**Why is it easy to move this stone?**

**Why it is difficult to move this stone?**

You might be thinking that it’s a simple question !!

Stone moves easily, as some **force** is given to it.

But what about the second case, why the stone is not moving easily?

The answer is simple !!

Because of its large size, the stone is not moving easily.

In short, the **acceleration **of stone depends upon both **force** as well as **mass**.

That’s all you need to understand in Newton’s second law of motion.

**Newton’s second law of motion states that:**

*“The **acceleration** is directly proportional to **net force** applied and inversely proportional to **mass** of the object”*

## Newton’s second law examples

You have definitely not understood the above statement of Newton’s second law, right?

Well, I know such statements are difficult to understand and make your mind confused.

**Don’t worry, **Let’s make it simple.

I have explained some real life examples of Newton’s second law of motion which are mentioned below.

From these examples,** you will surely get the exact idea** about what newton’s second law actually means.

Okay, So let’s see the examples one by one…

### The Car

How would you feel when you are going somewhere and your car gets **damaged?**

The same thing happened with one boy and his dad in this example.

In order to start the car, the boy pushes the car but it doesn’t work.

See this,

Do you have any idea how Newton’s second law is applied here?

The answer is simple.

A boy is applying force to the car but because of its large mass, it doesn’t accelerate easily.

In short, acceleration of the car is **inversely proportional** to its mass.

Now, how will this car accelerate further?

As you can see this car is accelerating easily when some guys are helping them.

Why did this happen?

Here, the force acting on the car is **more** compared to one single boy.

Because of this reason, the car accelerates further easily.

It means that these guys together give more impact compared to one single boy.

In short, acceleration of the car is **directly proportional** to the net force applied on it.

**Conclusion, **

In both cases, forces are acting on the car.

But in the second case, the force acting on the car is more and so the car accelerates further easily.

Therefore, acceleration depends upon both **mass** as well as **force.**

And this thing indicates Newton’s second law of motion.

(Acceleration is **directly proportional** to the net force applied on the object and **inversely proportional** to its mass)

### A horse

As you can see, one horse is pulling the cart.

When one single horse is pulling the cart, the cart is **not accelerating** **further easily.**

(As the mass of the cart is **more, **it requires **more force** in order to accelerate further easily)

It means, it’s not possible for one single horse to pull the cart.

So in this case, acceleration of the cart is **inversely proportional** to its mass.

Now, see what happens…

The cart accelerates further easily when two or three horses pull it together.

The reason behind this is,

Whatever force exerted by two to three horses is **very large** compared to force exerted by one single horse.

So,

In this case, acceleration of the cart is **directly** **proportional** to the net force applied to it.

(More the force applied on the cart, the more it will accelerates further easily)

**Conclusion,**

In both cases, horses are pulling the cart.

In the first case, it’s not easy for a single horse to pull the cart.

Whereas in the second case,

As two to three horses pulls the cart together, the cart accelerates further easily.

In short,

Acceleration depends upon both **mass** as well as **force **which shows the presence of newton’s second law of motion.

### The Ball

Do you know how Newton’s second law of motion works when you simply hit the cricket ball by bat?

**Simply think,**

What happens when a football is given to the player instead of a cricket ball?

See this,

As the football has **more mass, **the player has to apply **more force** by the bat.

So in this case, acceleration of football is **inversely proportional** to its mass.

Therefore, football doesn’t accelerate further easily.

Now when a cricket ball is given to the player instead of football, with** less amount of force** the ball easily travels to a longer distance.

Here, the player doesn’t have to apply a large amount of force in order to hit the ball.

(As the mass of the cricket ball is **very less** compared to football)

Therefore, acceleration of a cricket ball is **directly proportional** to the net force applied on it.

**Conclusion,**

In both cases, the player hits the ball.

In the first case, it’s not easy for the football to accelerate at a longer distance.

(**Player has to apply** **more force,** as the mass of the football is more)

But in the second case, a cricket ball easily accelerates further with less amount of force.

(As the mass of the cricket ball is **very less** compared to football)

In short, Acceleration depends upon both **mass** as well as **force.**

Which indicates the presence of Newton’s 2^{nd} law of motion.

If you want to read more on examples of Newton’s second law of motion,

**Check out:** Real life examples of Newton’s second law of motion

## Condition in Newton’s 2^{nd} Law of motion

You already know,

According to Newton’s first law of motion,

If the forces are **balanced,** then there will be **no acceleration** of the object.

Newton has already mentioned in his first law that objects will only accelerate if an unbalanced force acts on it.

(Object at rest remains at rest and object motion remains in motion)

Now, Newton’s 2^{nd} law of motion is all about how much the body will accelerate.

And you already know,

Acceleration of any object will take place only if an** unbalanced force **acts on it.

Newton’s 2^{nd} law of motion states two things:

- Acceleration of the object
**directly****depends upon the net force**applied to it.

(i.e. If the net force on the object increases, then there will be an increases in its acceleration)

**At the same time,**

- Acceleration of the object
**inversely depends upon the mass**of the object.

(i.e. If the mass of the object increases, then there will be a decrease in its acceleration)

## What are the directions of F and a?

As already discussed in the above section,

The acceleration of objects will take place only if an unbalanced force acts on it.

That’s why, according to Newton’s second law,

*“The **acceleration** is directly proportional to **net force** applied and inversely proportional to **mass** of the object”*

But, if we talk about the directions of the **net force** and **acceleration,** then?

Are they having the same directions? (or different?)

To understand these simple questions, let’s take one simple example.

