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# Tension Calculator

Select the number of ropes and provide necessary parameters to calculate the force of tension through the rope/s lifting the object.

Tension Scenario:

Number of Ropes:

Number of Objects Pulled:

Object's Mass:

Second Object's Mass:

Third Object's Mass:

Gravitational:

Angle α:

Angle β:

Pulling Force:

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This online cable tension calculator will assist you in finding tension in a rope or string required to lift an object. You can also find the acceleration of the physical object with which it is displaced while being tied with the rope.

## How Does This Tension Calculator Work?

Get through the guide below that will let you understand the working pattern of this free tension force calculator. Keep reading!

Input:

• From the first drop-down list, select the tension scenario.
• After making a selection, go for entering all the required parameters in their respective fields.
• Also, select the unit against each parameter entered.
• At last, hit the “Calculate” button.

Output:

The calculator helps in:

• Finding tension
• Determining acceleration
• Figuring out components of tension force and tension itself as a whole

## What is a Tension Force?

In the context of physics:

“A particular axial force that travels through a weightless object like rope to hold heavy things against gravity is known as the tension”

Tension is a very important physical phenomenon that follows Newton’s third law of motion that is “To every action, there is an equal but opposite reaction”. Usually materials with high tensile strength are utilized when you need to carry and displace heavier objects. Our online physics tension calculator allows you to figure out the force of tension that is necessary to lift the objects being in a state of rest, no matter how heavy they are.

Otherwise, if the objects are in changing accelerated motion, they keep on changing their direction even if the velocity remains constant. This is where the acceleration changes that could be figured out by using another acceleration calculator.

## Newton’s Second Law of Motion

In the above paragraph, we have discussed variation in acceleration. Here one more factor to consider is the Newton’s second law of motion that lets us know if the force applied on an object displaces it, it will be equivalent to the mass and acceleration product and is given a s follows:

$$F = m*a$$

Keep in mind that if the massive bodies get detach from the rope, they will continue to fall freely under the action of the gravitational pull. And this freefall motion can be analyzed by using the free fall calculator.

Also, we need to consider one more factor here. Which is that we can also consider the object in vacuum where even the mass appears to be zero. Even in this condition, this free cable tension calculator physics will let you understand how much force of tension is acting on the object.

## How to Calculate Tension In Rope Attached to Mass?

### One Rope:

Let us consider the following phenomenon as under:

In the above figure, there is a mass attached to the string and is lifted against gravity. At this point, it is affected by a couple of forces, one is tension and other is the weight. And as the object is in stationary condition, the overall effect of both of these forces becomes zero that is given mathematically as below:

$$ΣF = 0 = T + \left(-W\right)$$

As the above tension equation physics is the basic form of horizontal tension formula and contains two forces against each other, we can move one of these to the other side of the equation to verify that both of them are also equivalent to each other. And this equivalency is what keeps the object in the state of rest that is stationary. Our free online tension calculator physics also goes for finding tension in such a state. And the above formula becomes:

$$T = W$$

### Two Ropes:

Now look at the figure below:

In the pictorial representation, we have the same mass attached to a couple of strings. Now in this condition, the overall tension in both ropes depends upon the angles of the strings and the components of the angles in terms of trigonometric ratios. As we know only vertical components are there along which the tension acts, we will consider them here for computations:

$$ΣF = 0 = T_1y + T_2y + (-W)$$

$$W = T_1y + T_2y$$

$$\text{Horizontal Components} = T_1x, T_2x$$

$$\text{Vertical Components} = T_1y, T_2y$$

Now in terms of the trigonometric ratios, we have another expression of these vertical components:

$$T_1y = T_1 * sin\left(α\right)$$

$$T_2y= T_2 * sin\left(β\right)$$

$$W = T_1 * sin\left(α\right) + T₂_2 * sin\left(β\right)$$

Coming to the horizontal components of the angle that are given above, they tend to become zero as there will be no motion along this axis when the mass is lifted by a rope. And in this condition, the best online physics tension calculator will let you observe the force of tension along the vertical axis only. However, we will go through the trigonometric ratios as described for the parallel plane as well:

$$T_1x = T_2x$$

$$T_1 * cos\left(α\right) = T_2 * cos\left(β\right)$$

Now dividing the whole above tension equation physics by the term $$cos\left(\alpha\right)$$ will generate new expression for T_1 in terms of T_2

$$T_1 = T_2 * \frac{cos\left(β\right)}{cos\left(α\right)}$$

Now the overall sum of forces in terms of weight is given as below:

$$W = T_1 * sin\left(α\right) + T_2 * sin\left(β\right)$$

$$W = T_2 * [\frac{cos\left(β\right)}{cos\left(α\right)}] * sin\left(α\right) + T_2 * sin\left(β\right)$$

$$W = T_2 * [\frac{cos\left(β\right) * sin\left(α\right)}{cos\left(α\right) + sin\left(β\right)}]$$

$$T_2 = \frac{W}{[cos\left(β\right) * \frac{sin\left(α\right)}{cos\left(α\right) + sin\left(β\right)}]}$$

Similarly for T_1, we have:

$$T_1 = \frac{W}{[\frac{cos\left(β\right) * sin\left(α\right)}{cos\left(α\right) + sin\left(β\right)}] * [\frac{cos\left(β\right)}{cos\left(α\right)}]}$$

$$T_1 = \frac{W}{[\frac{cos\left(β\right) * sin\left(α\right)}{cos\left(α\right) + sin\left(β\right)}] * [\frac{cos\left(β\right)}{cos\left(α\right)}]}$$

$$T_1 = \frac{W}{[\frac{cos\left(α\right) * sin\left(β\right)}{cos\left(β\right) + sin\left(α\right)}]}$$

## How to Calculate Tension?

Get going to have a look at the examples below to understand the concept of the topic in more detail. Stay focused!

Example:

Suppose Jack lifts up a mass of about 45 kg with the help of a rope. Considering the acceleration zero, how to calculate tension force?

Solution:

Finding tension:

$$\text{Tension formula} = T = m*a + m*g$$

$$\text{Tension formula} = T = 45*0 + 45*9.8$$

$$\text{Tension formula} = T = 441N$$

You can also verify the values by using our free rope tension calculator physics.

## FAQ’s:

### How to Calculate the Tension of a Rope at any Angle?

Follow the below-mentioned steps to calculate the tension of a rope at any angle:

• When the rope is set, find the angle from horizontal.
• Multiply the applied force by the cosine of the angle to get the horizontal component.
• Multiply the applied force by the sin of the angle to get the vertical component.
• The total magnitude can be calculated by adding vertical and horizontal components.

### How to Calculate the Tension Produced by a 10kg Box on Two Ropes Suspended at 60 Degrees?

• Find the vertical and horizontal components of the tensile forces.
• You can balance the weight by using a vertical component.
• To balance each other, the horizontal component will be helpful.
• Solve both of the equations to get the answer.

### How do I find tension in two ropes at the same angle of suspension?

If such a condition arises when the suspension angle for the ropes become equal, the tension in both of them also becomes equal.

### Is tension a contact force?

Yes definitely! As the force of tension travels from one end to another through a massless rope, it is considered as the contact force.

## References:

From the source of Wikipedia: Tension (physics), System in equilibrium, System under net force

From the source of Khan Academy: The force of tension, Super hot tension, Tension in an accelerating system and pie in the face, Mild and medium tension

From the source of Lumen Learning: Normal Force, Tension, and Other Examples of Forces, Normal Force, Tension, Real Forces and Inertial Frames, Problem-Solving Strategies