**Newton’s second law** of motion, formulated by Sir Isaac Newton, describes the relationship between the acceleration of an object, the force applied to it, and its mass. According to this law, the acceleration of an object is directly proportional to the force exerted on it and inversely proportional to its mass. In simpler terms, when a net force acts on an object, it causes the object to accelerate in the direction of the force. The greater the force applied, the greater the resulting acceleration. Conversely, an object with a larger mass will experience a smaller acceleration for the same force. This law provides a fundamental understanding of how forces influence the motion of objects and is essential in various fields of physics and engineering.

## Examples

### Horse-drawn vehicle

Newton’s second law of motion is exemplified when a horse pulls a horse-drawn vehicle. According to this law, the acceleration of an object is directly proportional to the net force exerted on it and inversely proportional to its mass. In the case of a single horse pulling the vehicle, the lower net force, coupled with the greater mass of the vehicle, leads to a slower acceleration. However, when multiple horses work together to pull the vehicle, the combined net force increases, overpowering the greater mass and resulting in a higher acceleration. This illustrates how Newton’s second law showcases the relationship between net force, mass, and acceleration in the context of a horse-drawn vehicle.

### Ball

Newton’s second law of motion is evident when comparing the impact of a bat hitting a tennis ball and a football. According to this law, the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. In the case of the bat striking the tennis ball, the lower mass of the tennis ball results in a greater acceleration when the same force is applied compared to the football. This is because the smaller mass of the tennis ball allows for a more significant change in velocity in response to the force applied by the bat. On the other hand, the football, with its higher mass, experiences a smaller acceleration for the same applied force. The greater mass of the football resists a rapid change in velocity, leading to a smaller acceleration compared to the tennis ball. This example highlights how Newton’s second law demonstrates that a smaller mass allows for a greater acceleration when the same force is applied.

### Car

Newton’s second law of motion is exemplified in the scenario of pushing a car. This law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. When a single person applies a force to push the car, the resulting acceleration is slower due to the car’s greater mass. The larger mass resists a rapid change in velocity, requiring a higher force to achieve a significant acceleration. However, when multiple people join in to push the car, the combined force increases, resulting in a greater net force and subsequently a higher acceleration. This example demonstrates how Newton’s second law establishes a clear connection between the net force, the mass of the object being pushed, and the resulting acceleration. It highlights the importance of considering both force and mass when determining the acceleration of an object.

### Box

Newton’s second law describes the relationship between mass, force, and acceleration when pushing objects. According to this law, the acceleration of an object is inversely proportional to its mass. For example, when equal force is applied to two boxes of different masses, the box with less mass will experience greater acceleration compared to the box with greater mass. In simpler terms, lighter objects accelerate more easily than heavier objects when the same force is applied. This illustrates how Newton’s second law helps us understand the influence of mass on an object’s acceleration during pushing tasks.

## Equation

**Newton’s second law equation**, commonly represented as a = F_{net}/m, describes the relationship between the acceleration (a) of an object, the net force (F_{net}) acting upon it, and its mass (m). This equation states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. By utilizing this equation, one can gain insights into how changes in net force and mass influence the acceleration of an object. This equation serves as a valuable tool for analyzing and predicting the motion of objects under the influence of external forces.

### Practice problems

#### Problem #1

Determine the acceleration of a trolley weighing 100 kg when a net force of 50 N is applied to it.

**Solution**

Given data:

- Acceleration of a trolley, a = ?
- Mass of a trolley, m = 100 kg
- Net force applied to a trolley, F
_{net}= 50 N

Using the equation:

- a = F
_{net}/m - a = 100/50
- a = 2 m/s
^{2}

Therefore, the acceleration of a trolley is **2 m/s**** ^{2}**.

#### Problem #2

Find the acceleration of a tire weighing 2 kg when a net force of 8 N is acting on it.