See this,

### Water truck

You have definitely seen the water truck going on the road.

Now tell me one thing,

What will be the direction of the force and acceleration? (when this truck is moving on the road)

Are both the **force** and **acceleration **having the same directions?

Maybe these types of questions have surely not come into your mind, right?

**Don’t worry,**

From the below tests, you’ll get the exact idea about the directions of force and acceleration.

#### Test #1 What are the directions of F and a?

You can see clearly the water dropped on the road, as the water truck moves forward on the road.

So, what can you say about the directions of **force** and **acceleration**?

**A)** Both are having opposite directions

**B)** Both are having forward directions

**C)** Both are having backward directions

**D)** None of these

**Answer**

#### Test #2 What are the directions of F and a?

In this case, the water is slowly dropping onto the road.

But, **the water truck driver applies a brake**.

What are the directions of **force** and **acceleration** in this case? (when the water truck driver applies a brake)

**A)** Both are having opposite directions

**B)** Both are having forward directions

**C)** Both are having backward directions

**D) **None of these

**Answer**

**Conclusion is,**

Both the net force and acceleration have the same directions.

In whichever direction the force acts, acceleration will also take place in that direction only.

*(Direction of the net force is **always** in the direction of acceleration)*

## Newton’s second law equation

(F = ma)

**Numerical 1:**

Consider one car which is accelerating at a rate of 6 m/s^{2}. If the mass of the car is 400 kg, then how much force is applied on the car?

**Solution:**

**Given data:**

Mass of the car, m = 400 kg

Acceleration of the car, a = 6 m/s

^{2}

Force applied on the car, F

_{net}=?

**According to Newton’s second law formula,**

F

_{net}= ma

F

_{net}= 400 × 6

F

_{net}= 2400 N

Therefore, when the car accelerates at a rate of 6 m/s

^{2}, a force of

**2400 N**is applied to it.

**Numerical 2:**

If the mass of the object is 20 kg, Calculate the force required to accelerate the object at a rate of 4 m/s^{2}.

**Solution:**

**Given data:**

Mass of the object, m = 20 kg

Acceleration of the object, a = 4 m/s

^{2}

Force required, F

_{net}=?

**According to Newton’s second law formula,**

F

_{net}= ma

F

_{net}= 20 × 4

F

_{net}= 80 N

Therefore, a force of

**80 N**is required to accelerate the object at a rate of 4 m/s

^{2}.

**Numerical 3:**

A vehicle having a mass of 800 kg accelerates at a rate of ‘a’ m/s^{2}. If a force of 4000 N is applied to it, at what rate the vehicle will accelerate further?

**Solution:** **Given data:**

Mass of the vehicle, m = 800 kg

Force applied on the vehicle, F_{net} = 4000 N

Acceleration of the car, a =? **According to Newton’s second law formula,**

F_{net} = ma

a = F_{net} / m

a = 4000 / 800

a = 5 m/s^{2}

Therefore, the vehicle accelerates at a rate of **5 m/s ^{2 }**when a force of 4000 N is applied to it.

**Numerical 4:**

An object having a mass of ‘m’ kg accelerates at a rate of 20 m/s^{2} when a force of 400 N is applied to it. Calculate the mass of the object.

**Solution:** **Given data:**

Acceleration of the object, a = 20 m/s^{2}

Force applied on the object, F_{net} = 400 N

Mass of the object, m =? **According to Newton’s second law equation,**

F_{net} = ma

m = F_{net }/ a

m = 400 / 20

m = 20 kg

Therefore, the mass of the object is **20 kg.**

### What are your views?

**1)**

As you can see, the book is moving forward in the horizontal direction when this boy exerts some force on it.

Due to this force, the book accelerates further at a rate of 3 m/s^{2}.

Guess the force that is acting on the book, if the mass of the book is 2 kg.

**A) **5 N

**B)** 4 N

**C)** 6 N

**D)** 10 N

**Answer**

**2)**

Dwayne everyday uses his bicycle for going to school which is having the mass of 5 kg.

When Dwayne is getting late for his school, he exerts a force of about 150 N on his bicycle in order to reach the school faster.

What will be the acceleration of the bicycle?

**A)** 9 m/s^{2}

**B)** 6 m/s^{2}

**C)** 4 m/s^{2}

**D)** 3 m/s^{2}

**Answer**

**3)**

In order to move this 5 kg box, this boy exerts some amount of force on it.

Can you guess how much force is applied to the box so that the box will accelerate at a rate of 4 m/s^{2}?

**A)** 20 N

**B)** 10 N

**C)** 4 N

**D)** 5 N

**Answer**

**4)**

When a force of 6 N is given to this football, it accelerates further at a rate of 3 m/s^{2}.

Whether you like to play football or not, you have to tell me the mass of this football.

**A)** 4 kg

**B)** 2 kg

**C)** 3 kg

**D)** 1 kg

**Answer**

**5)**

In order to move this box, there must be some force exerted on it right?

When the force of ‘F’ N is applied on the box, the box accelerates at a rate of 4 m/s^{2}.

Now, if the mass of the box is 1.5 kg, then calculate the amount of force that is exerted on the box.

**A) **5 N

**B) **4 N

**C) **6 N

**D) **1.5 N

**Answer**

**6)**

This car which is having a mass of 1000 kg, accelerates further when a force of 4500 N is exerted on it.

At what rate the car will accelerate further?

**A) **4.5 m/s^{2 }

**B) **3.5 m/s^{2}

**C) **2.5 m/s^{2}

**D) **1.5 m/s^{2}

**Answer**

## Newton’s 2^{nd} Law – Misconception

If you have read the above section completely, then it’s easy to remember Newton’s second law of motion.

