension in a string is not always equal to the weight of the object it supports. When the object accelerates, the net force changes, which directly affects the tension. If an elevator accelerates upwards, you feel heavier because the tension in the cable must support your weight AND provide the upward force for acceleration (T = mg + ma), making tension greater than the weight. Conversely, when it accelerates downwards, you feel lighter because the tension required is less than the weight (T = mg - ma).
4. What is the SI unit of tension, and what are its dimensions?
Since tension is a type of force, its SI unit is the Newton (N). The dimensional formula for tension is the same as that for force, which is [MLT⁻²], where M represents mass, L represents length, and T represents time.
5. Provide a real-world example where understanding the tension formula is crucial.
A crucial real-world application of the tension formula is in civil engineering, specifically in the design of bridges and cranes. For a crane lifting a heavy container, engineers must calculate the maximum tension the cable will experience. This occurs not just when holding the load stationary (T=mg), but especially when accelerating it upwards (T=mg+ma). The cable must be strong enough to withstand this maximum tension to prevent snapping and ensure safety.
6. Why can tension only be a pulling force and not a pushing force?
Tension can only be a pulling force because of the physical nature of the objects that transmit it, like strings, ropes, or chains. These objects are flexible and can only transfer a force when they are pulled taut. If you try to push an object with a rope, the rope will simply go slack and bend, failing to transmit any force. The force of compression, which is the opposite of tension, requires a rigid object like a rod or a pillar.
7. What is the difference between tension in a massless string and a string that has mass?
In introductory physics problems, strings are often assumed to be massless. In a massless string, the tension is uniform throughout its entire length. However, in a real-world string that has mass, the tension is not uniform. For a vertical hanging string with mass, the tension is greatest at the top (where it supports the entire string's weight plus any attached object) and decreases as you move down, becoming lowest at the bottom.