**Solution**

Given data:

- Acceleration of a tire, a = ?
- Mass of a tire, m = 2 kg
- Net force applied to a tire, F
_{net}= 8 N

Using the equation:

- a = F
_{net}/m - a = 8/2
- a = 4 m/s
^{2}

Therefore, the acceleration of a tire is **4 m/s**** ^{2}**.

#### Problem #3

If a net force of 10 N is applied to a crate with a mass of 5 kg, what is the acceleration of the crate?

**Solution**

Given data:

- Net force applied to a crate, F
_{net}= 10 N - Mass of a crate, m = 5 kg
- Acceleration of a crate, a = ?

Using the equation:

- a = F
_{net}/m - a = 10/5
- a = 2 m/s
^{2}

Therefore, a crate accelerates forward at the rate of **2 m/s**** ^{2}**.

#### Problem #4

Given that a car with a mass of 1,000 kg experiences a net force of 100 N, what is the acceleration of the car?

**Solution**

Given data:

- Mass of a car, m = 1,000 kg
- Net force experienced by a car, F
_{net}= 100 N - Acceleration of a car, a = ?

Using the equation:

- a = F
_{net}/m - a = 1,000/100
- a = 10 m/s
^{2}

Therefore, the acceleration of a car is **10 m/s**** ^{2}**.

## Related

- Frame of reference
- Newton’s first law
**Newton’s second law**- Newton’s third law

## More topics

- Balanced force
- Unbalanced force
- Friction
- Tension (physics)
- Applied force
- Normal force
- Drag (physics)
- Gravity
- Centripetal force
- Centrifugal force
- Buoyancy
- Net force
- Compression (physics)

## External links

- Newton’s Second Law of Motion – The Physics Classroom
- Newton’s laws of motion – Wikipedia
- Newton’s Laws of Motion – NASA (.gov)
- What is Newton’s second law? (article) – Khan Academy
- Science in Action: Newton’s Second Law of Motion – Space Center Houston
- Newton’s laws of motion – Force, Mass, Acceleration – Britannica
- 4.3 Newton’s Second Law of Motion: Concept of a System – OpenStax
- Force, Mass & Acceleration: Newton’s Second Law of Motion – Live Science
- Newton’s Second Law of Motion – Turito
- Newton’s Second Law of Motion – Indianapolis Public Library
- Newton’s Laws: Force and Acceleration – Texas Gateway
- 4.3 Newton’s Second Law of Motion: Concept of a System – IU Pressbooks
- Newton’s Second Law – Mechanics Map
- Newtons Second Law – Jack Westin
- Newton’s Second Law – ScienceDirect
- What is Newton’s Second Law of Motion? (Video) – Mometrix Test Preparation
- Law of Force and Acceleration – Newton’s Second Law of Motion – Brightstorm
- What Is Newton’s Second Law? – Teach Engineering
- Lesson Explainer: Newton’s Second Law of Motion – Nagwa
- Newton’s Second Law: Definition, Equation & Examples – Vaia
- Newton’s Second Law – Isaac Physics
- How Newton’s Laws of Motion Work – HowStuffWorks
- What is Newton’s second law of motion? – The Guardian
- Newton’s Second Law of Motion | Overview & Examples – Study.com
- Newton’s Second Law of Motion – The University of Texas at Austin
- Newton’s second law – Examples – Mammoth Memory
- Newton’s Second Law – Wolfram Demonstrations Project
- 5.3 Newton’s Second Law – UCF Pressbooks
- High School Physics : Understanding Newton’s Second Law – Varsity Tutors
- Newton’s Laws – University of Toronto
- 2.6 Newton’s Second Law – Fiveable
- Newton’s second law – BBC
- Motion and Forces: Newton’s Second Law of Motion – Perkins School For The Blind
- Newton’s second law – The Free Dictionary
- What is Newton’s Second Law of Motion? – Interesting Engineering
- Newton’s Second Law Calculator – Omni Calculator

Deep

Forceinphysics.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.