You can even speak this law word to word, right.

Now the point is,

**What you believe is important, **how well you have understood, doesn’t matter.

If you have read Newton’s first law,

You already know, the object will change its behaviour only if an **external force** acts on it, right.

(This external force is nothing but an unbalanced force only)

Now the question is,

*In order to keep the object moving,* external force should be given continuously?

**You might be thinking, **the answer is YES, right?

If you are thinking so, then you are wrong**.**

That’s why, You need to first clear this misconception.

The most common misconception that people used to believe from the ages,

*External force is needed to be given **continuously** on the object.* (To keep it’s motion continue)

**Are you believing the same?** (Let me know in the comments)

There is one similar big Misconception in Newton’s third law which we’ll see it later.

### Clear this misconception (Right Now)

**Even today,** people still believe this misconception that…

*External force is needed to be given **continuously** on the object.* (To keep it’s motion continue)

If you still have some doubts or any kind of misconception left in your mind,

**Don’t worry.**

Let’s clear this Misconception, by considering some basic examples mentioned below.

(Also change your belief system)

#### The Ball

Consider this ball is moving with **uniform speed.**

Now the question is,

Does any external force is required to keep this ball moving forward? (If the friction and air resistance are neglected)

What can you say about the ball? (If **no external force** is given to the ball)

**A) **Speed of the ball increases slowly

**B) **Speed of the ball decreases slowly

**C) **Ball will continue its motion (with same speed, in the same direction)

**D) **None of these

**Answer**

#### The Book

Loki and Sara were the two good friends.

Once, both of them are discussing the topic of one book.

Before going in detail, tell me one thing…

What if the book is simply lying on the floor, is it balanced or unbalanced?

**Obviously Yes,** right. (The book is in balanced condition)

See this,

As mentioned in Newton’s first law, the object will not change its behaviour unless an **unbalanced force** acts on it.

Now what if this book is in motion?

Does any external force is required to keep this book moving forward? (If the friction and air resistance are neglected)

The same question Sara asks Loki, while discussing the topic of the book.

Sara tells Loki that the book will start moving in the horizontal direction.

(If there is no air resistance or some kind of friction acting on the book)

In short,

**Sara believes** that the book could also have a motion in the horizontal direction.

But,

**Loki believes** that the object can not move in the horizontal direction. (If only vertical forces are acting on it)

Loki believes that the book will remain in rest position only.

Both of them are having different belief systems.

According to you, who do you think has the right belief system?

**A) **Loki is correct

**B) **Sara is correct

**C) **Sara and Loki both are correct

**D) **None of these

**Answer**

#### Toy Car

Have you played with the toy car in your childhood like this?

**Obviously yes,** right.

All of us have played like this in our childhood.

Now you already know,

When the boy releases the car from his hand, the car starts moving forward in the horizontal direction.

In short, when the boy releases the car, the car comes in the motion.

Now the question is,

Imagine, if there was **no friction** along the level surface and there was **no air drag** to pull the car forward.

Does any external force is required to keep this car moving forward? (If the friction and air resistance are neglected)

What do you think of this car, how long the car will travel further?

**A) **Car travels forever with the uniform speed

**B) **Car immediately stops

**C) **Car’s speed slowly increases

**D) **None of these

**Answer**

## Conclusion

If you have read all the above cases, **one thing is common.**

Objects can have motion in the horizontal direction.

It means objects can move in the horizontal direction even if only vertical forces are acting on them.

**Let’s make it simple.**

What happens when a boy is moving on a skateboard with **uniform speed,** *still an external force is required* to keep a skateboard moving?

Will this skateboard keep moving **forever?**

Remember these questions? (Which we have discussed earlier in newton’s first law)

In short, *External force is not needed to be given continuously* on a skateboard to keep its motion continue.

(A skateboard moving with uniform motion will continue moving forward)

**A force is not needed to be given on the object continuously,** to keep its motion continue.

**Always Remember,**

External force is ** not needed** to produce the motion of any object.

External force only helps in accelerating the object forward.

(Object will not change its behaviour, if *no external force is given to it*)

## Newton’s Second Law in terms of Momentum

Think, what happens when a car, bike, train or any vehicle running with high speed applies a **sudden brake**?

**Let’s make it simple.**

In order to stop the train,

The train driver must have to apply the brake at some distance before reaching the next station right?

(Train driver will not wait for the next station to come and applies a sudden brake)

Even when you are walking or running somewhere, **you can’t stop suddenly.**

(If you stop at once, you may fall down)

In fact, anything that is in motion can’t stop suddenly, right.

Do you know the reason behind all these things?

It only happens because of **Momentum.**

As the train has high momentum, a higher amount of force is required to stop its motion.

*(More the momentum the object has, the more it is difficult to stop its motion)*

Therefore, to stop such objects, they require a large amount of *force *and *time* as well.

In terms of Momentum,

**Newton’s 2 ^{nd} law of motion can be stated as:**

*“The **net force** applied on the body is equal to its **rate of change of momentum** and takes place always in the direction of force applied”*

What does the above statement actually mean?

Don’t worry. (We’ll see it step by step)

But before that, understand the definition of momentum.

### What is Momentum?

Simply, Momentum is defined as the product of mass and velocity.

Its symbol is ‘**p**‘ and its unit is **kg m/s**** ^{2}**.

