# Newton’s second law

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.

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## 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, and requires a higher force to achieve a significant acceleration. As more people join forces to push the car, the total exerted force increases. This greater net force results in a subsequent increase in the car’s 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 = Fnet/m, describes the relationship between the acceleration (a) of an object, the net force (Fnet) 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 using this equation, we can explore the relationship between changes in net force, mass, and the resulting 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, Fnet = 50 N

Using the equation:

• a = Fnet/m
• a = 100/50
• a = 2 m/s2

Therefore, the acceleration of a trolley is 2 m/s2.

#### 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, Fnet = 8 N

Using the equation:

• a = Fnet/m
• a = 8/2
• a = 4 m/s2

Therefore, the acceleration of a tire is 4 m/s2.

#### 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, Fnet = 10 N
• Mass of a crate, m = 5 kg
• Acceleration of a crate, a = ?

Using the equation:

• a = Fnet/m
• a = 10/5
• a = 2 m/s2

Therefore, a crate accelerates forward at the rate of 2 m/s2.

#### 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, Fnet = 100 N
• Acceleration of a car, a = ?

Using the equation:

• a = Fnet/m
• a = 1,000/100
• a = 10 m/s2

Therefore, the acceleration of a car is 10 m/s2.