**Spring force** is the force exerted by a compressed or stretched spring upon any object that is attached to it. This force acts to return the spring to its natural length, pulling objects back when stretched and pushing them back when compressed. For example, when you stretch a spring by pulling its ends apart, you feel the spring pulling back towards its original position. Conversely, when you compress the spring by pushing its ends together, it pushes back against the compression. This force is at play in various everyday objects, such as the suspension systems in vehicles, which absorb shocks from the road, and in mechanical pens, where the spring enables the pen to retract and extend.

The equation for spring force, described by Hooke’s law, is given by:

$$F = -kx$$where F is the spring force, k is the spring constant (a measure of the stiffness of the spring), and x is the displacement of the spring from its equilibrium position. The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement, acting to restore the spring to its natural length.

## Practice problems

### Problem #1

Calculate the force exerted by a spring on a block when the block, attached to a spring with a natural length of 25 cm, moves rightwards and stretches the spring by 50 cm. The spring constant is 75 N/m.

**Solution**

Given data:

- Force exerted by spring on a block, F
_{s}= ? - Initial length of a spring, x
_{0}= 25 cm = 0.25 m - Final length of a spring, x = 50 cm = 0.5 m
- Spring constant, k = 75 N/m

Applying the formula:

- F
_{s}= k Δx = k × (x – x_{0}) - F
_{s}= 75 × (0.5 – 0.25) - F
_{s}= 75 × 0.25 - F
_{s}= 18.75 N

Therefore, the force exerted by spring on a block is **-18.75 N**. (left)

### Problem #2

Determine the force exerted by a spring on a block when the block, attached to a spring with a natural length of 15 cm, moves leftwards and compresses the spring by 5 cm. The spring constant is 55 N/m.

**Solution**

Given data:

- Force exerted by spring on a block, F
_{s}= ? - Initial length of a spring, x
_{0}= 15 cm = 0.15 m - Final length of a spring, x = 5 cm = 0.05 m
- Spring constant, k = 55 N/m

Applying the formula:

- F
_{s}= k Δx = k × (x – x_{0}) - F
_{s}= 55 × (0.05 – 0.15) - F
_{s}= 55 × (-0.01) - F
_{s}= -5.5 N

Therefore, the force exerted by spring on a block is **5.5 N**. (right)

### Problem #3

A spring is in equilibrium, with its left end fixed to a wall and its right end fixed to a wooden crate. When the wooden crate is moved to the right, the spring stretches from a length of 0.5 m to 0.65 m. Calculate the force exerted by the spring on the wooden crate, given that the spring constant is 150 N/m.

**Solution**

Given data:

- Initial length of a spring, x
_{0}= 0.5 m - Final length of a spring, x = 0.65 m
- Force exerted by spring on a wooden crate, F
_{s}= ? - Spring constant, k = 150 N/m

Applying the formula:

- F
_{s}= k Δx = k × (x – x_{0}) - F
_{s}= 150 × (0.65 – 0.5) - F
_{s}= 150 × (0.15) - F
_{s}= 22.5 N

Therefore, the force exerted by spring on a wooden crate is **-22.5 N**. (left)

### Problem #4

A spring is in equilibrium, with its left end fixed to a wall and its right end fixed to a wooden crate. When the wooden crate is moved to the left, the spring compresses from a length of 0.5 m to 0.2 m. Calculate the force exerted by the spring on the wooden crate, given that the spring constant is 170 N/m.

**Solution**

Given data:

- Initial length of a spring, x
_{0}= 0.5 m - Final length of a spring, x = 0.2 m
- Force exerted by spring on a wooden crate, F
_{s}= ? - Spring constant, k = 170 N/m

Applying the formula:

- F
_{s}= k Δx = k × (x – x_{0}) - F
_{s}= 170 × (0.2 – 0.5) - F
_{s}= 170 × (-0.3) - F
_{s}= -51 N

Therefore, the force exerted by spring on a wooden crate is **51 N**. (right)

## More topics

- Compression (physics)
- Net force
- Magnetism
- Centripetal force
- Centrifugal force
**Spring force**- Tension (physics)
- Electric force

## External links

- Hooke’s law – University of Tennessee, Knoxville
- How to Calculate the Force of a Spring on an Object – Study.com
- Spring potential energy and Hooke’s law review (article) – Khan Academy
- How to Calculate Spring Force – Sciencing
- Hooke’s law – Wikipedia
- Spring Force Calculator Online – The Spring Store
- How to Calculate a Spring Constant Using Hooke’s Law – Dummies
- Hooke’s Law and Spring Force – StickMan Physics
- Hooke’s Law Calculator – Omni Calculator
- Hooke’s Law Calculator F = -kx – Calculator Soup
- 4.5 Normal, Tension, and Spring Forces – BCcampus Pressbooks
- AP Physics 1 : Spring Force – Varsity Tutors
- 2.7: Spring Force- Hooke’s Law – Physics LibreTexts
- Work by Variable Force, and Spring Force – Rochester Institute of Technology
- Motion of a Mass on a Spring – The Physics Classroom
- Spring Force: Definition, Formula & Examples – Vaia
- Hooke’s law – Xaktly
- A Hooke’s Law Spring Determine the Spring Constant – Temple Mathematics
- Calculate the Spring Constant Using Hooke’s Law: Formula, Examples, and Practice Problems – wikiHow
- Constant Force Spring Design Equations and Calculator – Engineers Edge
- Spring Force: Definition, Formula, and Examples – Science Facts
- Spring Constant Formula – SoftSchools.com

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.