The formula for the momentum can be given as:

**Momentum (p) = mass (m) × velocity (v)**

In simple words,

*“**Momentum** is that quantity by which how much **amount of motion present** in the body can be known”*

(i.e. when you are walking or running, how much motion is present in your body can be known by Momentum)

Let’s make this simple.

**Imagine, **while playing a game of cricket by mistake you hit the ball to a small girl standing over there.

When the cricket ball hits this girl, the girl causes some minor injury.

But, what happens when a football is coming towards her?

In both cases, there are chances of injury.

But, in which case, there will be a chance of more injury?

Obviously, **football gives more injury **compared to a cricket ball, right.

In short,

As the momentum of football is **high** compared to a cricket ball, it causes more injury.

**Conclusion,**

If the object has more mass, then its momentum will also be high.

(Momentum is ** directly proportional** to mass of the object)

In the above example, as the football has more mass compared to a cricket ball, its momentum will be high.

(So, there are more chances of injury in the second case)

Let’s take one more example.

#### The Ball

Do you know why you should take your hands backwards **while catching the ball?**

Maybe you are uncomfortable while catching the ball?

Or, you can’t see the ball properly?

Is the ball having any relation with the Momentum?

You’ll get all the answers in this example.

**Simply think, **

When you catch the ball, you apply some force with your hand in order to stop the ball, right.

In this case, as you can see the **fielder is not taking his hand backwards. **

(However, he is applying force on the ball by his hand)

But, as the fielder is not taking his hand backwards, **he has to apply more force** in order to stop the ball.

And also, the momentum of the ball is very high.

So the fielder feels **more pain** in his hand. (As he is not taking his hand backward)

Now,** when the fielder takes his hand backwards,** does he feel the same amount of pain as before?

See this,

In this case, **the fielder has to apply less force** to stop the ball.

As he takes his hand backwards, the momentum of the ball gets** distributed** in his hand.

Because of this reason, **he feels less pain** in his hand.

In short, whenever you catch the ball you should take your hands backwards.

That’s why Momentum is *directly proportional* to mass of the object.

The most interesting part of this section comes after the numericals. **(Keep reading)**

Before that, check out some numerical based on the equation. [p = mv]

## Newton’s second law equation

(p = mv)

**Numerical 1:**When a bullet which is having a mass of 40 grams is fired from a gun, it reaches the velocity of 160 m/s. Calculate the momentum of a bullet.

**Solution:** **Given data:**

Mass of a bullet, m = 40 grams

Now, 1 kg = 1000 grams (So, 40 grams = 0.04 kg)

Velocity of a bullet, v = 160 m/s

Momentum of the bullet, p =? **According to the momentum formula,**

Momentum (p) = mass (m) × velocity (v)

p = m × v

p = 0.04 × 160

p = 6.4 kg m/s

Therefore, the momentum of a bullet is **6.4 kg m/s.**

**Numerical 2:**A trolley bag having a mass of 4 kg carries a luggage of 40 kg. If the bag is moving with the velocity of 2 m/s, what will be the momentum of the bag?

**Solution:** **Given data:**

Mass of trolley bag, m_{1} = 4 kg

Mass of the luggage inside the trolley bag, m_{2} = 40 kg

Total mass, m = (m_{1} + m_{2}) = 44 kg

Velocity of trolley bag, v = 2 m/s

Momentum of a trolley bag, p =? **According to the momentum formula,**

Momentum (p) = mass (m) × velocity (v)

p = m × v

p = 44 × 2

p = 88 kg m/s

Therefore, the momentum of a trolley bag is **88 kg m/s.**

**Numerical 3:**A bicycle running with a velocity of 3 m/s is having a momentum of 12 kg m/s. Calculate the mass of the bicycle.

**Solution:** **Given data:**

Momentum of the bicycle, p = 12 kg m/s

Velocity of the bicycle, v = 3 m/s

Mass of the bicycle, m =? **According to the momentum formula,**

Momentum (p) = mass (m) × velocity (v)

p = m × v

m = p / v

m = 12 / 3

m = 4 kg

Therefore, the mass of the bicycle is **4 kg.**

### What are your views?

**1)**

While playing the game of bowling, this boy throws the ball which is having a mass of 4 kg.

If the ball moves forward with the velocity of 10 m/s, what will be its momentum?

**A) **30 kg m/s

**B) **40 kg m/s

**C) **10 kg m/s

**D) **20 kg m/s

**Answer**

**2)**

A 75 kg missile attains some amount of velocity after it is launched.

After some time, this missile reaches the momentum of 4500 kg m/s.

What will be the velocity of a missile?

**A) **20 m/s

**B) **30 m/s

**C) **40 m/s

**D) **60 m/s** **

**Answer**

**3)**

How far can you throw this brick with your hand which is having a mass of 200 grams?

How much momentum the brick will gain? (If its velocity reaches to 4 m/s)

**A) **0.4 kg m/s

**B) **0.8 kg m/s** **

**C) **0.1 kg m/s

**D) **0.6 kg m/s

**Answer**

**4)**

A bird which has a mass of 5 kg is flying at some height.

What will be the velocity of the bird when it attains a momentum of about 25 kg m/s?

**A) **2 m/s

**B) **4 m/s

**C) **1 m/s

**D) **5 m/s

**Answer**

**5)**

A car which is having a mass of ‘m’ kg, is moving forward with the velocity of 2 m/s.

If the momentum of a car is 2000 kg m/s, then what will be the mass of the car?

**A) **400 kg

**B) **100 kg

**C) **1000 kg

**D) **150 kg

**Answer**

**6)**

A heavy stone of mass 20 kg is falling from the hill.

