# Newton's 2nd Law of Motion with Examples

## Introduction to Newton's 2nd Law of Motion

**Newton’s 2nd law of motion **originated from the lap of Newton’s first law of motion, the law of inertia. The law of inertia is the resistance of a thing to change in itself. Inertia is proportional to the mass of a thing. If we apply a force on an object, the object will resist the change in itself. If the change is supposed as a change in the velocity of the object since the object has mass also, therefore, the change will be in its momentum. According to the 2nd law of Newton’s, the force is directly proportional to the rate of change in momentum and concluded to the fact that the acceleration produced on the object is inversely proportional to the mass.

2nd law of motion is among Newton’s three laws of motion, the 2nd law of motion is the relationship between mass and acceleration. Newton’s 2nd law of motion states that the force is proportional to the rate of change of momentum, and mass is always constant, so we can also say the force is proportional to the acceleration.

## The Mathematical Formulation of the Newton's 2nd Law of Motion

Newton’s 2nd Law of Motion is expressed mathematically as:

**F = ma **

where:

represents the net force applied to the object,**F**denotes the mass of the object,**m**stands for the acceleration of the object.**a**

This equation indicates that the force applied to an object is directly proportional to the acceleration it experiences and inversely proportional to its mass.

## Newton's 2nd Law of Motion Examples

### 1. Newton's 2nd Law of Motion in Car

In the car, Newton’s 2nd law of motion is very important for understanding how cars move. Engineers use this law to figure out the forces needed for speeding up, slowing down, and turning, which helps make cars safe and effective.

### 2. Newton's 2nd Law of Motion in Space Travel

In space travel, engineers rely on Newton’s 2nd Law to calculate the forces that affect planes and rockets. This law helps determine the thrust needed for takeoff, the forces during flight, and the slowing down needed for a safe landing.

### 3. Newton's 2nd Law of Motion in Sports

In sports, understanding the relationship between force, mass, and speed is key to improving athletic performance. Coaches and trainers use this law to enhance athletes’ techniques in activities like running, jumping, and throwing.

## Examples of Newton's 2nd Law of Motion in Everyday Life

### 1. Newton's 2nd Law of Motion in Driving a Car

When driving a car, pressing the gas pedal increases the force on the car, making it speed up. The car’s weight and the force applied determine how fast it accelerates.

### 2. Newton's 2nd Law of Motion in Lifting Objects

When driving a car, pressing the gas pedal increases the force on the car, making it speed up. The car’s weight and the force applied determine how fast it accelerates.

## Additional Questions Explained by Newton's 2nd Law of Motion

- If mass changes with the change in velocity then how will you explain the 2nd law of motion?
- Do you know why the moon revolves around the earth and not the earth does the same around the moon?
- Where does your energy go out when you push a truck and truck doesn’t move.
- How does the Earth spin around its own axis?

All these questions can be answered using Newton’s 2nd law of motion.

## Understanding Newton's 2nd Law of Motion with another Example

Observe two stones one is heavier than the other one, and throw them one by one, of course, you can through the lighter object up to more distance as compared to a heavier object. To understand this we have to go through Newton’s 2nd law of motion.

Suppose an object with mass m moves with velocity u and due to an external force applied on it its velocity changes to v in time t.

∵ The momentum (p) = mass × velocity

Initial momentum = mu and final momentum = mv

Change in momentum = mv – mu

The time is taken t to achieve the momentum mv from mu

The rate of change in momentum =(mv -mu)/t

According to Newton’s 2nd law of motion, the force(F) is directly proportional to the rate of change of momentum.

F∝ (mv -mu)/t

F∝ m(v -u)/t

Since (v -u)/t = a

F ∝ ma

F = kma

k is the constant of proportionality.

Evaluation of k- As we know 1N force is defined as the force which accelerates an object of mass 1kg by 1 m/s². So,if F = 1N, m =1kg and a = 1m/s²

from the above equation f = kma, 1N = kg.m/s²

k = F/ma = 1N/(1kg× 1m/s²) = 1NKg-1m-1s²

Therefore substituting the value of k =1, the equation become

F = ma

This is the equation of Newton’s 2nd law of motion, which tells us answers of all the above questions mentioned in the first paragraph of this post.

## Applying Newton's 2nd Law of Motion to Changing Mass

The 2nd law of Newton states that an external force applied on an object of mass which results to accelerate the object from u to v, here mass is constant, then what do you think in the case where mass is not constant, as an example a vehicle moves from the position (u) to position (v), at the expense of fuel inside it, definitely its mass also changes. Actually, Newton 2nd law of motion tells about change in momentum means the change in the product of mass and velocity (mv) and not about the individual changes in velocity or mass. Therefore with the loss of fuel how much velocity of vehicle increases, we should have to consider that.

### Newton's 2nd Law of Motion in Pushing a Truck

If we push a truck by applying a muscular force but the truck doesn’t move as it is requiring significant changes in the momentum of the truck (mv–mu) , the force applied by us generates energy which is absorbed by truck in the form of potential energy and rest of energy transferred to the environment as an example heat and sweats generated by our body.

