Table of Contents

**Newton’s Second Law Formula**

**Statement of Newton’s Second Law of Motion:**

Newton’s Second Law states that the force acting on an object is directly proportional to the mass of the object and the **acceleration** produced. If the force acting on an object is increased, the acceleration will also increase, assuming the mass remains constant. Similarly, if the mass of the object is increased, the acceleration will decrease for a given force.

**Formula For Newton’s Second Law of Motion:**

The formula for Newton’s Second Law is expressed as:

F = m x a

where:

F represents the force acting on the object,

m is the mass of the object, and

a is the acceleration produced by the force.

**Meaning of Variables:**

**Force (F):**It represents the physical quantity that causes an object to accelerate or change its state of motion. The SI unit of force is the newton (N).**Mass (m):**It represents the amount of matter contained in an object. The SI unit of mass is the kilogram (kg).**Acceleration (a):**It represents the rate at which the velocity of an object changes per unit of time. The SI unit of acceleration is meters per second squared (m/s²).

**Understanding Newton’s second law using momentum: **

When a net force is applied, the velocity of the object changes and when **velocity **changes, its momentum also changes.

So, net force is nothing but the rate of change of momentum.

Therefore,

Net force = (p2 – p1)/t

where, p1 = initial momentum, p2 = final momentum and t = time taken

The rate of change of momentum of an object is proportional to the applied unbalanced

force in the direction of the force.

Understanding Newton’s second law using momentum

If v is the final velocity and u is the initial velocity,

Net force = (mv – mu) / t (Since p = m x v)

if we denote Net force by F, then

F = m(v – u) / t

v-u is the change in velocity

This means (v-u)/t is the rate of change of velocity; and rate of change of velocity is called

acceleration

(v-u)/t = a

Substituting this value in the above equation, we get,

F = m X a

which is nothing but Newton’s second law of motion.

**Solved Examples of Newton’s Second Law of Motion:**

**Example 1:** A little boy pushes a wagon with his little sister in it. The mass of his sister and wagon together is 50 kg. The wagon accelerates at 0.75 m/s2. What force is the boy pushing with?

Solution:

According to Newton’s second law, Force (F) = m X a

For the given problem, the total mass that the boy is pushing is the sum of the masses of his

little sister and the wagon; which is given as 50 kg.

So, m = 50 kg and the acceleration of the wagon, a = 0.75 m/s2

Substituting these values in the formula of force, we get:

F = 50 kg X 0.75 m/s2

= 37.5 kg m/s2

= 37.5 N

The force with which the boy is pushing the wagon is 37.5 N.

**Example 2:** When hit by a tennis player, a tennis ball weighing 300 grams, is accelerated at a rate of 150 m/s2. What force does the player’s tennis racket exert on the ball?

Solution:

In this problem, the mass of the ball is given in grams. Since the SI unit of force is kg m/s2, the

mass of the ball has to be converted into kilograms.

Therefore, mass of the tennis ball, m = 300 g = 0.3 kg

Acceleration a = 150 m/s2

Now substituting the values in the formula of Force (F) = m X a, we get:

F = 0.3 kg X 150 m/s2

= 45 kg m/s2

= 45 N

The force that the player’s tennis racket exerts on the ball is 45 N.

**FAQs on Newton’s Second Law Formula**

### State Newton’s second law of motion.

Newton’s second law of motion states that Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.

### Write the formula for Newton's 2nd law of motion?

The formula used in Newton's second law of motion is: F = ma Where: F represents the net force applied to an object, m represents the mass of the object, a represents the acceleration of the object. This formula states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, when a net force is applied to an object, it causes the object to accelerate, and the magnitude of that acceleration is determined by the ratio of the force to the mass of the object.

### Why is Newton's second law called real?

Newton's second law is often referred to as the real law of motion because it provides a quantitative relationship between force, mass, and acceleration. Unlike the first law (inertia) that describes the tendency of objects to remain at rest or in uniform motion, the second law introduces the concept of force and its effect on the motion of an object. By stating that the acceleration is directly proportional to the net force and inversely proportional to the mass, Newton's second law provides a mathematical framework to calculate and predict the motion of objects under the influence of forces, making it a fundamental and practical law in physics.

### How is Newton's second law verified?

To verify Newton’s second, an inclined plank is used to observe the motion of an iron ball and an aluminum ball. The iron ball is released from a height on the inclined plank, rolls down, and collides with a lead ball placed on the horizontal plank. The distance moved by the lead ball is noted. The same experiment is then conducted with an aluminum ball, and it is found that the aluminum ball moves a greater distance after being struck by the iron ball. This is due to the fact that the lighter aluminum ball experiences more acceleration when the same force is applied to it compared to the heavier lead ball. Furthermore, when the iron and aluminum balls separately strike a glass marble, it is observed that the iron ball imparts a greater velocity to the marble, indicating that it applies a greater force than the aluminum ball. These observations confirm Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. The relationship F = ma is derived from these experiments, verifying the second law of motion.

### What is Newton's second law of motion known as?

Newton's second law of motion is commonly known as the quantitative law of acceleration. This is because it establishes a quantitative relationship between the force applied to an object, the mass of the object, and the resulting acceleration.

### What are 2 examples of Newton's 2nd law?

Acceleration of a Car: When a car accelerates, the net force acting on the car is the product of its mass and acceleration. According to Newton's second law, the acceleration of the car is directly proportional to the applied force and inversely proportional to its mass. Therefore, a car with a greater force applied to it will experience a greater acceleration, while a car with a larger mass will have a lower acceleration for the same force. Projectile Motion: When an object is thrown into the air, such as a ball or a projectile, the force of gravity acts upon it. According to Newton's second law, the acceleration of the object due to gravity is directly proportional to its mass. Therefore, objects with larger masses experience a greater gravitational force and consequently a greater acceleration towards the ground. This explains why heavier objects, like a cannonball, fall faster than lighter objects, like a feather, in the absence of air resistance.

### What is the SI unit for force?

The SI unit for force is the Newton (N). It is named after Sir Isaac Newton, the physicist who formulated Newton's laws of motion. The Newton is defined as the amount of force required to accelerate a one-kilogram mass by one meter per second squared.

### What is 1 newton equal to?

Answer: One Newton (1 N) is equal to the force required to accelerate a one-kilogram mass by one meter per second squared. Mathematically, it can be expressed as: 1 N = 1 kg x 1 m/s² This means that if a force of 1 Newton is applied to an object with a mass of 1 kilogram, it will experience an acceleration of 1 meter per second squared. In simpler terms, the Newton is a unit of force that represents the amount of push or pull required to cause a certain acceleration on an object with a particular mass.