While falling from the hill, stone reaches to the momentum of 400 kg m/s.

At what velocity the stone will collide with the ground?

**A) **30 m/s

**B) **60 m/s

**C) **40 m/s

**D) **20 m/s

**Answer**

## Importance of Velocity in Newton’s 2^{nd} law?

…continuing the above section,

You already know the relation of Momentum and mass, right?

In short, if the object has more mass, then its momentum will also be high.

**Here is the interesting part.**

What happens when a bullet is fired from a gun?

See this,

Obviously, **it can cause a serious injury.**

(As the momentum of the bullet is extremely high)

**Wait a second,**

If you have noticed, the mass of the bullet is **very small** compared to both cricket ball as well as football.

So, its momentum should be less, right?

Don’t you think** something is missing?**

**Let’s make it simple.**

See this,

When a bullet is fired from a gun, the bullet releases with **extremely high momentum.**

Therefore, we can say that…

Momentum of a bullet is ** directly proportional** to its velocity.

Even though the bullet has small mass, it travels with extremely high velocity.

(Momentum is ** directly proportional** to velocity of the object)

### Conclusion

**Momentum** of any object depends upon both **mass** as well as **velocity**.

So, once again remember Newton’s 2^{nd} law of motion in terms of momentum.

*“The **net force** applied on the body is equal to its **rate of change of momentum **and takes place always in the direction of force applied”*

Let,

F_{net} = net force applied to the body

m (v – u) / t = rate of change in momentum

mu = initial momentum

mv = final momentum

u = initial velocity of the object

v = final velocity of the object

t = time

So, we get the following equation for newton’s second law:

F_{net} = m (v – u) / t

F_{net} = (mv – mu) / t

## Newton’s second law equation

[F_{net} = m (v – u) / t]

**Numerical 1:**A ball having a mass of 2 kg is moving with the initial velocity of 3 m/s. When one person hits the ball, a force of 50 N acts on it. The speed of the ball increases and reaches up to ‘v’. Calculate the speed of the ball after 10 seconds.

**Solution:** **Given data:**

Mass of the ball, m = 2 kg

Initial velocity of the ball, u = 3 m/s

The net force applied on the ball, F_{net} = 50 N

After time, t = 10 seconds

Final velocity of the ball, v =? **According to Newton’s second law formula,**

F_{net} = m (v – u) / t

50 = 2 (v – 3) / 10

2 (v – 3) = 50 × 10

2 (v – 3) = 500

v – 3 = 250

v = 253 m/s

Therefore, the speed of the ball will be **235 m/s** after 10 seconds.

**Numerical 2:**

A shopping tray which has a mass of 2 kg is at rest. When a force of 40 N is applied on the tray, its speed increases and reaches up to ‘v’. What will be the speed of the tray after 5 seconds?

**Solution:** **Given data:**

Mass of the shopping tray, m = 2 kg

The net force applied on the shopping tray, F_{net} = 40 N

After time, t = 5 seconds

Final velocity of the shopping tray, v =?

Here, the shopping tray is **at rest.**

Therefore, the initial velocity of the shopping tray is u = 0 m/s**According to Newton’s second law formula,**

F_{net} = m (v – u) / t

40 = 2 (v – 0) / 5

2 (v – 0) = 40 × 5

2 v = 200

v = 200 / 2

v = 100 m/s

Therefore, the speed of a shopping tray will be **100 m/s** after 5 seconds.

**Numerical 3:**An object having a mass of 2 kg is moving with the initial velocity of 40 m/s. The velocity of the object starts decreasing when an

**opposing force**of 5 N is applied to it. Calculate the velocity of the object after 10 seconds.

**Solution:** **Given data:**

Mass of the object, m = 2 kg

Initial velocity of the object, u = 40 m/s

Here, the **opposing force** of 5 N is applied to the object.

The net force applied on the object, F_{net} =** – 5 N**

After time, t = 10 seconds

Final velocity of the ball, v =? **As per the definition of Newton’s second law,**

F_{net} = m (v – u) / t

(- 5) = 2 (v – 40) / 10

2 (v – 40) = (- 5) × 10

2 (v – 40) = (- 50)

(v – 40) = (- 25)

v = 40 – 25

v = 15 m/s

Therefore, after 10 seconds the velocity of the object will be **15 m/s.**

**Numerical 4:**A ball having a mass of 4 kg is moving forward with the initial velocity of 50 m/s. The velocity of the ball slowly decreases when an

**opposing force**of 30 N is applied to it. How much time will the ball take to come into rest position?

**Solution:** **Given data:**

Mass of the ball, m = 4 kg

Initial velocity of the ball, u = 50 m/s

Here, the **opposing force** of 30 N is applied to the ball.

The net force applied on the ball, F_{net} =** – 30 N**

After what time, t =?

Final velocity of the ball becomes zero, v = 0 m/s **According to Newton’s second law formula,**

F_{net} = m (v – u) / t

(- 30) = 4 (0 – 50) / t

(- 30 × t) = 4 × (- 50)

(- 30 × t) = (- 200)

30 t = 200

t = 200 / 30

t = 6.66 seconds

Therefore, after **6.66 seconds** the ball comes into the rest position.

**Numerical 5:**A ball of mass 4 kg is moving with the initial velocity of 2 m/s when a force of 15 N is applied to it. The velocity of the ball further increases and reaches up to ‘v’ when a force of 30 N is applied to it. What will be the speed of the ball after 20 seconds?

