The **tension force formula**, used to calculate the force exerted by a string, rope, or cable, is given by F_{T} = mg ± ma, where F_{T} represents the tension force, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object. This formula allows for the accurate determination of the tension force acting on an object in various scenarios.

When an object is moving upward, the tension force is given by F_{T} = mg + ma, taking into account the additional force required to overcome gravity and accelerate the object upward. Conversely, when the object is moving downward, the tension force is expressed as F_{T} = mg – ma, accounting for the opposing forces of gravity and the acceleration of the object in the downward direction. Finally, when the object is at rest, the tension force is equal to the weight of the object, resulting in F_{T} = mg.

## Practice problems

### Problem #1

A wooden block with a mass of 2 kg is hanging from a rope. If the block is assumed to be accelerating upward at a rate of 25 m/s^{2}, calculate the tension force acting on the block. Take the value of gravitational acceleration, g, to be 9.81 m/s^{2}.

**Solution**

Given data:

- Mass of a wooden block, m = 2 kg
- Acceleration of a wooden block, a = 25 m/s
^{2} - Tension force acting on a wooden block, F
_{T}= ? - Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula, when an object is moving upward:

- F
_{T}= mg + ma - F
_{T}= (2 × 9.81) + (2 × 25) - F
_{T}= 19.62 + 50 - F
_{T}= 69.62 N

Therefore, the tension force acting on a wooden block is **69.62 N**.

### Problem #2

An 8 kg block is attached to a string and is accelerating downward at a rate of 5 m/s^{2}. Determine the tension force acting on the block.

**Solution**

Given data:

- Mass of a block, m = 8 kg
- Acceleration of a block, a = 5 m/s
^{2} - Tension force acting on a block, F
_{T}= ?

Applying the formula, when an object is moving downward:

- F
_{T}= mg – ma - F
_{T}= (8 × 9.81) – (8 × 5) - F
_{T}= 78.48 – 40 - F
_{T}= 38.48 N

Therefore, the tension force acting on a block is **38.48 N**.

### Problem #3

What is the tension force acting on a rubber tire with a mass of 2 kg that is hanging from a rope? Assuming the rubber tire is stationary and not accelerating.

**Solution**

Given data:

- Mass of a rubber tire, m = 2 kg
- Tension force acting on a rubber tire, F
_{T}= ?

Applying the formula, when an object is at rest:

- F
_{T}= mg - F
_{T}= 2 × 9.81 - F
_{T}= 19.62 N

Therefore, the tension force acting on a rubber tire is **19.62 N**.

### Problem #4

Calculate the tension force acting on a 4 kg box in the following scenarios:

(a) When the box is moving upward with an acceleration of 8 m/s^{2}.

(b) When the box is moving downward with an acceleration of 6 m/s^{2}.

(c) When the box is at rest.

**Solution**

Given data:

- Mass of a box, m = 4 kg
- Tension force acting on a box, F
_{T}= ?

**(a)** When the box is moving upward with an acceleration of 8 m/s^{2}

- Acceleration of a box, a = 8 m/s
^{2}

Applying the formula, when an object is moving upward:

- F
_{T}= mg + ma - F
_{T}= (4 × 9.81) + (4 × 8) - F
_{T}= 39.24 – 32 - F
_{T}= 7.24 N

Therefore, the tension force acting on a box is **7.24 N**.

**(b)** When the box is moving downward with an acceleration of 6 m/s^{2}

- Acceleration of a box, a = 6 m/s
^{2}

Applying the formula, when an object is moving downward:

- F
_{T}= mg – ma - F
_{T}= (4 × 9.81) – (4 × 6) - F
_{T}= 39.24 – 24 - F
_{T}= 15.24 N

Therefore, the tension force acting on a box is **15.24 N**.

**(c)** When the box is at rest

Applying the formula, when an object is at rest:

- F
_{T}= mg - F
_{T}= 4 × 9.81 - F
_{T}= 39.24 N

Therefore, the tension force acting on a box is **39.24 N**.

## Related

- Force equation
- Normal force equation
- Net force formula
- Applied force formula
- Magnetic force equation
- Centripetal force equation
- Centrifugal force equation
- Spring force equation
**Tension force formula**- Electric force equation

## External links

- 3 Ways to Calculate Tension in Physics – wikiHow
- What is tension? (article) – Khan Academy
- Tension Calculator – Omni Calculator
- Tension Formula – SoftSchools.com
- How can i calculate force of tension? + Example – Socratic
- Tension in Strings: Equation, Dimension & Calculation – Vaia
- Tension (Physics): Definition, Formula, How to Find (w/ Diagrams & Examples) – Sciencing
- Calculating the Net Tension Force from Multiple Forces Acting on an Object – Study.com
- 4.5 Normal, Tension, and Other Examples of Forces – OpenStax
- 2.6: Normal Force and Tension – Physics LibreTexts
- Tension (Tension Force): Definition, Formula, and Examples – Science Facts
- Tension (physics) – Wikipedia
- How to Find the Force of Tension – Physics Calculations
- Lifting a Mass – HyperPhysics Concepts
- How To Find Tension Force With Acceleration: Steps, Problem Examples – Lambda Geeks
- Tension Formula| Daily Life Examples – What’s Insight
- How to calculate force of tension – The Tech Edvocate
- (Physics) Tension in a rope and normal force – Wyzant
- Tension Spring Force Calculation – The Spring Store
- Tension: Force That Results From Stretching – StickMan Physics
- How to calculate the force of tension in a pulley system – Quora

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.