### Newton's 2nd Law of Motion in Comparing Two Objects

Newton’s 2nd law of motion F = ma tells us if we apply the same force on two objects one is lighter and another one heavier then the lighter object will be accelerated more as compared with the heavier object, as an example stones of 4 kg and 2 kg are thrown by a force of 5 N.Let the accelerations produced by the force 5N on them are a1 and a2 .

a1 = F/m = 5/2 =2.5 m/s²,a2 = 5/4 =1.25 m/s²

Thus the lighter object i.e of 2 kg will be accelerated more and hence transported to more distance.

The fact explained above is also applicable in the case of moon revolves around the earth and not the earth around the moon.

### Newton's 2nd Law of Motion in Moon and Earth

The moon and the earth attract each other by the same gravitational force, moon revolves around the earth but the earth does not revolve around the moon because the mass of the moon is lesser than the earth, the moon is accelerated relative to the earth, it is that’s why moon revolves around the earth.

### Newton's 2nd Law of Motion in Earth's Spin

The cause of the earth spin around its own axis is, newton’s rotational version of the second law of motion τ = I. α where I is inertia= mr² (r radius of the earth) and α is angular momentum, τ is torque. The torque τ is responsible for the spinning of the earth around its own axis.

## Frequently Asked Questions (FAQ's) - Newton's 2nd Law of Motion

Newton’s 2nd law of motion originated from the lap of Newton’s first law of motion, the law of inertia. The law of inertia is the resistance of a thing to change in itself. Inertia is proportional to the mass of a thing. If we apply a force on an object, the object will resist the change in itself. If the change is supposed as a change in the velocity of the object since the object has mass also, therefore, the change will be in its momentum. According to the 2nd law of Newton’s, the force is directly proportional to the rate of change in momentum and concluded to the fact that the acceleration produced on the object is inversely proportional to the mass.

2nd law of motion is among Newton’s three laws of motion, the 2nd law of motion is the relationship between mass and acceleration. Newton’s 2nd law of motion states that the force is proportional to the rate of change of momentum, and mass is always constant, so we can also say the force is proportional to the acceleration.

Newton’s 2nd law says that if you push something harder, it will move faster. And if something is heavier, you need to push harder to make it move at the same speed as something lighter.

Newton’s 2nd Law of Motion is called the law of momentum.

Newton’s 2nd law of motion originated from the lap of Newton’s first law of motion, the law of inertia. The law of inertia is the resistance of a thing to change in itself. Inertia is proportional to the mass of a thing. If we apply a force on an object, the object will resist the change in itself. If the change is supposed as a change in the velocity of the object since the object has mass also, therefore, the change will be in its momentum. According to the 2nd law of Newton’s, the force is directly proportional to the rate of change in momentum and concluded to the fact that the acceleration produced on the object is inversely proportional to the mass.

2nd law of motion is among Newton’s three laws of motion, the 2nd law of motion is the relationship between mass and acceleration. Newton’s 2nd law of motion states that the force is proportional to the rate of change of momentum, and mass is always constant, so we can also say the force is proportional to the acceleration.

Newton’s 2nd Law of Motion is expressed mathematically as:

**F = ma **

where:

represents the net force applied to the object,**F**denotes the mass of the object,**m**stands for the acceleration of the object.**a**

This equation indicates that the force applied to an object is directly proportional to the acceleration it experiences and inversely proportional to its mass.

**Here are five simple examples of Newton’s 2nd Law of Motion:**

**Pushing a Car:**When you push a car that isn’t moving, the harder you push, the faster it starts to move. This is because the force you apply (pushing force) makes the car accelerate (start moving), depending on how heavy the car is.**Kicking a Soccer Ball:**When you kick a soccer ball, how far and fast it goes depends on how hard you kick it. A stronger kick (more force) makes the ball accelerate more quickly (move faster).**Braking a Bicycle:**When you squeeze the brakes on a bicycle, how quickly you slow down depends on how hard you press the brakes. The harder you press (more force), the faster you slow down (more deceleration).**Throwing a Ball:**When you throw a ball, the force of your throw determines how fast it goes. A harder throw (more force) means the ball accelerates faster (moves quicker).**Lifting Weights:**When you lift weights, how fast you can lift them depends on how much force you use and how heavy the weights are. More force makes the weights accelerate upward faster.

In each example, Newton’s 2nd Law * F=ma* explains that the acceleration (how fast something speeds up, slows down, or changes direction) of an object depends on the force applied to it and how heavy it is.

Newton’s 2nd Law of Motion is important because it tells us how pushing or pulling on something (force) makes it speed up or slow down (accelerate). This law helps us understand and predict how things move, which is crucial for physics, engineering, and designing everyday technology.

Newton’s 2nd Law of Motion is considered a real law because it accurately explains how pushing or pulling on something (force) affects how fast it speeds up or slows down (acceleration). It’s real because it’s been tested in many experiments and always shows how things move in predictable ways, from small things like balls to big things like planets. This makes it a trusted rule for understanding how objects move when forces act on them.