**Solution:** **Given data:**

Mass of the ball, m = 4 kg

Force applied on the ball, F_{1} = 15 N

Initial velocity of the ball, u = 2 m/s

Force applied on the ball, F_{2} = 30 N

The net force applied on the ball,

F_{net} = (15 + 30)

F_{net} = 45 N

After time, t = 20 seconds

Final velocity of the ball, v =? **According to Newton’s second law formula,**

F_{net} = m (v – u) / t

45 = 4 (v – 2) / 20

4 (v – 2) = 45 × 20

4 (v – 2) = 900

v – 2 = 900 / 4

v – 2 = 225

v = 227 m/s

Therefore, after 20 seconds the speed of the ball will be **227 m/s.**

**Numerical 6:**A bus having a mass of 500 kg starts from rest. In 10 seconds the velocity of the bus reaches 15 m/s. Calculate the net force acting on the bus.

**Solution:** **Given data:**

Mass of the bus, m = 500 kg

Initial velocity of the bus, u = 0 m/s

In time, t = 10 seconds

Final velocity of the bus, v = 15 m/s

The net force acting on the bus, F_{net} =? **As per the equation of Newton’s second law,**

F_{net} = m (v – u) / t

F_{net} = 500 (15 – 0) / 10

F_{net} = 50 × 15

F_{net} = 750 N

Therefore, a net force of **750 N** is acting on the bus.

### What are your views?

**1)**

While going to the market, Alex uses his scooter to reach faster.

In 4 seconds, Alex increases his scooter’s speed from 20 m/s to 50 m/s.

Can you guess the force that is acting on the 100 kg scooter?

**A) **800 N

**B) **600 N

**C) **750 N

**D) **900 N

**Answer**

**2)**

A dish of chicken having a mass of 1 kg is initially at rest.

When a force of 5 N is applied to the dish, it moves forward with the ‘v’ velocity.

What will be the velocity of the dish after 6 seconds?

**A) **10 m/s

**B) **15 m/s

**C) **40 m/s

**D) **30 m/s** **

**Answer**

**3)**

A rubber tyre which is having a mass of 5 kg is moving forward with the initial velocity of 35 m/s.

The velocity of tyre decreases when an **opposing force** of 15 N is applied on it.

What will be the velocity of tyre after 4 seconds?

**A) **20 m/s

**B) **23 m/s

**C) **18 m/s

**D) **25 m/s

**Answer**

**4)**

When a force of 15 N is applied on a trolley of mass 5 kg, it moves forward with the initial velocity of 4 m/s.

The velocity of the trolley further increases, when another force of 25 N force is applied to it.

What will be the velocity of the trolley after 10 seconds?

**A) **84 m/s

**B) **60 m/s

**C)** 44 m/s

**D) **90 m/s

**Answer**

**5)**

This car is initially at rest, which is having a mass of 400 kg.

After 20 seconds, the velocity of the car reaches up to 25 m/s.

Can you guess the force that is acting on the car?

**A) **600 N

**B) **400 N

**C) **900 N

**D) **500 N

**Answer**

**6)**

A football is moving forward with the initial velocity of 60 m/s.

Its velocity decreases and reaches to 30 m/s when an **opposing force** of 4 N is applied to it.

If the mass of the ball is 400 grams, after what time the ball comes into rest position?

**A) **10 seconds

**B)** 3 seconds

**C) **8 seconds** **

**D) **9 seconds

**Answer**

## What is Acceleration due to gravity?

You have definitely heard that the value of acceleration is **9.81 m/s**^{2}**,** right?

But, what is acceleration due to gravity?

It’s simple.

*“The acceleration gained by an object because of the **gravitational force** is known as acceleration due to gravity”*

Let’s take one simple example.

What happens when a 2000 kg hippo and a 10 kg dog are dropped from the same height at the same time?

**For hippo,**

Gravitational force,

F_{grav(hippo)} = 19620 N

and

Acceleration,

a = F / m

a = 19620 / 2000

a = 9.8 m/s^{2}

**For dog,**

Gravitational force,

F_{grav(dog)} = 98.1 N

and

a = F / m

a = 98.1 / 10

a = 9.8 m/s^{2}

**Remember,**

The acceleration of any **free falling** object is 9.8 m/s^{2}.

Whether an object is thrown up in the air or dropped from some height, this value remains** **the** **same** **for all objects.

This value of acceleration is known as **acceleration due to gravity **and it is denoted by **‘g’**.

**Acceleration due to gravity,** **g = 9.8 m/s ^{2}**

## What is Gravitational field strength?

As seen above, **the value of acceleration is the same for both** Hippo as well as dog.

In short, Both the objects fall with the same acceleration.

Now, what is Gravitational field strength?

See this,

From the above free body diagram, it is clearly seen that hippo experiences a larger gravity force than the dog.

**Because of the large gravity force,** the acceleration of the hippo will be more than the dog.

(According to Newton’s second law of motion)

And,

You already know that the acceleration of any object depends upon both **force** as well as **mass.**

So, the acceleration of hippo will be less because of its large mass as compared to a dog.

And, the gravity force acting on the hippo will be **very large** because of its large mass.

Therefore,

In the case of free fall,

**The ratio of F/m is the same **for both hippo as well as the dog and both accelerates with the same rate of **9.8 m/s**^{2}**.**

This ratio of* gravitational force per unit mass *is known as* ***gravitational field strength.**

The symbol for the gravitational field strength is **‘g’** and in case of free fall, its value is 9.8 m/s^{2}.

The ratio of F/m varies based upon different locations.

**(Within Earth’s surface, its value is 9.8 N/kg)**

It means that every object on earth experiences 9.8 N of force upon every 1 kg of mass within the object.

In short, the value of acceleration remains the same for all objects in case of free fall.

(All objects fall at the same rate of acceleration **if only gravity force is acting on it)**

## What is Free fall?

How will you define free fall?

It’s simple.

Free fall is simply a free falling of the object.

*“Free fall** is that type of motion of the object in which object falls **only under the effect of gravity force”*

**Objects which are free falling, **do not experience any kind of air drag.

Under such condition,

All objects fall at the same rate.

(Whether of large mass or small mass, dropped from a long distance or short distance)

**Let’s make this simple. **

Simply think,

What happens when you drop a **small** **feather **and a **large stone** from some height?

Obviously, the stone falls faster than a feather. (Because of its large mass)

But, if both these objects are allowed to **free fall, **then?

What do you think?

In case of **free fall,** which of these two objects reach the ground first? (Feather or a Stone)

You might be thinking, the feather travels slower (as it has less mass) compared to stone, right?

If you are thinking so, then** **you are Wrong.

**Always remember,**

If you are considering a free falling motion, then the answer to this question is definitely **NO.**

### Think Practically

Suppose one feather and a stone are dropped from a tall building from the same height and at the same time.

Assume that the air resistance is somehow **neglected.**

(Such that **neither feather nor a stone** would experience some kind of air drag while falling)

What do you think, which of these two will strike the ground first?

**A) **Feather

**B) **Stone

**C) **Both Feather and Stone

**D)** None of these

**Answer**

If your concept of free fall is clear, then it is not surprising for you.

See this,

**Many people are surprised to know,** why these two objects strike the ground at the same time?

The answer is simple.

In short, in the absence of air resistance both the objects fall at the same rate.

And the only force which is pulling down both the objects is the gravity force.

Because of this gravity force, both feather and stone accelerates downwards **at the same rate.**

After understanding the concept of free fall, a question arises in mind that…

**What happens if there is air resistance?**

In the presence of air resistance, which of these two objects falls faster?

To get the answer to these questions, let’s move onto the next topic…

## Free fall with Air resistance

You already know the definition of free fall, right.

Now, how will you define Air resistance?

In simple words,

Air resistance means one kind of **air drag.**

Or

Simply, air resistance means collision of an object’s surface with the air particles.

The **Speed & Cross-section area** of the object are the two main factors on which the air resistance depends.

Air resistance **depends on both** Speed as well as Cross-section area of the object.

(If the object’s speed increases, it’s air resistance will also increases)

### Think Practically

Any object when dropped from some height experiences some kind of air resistance, right?

As per the above example,

Again, one feather and a stone are dropped from a tall building from the same height and at the same time.

Here, both the objects are **experiencing air resistance.**

What do you think, which of these two objects will hit the ground first?

**A)** Feather

**B)** Stone

**C)** Both feather and stone

**D)** None of these

**Answer**

Nothing to surprise here that stone hits the ground first.

But do you know why this happened?

In fact, here also both these objects are getting pulled downwards due to gravity force.

Okay, **let’s make it simple.**

When they are dropped,

The *gravity force acts as an *** unbalanced force** and both the feather and stone begin to accelerate downwards.

As they move downwards, both these objects start experiencing air resistance in an upward direction.

(i.e. Objects surface starts colliding with the air particles)

See this,

In short,

The more air particles collide with the object’s surface, the greater air resistance force acts on them in the upward direction.

Now as discussed earlier, the **Speed & Cross-section area** are the two main factors on which the air resistance depends.

Therefore, Stone experiences more air resistance compared to feather.

**Now the question is,**

Why does the stone which experiences more air resistance falls faster?

As the air resistance acting on stone should slow down its speed, right?

Why still the object which is experiencing more air resistance falls faster?

To answer the above questions, you need to understand one important concept which is…

## What is Terminal Velocity?

Newton has already mentioned in his first law that objects will only accelerate further if an **unbalanced force** acts on it.

Comparing with the above situation,

As the stone falls downwards… Its speed keeps on increasing and stone experiences more and more air resistance in the upward direction.

In short, there is no such force **which balances the downward force of gravity.**

**The stone will continue to accelerate until** the value of air resistance force and the gravity force are **equal.**

In short,

Once the **air resistance force** (in the upward direction) and **gravity force** (in the downward direction) are balanced,

The object is said to have reached its **terminal velocity**.

Therefore,

*Terminal velocity is the **final velocity** of the object.*

Then, the object will continue to fall towards the ground with this terminal velocity.

In this case, the stone has to travel for a longer period in order to reach the terminal velocity.

The stone should require more upward air resistance, **in order to balance the gravity force** (which is acting in the downward direction)

**The stone never reaches the terminal velocity** and thus falls faster on the ground compared to feather.

Stone needs to accelerate more in order to get balanced.

**Conclusion,**

From the above diagram, the feather quickly reaches the terminal velocity.

(i.e. Forces gets balanced in a **very short interval of time**)

On the other hand, stone never reaches the terminal velocity (Forces never get balanced) and there is still an acceleration of stone.

The stone falls faster than the feather because **it never reaches the terminal velocity.**

### Think Practically

Forces acting on the **100 kg** **skydiver** are shown in the below figure.

From the below tests, determine the net force and acceleration of the skydiver at different time intervals.

#### Test #1 What are the values of F and a?

How much **net force** is acting on the skydiver and with what **acceleration** the skydiver will accelerate downwards?

**A)** 600 N, 5.6 m/s^{2}

**B)** 700 N, 7.6 m/s^{2}

**C)** 650 N, 5.8 m/s^{2}

**D)** 800 N, 8.0 m/s^{2}

**Answer**

#### Test #2 What are the values of F and a?

How much **net force** is acting on the skydiver and with what **acceleration** the skydiver will accelerate downwards?

**A)** 650 N, 6.5 m/s^{2}

**B) **750 N, 8.9 m/s^{2}

**C)** 550 N, 5.5 m/s^{2}

**D)** 450 N, 9.8 m/s^{2}

**Answer**

#### Test #3 What are the values of F and a?

How much **net force** is acting on the skydiver and with what **acceleration** the skydiver will accelerate downwards?

**A) **240 N, 2.2 m/s^{2}

**B)** 200 N, 2.0 m/s^{2}

**C)** 250 N, 2.5 m/s^{2}

**D)** 270 N, 2.8 m/s^{2}

**Answer**

#### Test #4 What are the values of F and a?

**net force** is acting on the skydiver and with what **acceleration** the skydiver will accelerate downwards?

**A)** 0 N, 0.0 m/s^{2}

**B)** 10 N, 0.5 m/s^{2}

**C)** 20 N, 0.8 m/s^{2}

**D)** 30 N, 9.8 m/s^{2}

**Answer**

From the above tests,

**Have you noticed one thing?**

With the increase in speed, there is an also increase in the air resistance.

In the last figure,

As both the forces get balanced, the object is said to have reached its terminal velocity.

(i.e. **air resistance force** (in the upward direction) and **gravity force** (in the downward direction) gets balanced)

That’s why, the skydiver is said to have reached its **terminal velocity**.

(*Terminal velocity is the **final velocity** of the object*)

## Summary (Short and Simple)

**It’s time to revise** all the main points which we have seen till now in Newton’s second law of motion.

**What is Newton’s second law of motion?**

*“The **acceleration** is directly proportional to **net force** applied and inversely proportional to **mass** of the object”*

In short, Acceleration of any object depends upon both **force** as well as **mass.**

**Condition in Newton’s 2**^{nd}**Law of motion**

As per the** **first law of motion, If the forces are **balanced,** then there will be **no acceleration** of the object.

Now,

According to Newton’s 2^{nd} law of motion,

Acceleration of an object takes place only if an** unbalanced force **acts on it.

**What are the directions of Force and Acceleration?**

Direction of the net force is **always** in the direction of acceleration.

(In whichever direction the net force acts, acceleration will also take place in that direction only)

**Newton’s 2**^{nd}**Law – Misconception**

Does any external force required to keep any object moving?

What do you think?

**Even today,** people still believe this misconception that…

*External force is needed to be given **continuously** on the object.* (To keep it’s motion continue)

If you remember the first law of motion, it is clearly mentioned that…

Object will change its behaviour only if an unbalanced force acts on it, otherwise NOT.

**Always Remember,**

External force is ** not needed** to produce the motion of any object.

External force only helps in accelerating the object forward.

(Object will not change its behaviour, if *no external force is given to it*)

**Newton’s second law in terms of Momentum**

In terms of Momentum, Newton’s 2^{nd} law of motion can be stated as:

*“The **net force** applied on the body is equal to its **rate of change of momentum** and takes place always in the direction of force applied”*

**What is Momentum?**

In simple words,

*“**Momentum** is that quantity by which how much **amount of motion present** in the body can be known”*

Momentum is defined as the product of mass and velocity.

**Momentum (p) = mass (m) × velocity (v)**

Symbol of Momentum: **p**

Unit of Momentum: **kg m/s ^{2}**

**What is Acceleration due to gravity?**

*“The acceleration gained by an object because of the **gravitational force** is known as acceleration due to gravity”*

The acceleration of any **free falling** object is 9.8 m/s^{2}.

This value of acceleration is known as **acceleration due to gravity **and it is denoted by **‘g’**.

**Acceleration due to gravity, g = 9.8 m/s ^{2}**

**What is Gravitational field strength?**

The ratio of* gravitational force per unit mass *is known as* ***gravitational field strength.**

The symbol for the gravitational field strength is **‘g’** and in case of free fall, its value is 9.8 m/s^{2}.

The ratio of F/m varies based upon different locations.

**(Within Earth’s surface, its value is 9.8 N/kg)**

**What is Free fall?**

Free fall is simply a free falling of the object.

*“Free fall** is that type of motion of the object in which object falls **only under the effect of gravity force”*

**Objects which are free falling, **do not experience any kind of air drag.

**What is Air resistance?**

Air resistance means one kind of **air drag.**

Simply, air resistance means collision of an object’s surface with the air particles.

While falling, If the object’s speed increases, then it’s air resistance will also keep on increasing.

**What is Terminal velocity?**

Terminal velocity is the **final velocity** of the object.

Once the **air resistance force** (in the upward direction) and **gravity force** (in the downward direction) are balanced,

The object is said to have reached its **terminal velocity**.

Then, the object will continue to fall towards the ground with this terminal velocity.

**........**Don’t you think, is easy to remember the statement of Newton’s second law of motion?

(Let me know by leaving a **comment**)

If you want to **read more** about the Newton’s laws,

**You can check here:**

Newton’s second law example

Newton’s second law equation

Definition of newton’s second law**Newton’s first law of motion**Newton’s first law example

**Newton’s third law of motion**

Newton’s third law example

**Newton’s laws of motion**

How many newton’s laws are there

**Newton’s law of cooling**

Newton’s law of cooling formula

**Newton’s law of inertia**

Newton’s law of inertia examples

**Newton’s universal law of gravitation**