Newton’s Second Law of Motion

Before we dive in the 2nd​​ law of motion, it is essential to have the understanding of the concept of momentum.​​ 

Momentum​​ is defined as the product of mass and velocity of the body.

ρ=mv

The SI unit of momentum is​​ .

Sometimes you may be asked too derive the unit of momentum as​​ N.s. So how to derive it? lets see.​​ 

Multiply ‘s’ with numerator and denominator. Consequently, it would be​​ 

=kgms×ss

=kgms2×s

As we know,​​ N=kgms2

Hence, the derived unit of momentum is​​ N.s.

  • Momentum is a vector quantity.​​ 

  • Its direction is same as the direction of momentum.​​ 

  • Momentum is the quantity of motion. It means when we try to stop the body, we don’t only consider mass but also velocity. For example, it is difficult to stop the bullet in motion though it has less mass, but due to its high velocity so its momentum is greater. Kindly note, in 1st​​ law of motion, mass was to be considered for bringing an object in motion. But to stop or make the object​​ come to rest from motion, not only its mass but also its velocity considered.​​ 

Now let us learn about​​ 2nd​​ law of motion.

The second law of newton says that unbalanced forces always have some resultant force, and they make impact. It is important to note that resultant force is always in the direction of acceleration.​​ 

The body decelerates when resultant force and velocity are in opposite direction.​​ 

Furthermore, ​​ 

aF

a1m

On combining both proportionalities we get​​ 

aFm

On removing proportionality sign, we get​​ 

a=kFm

On considering​​ k=1, the formula comes out to be

a=Fm

F=ma

This is the famous formula of IGCSE or O level. Let’s take this formula a step ahead.​​ 

Now, since acceleration is the rate of change of velocity.​​ 

F=mvt

And we have learned above that the product of mass and velocity is known as momentum. So the formula would be​​ 

F=m×vt

F=Pt 

Hence, one may define force as Rate of change of momentum. And, remember, in A level physics, we define force not merely as a pull or a push but as the rate of change of momentum.​​ 

Similarly, if asked about the 2nd​​ law of motion in A level physics, whether Edexcel or Cambridge, we would define it as ‘Force is rate of change of momentum’.​​ 

​​ 

 

Q1: MJ 23/ P12/ Q9

A box in air slides with increasing speed down a rough slope from point P to point Q.

The slope surface exerts a constant frictional force on the box.

As the box moves from P to Q, there are changes to the magnitudes of its acceleration and the​​ total resistive force acting on it.

Which row describes the changes?​​ 

QUESTION BREAKDOWN

Context:​​ The box slides in air from P to Q, with a constant frictional force.

Focus:​​ Identify the changes to magnitude of acceleration and total resistive force asteh box slides down the slope. ​​ 

SOLUTION

  • How to know this question is about the application of 2nd​​ Law of Newton?

The question says that the box moves at an increasing speed, a condition which aligns with the principles of Newton's Second Law.

  • Understanding the Forces

Weight acting at the centre of the box; the horizontal component of weight causes the box slide down the slope.​​ 

Friction force opposes the motion of the box from P to Q.​​ 

Air resistance acts on the box as the box in air slides.​​ 

Therefore, the total resistive force means the sum of forces opposing the motion of the box: frictional force and air resistance. ​​ 

Total Resistive Force=Air Resistance+Frictional Force

 

Since frictional force acting on the box is constant, it wouldn’t change across the motion of the box. And as the box is in the air as well, the air resistance would vary down the slope. As the question states that the box slides with increasing speed, the body accelerates down the slope. On the other hand, this would also cause the air resistance acting on the box increase. Consequently, the total resistive force would increase as the box moves down the slope. ​​ 

Total Resistive Force=Air Resistance+Frictional Force (constant)

Now, using the formula​​ 

Fnet=ma

forward force-backward force=ma

Wsin θ-(air resistance+frictional force)=ma

Wsin θ-total resistive force=ma

a=Wsin θ-total resistive forcem

So as the total resistive force increases as the box moves down the slope, the magnitude of acceleration would become smaller because the component of weight (Wsin θ) remains constant but the total resistive force keeps on increasing. ​​ 

a=Wsin θ-total resistive forcem

Therefore, the magnitude of acceleration would decrease.​​ 

  • Correct Answer

The correct​​ answer is option D, where the magnitude of acceleration decreases and the magnitude of total resistive force increases.​​ 

Q2: MAR 22/ P12/ Q8

A car of mass 750 kg has a horizontal driving force of 2.0 KN acting on it. It has a forward horizontal acceleration of 2.0 m s–2.

 ​​ ​​​​ 

What is the resistive force acting horizontally?

A ​​ O.50 KN  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

B ​​ 1.5 KN  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

C ​​ 2.0 KN

D 3.5 KN

QUESTION BREAKDOWN

Context:​​ The car moves horizontally with driving force and resistive force mentioned in the question.

Focus: Calculate the resistive force horizontally acting on the car.​​ 

SOLUTION

  • How to know this question is about the application of 2nd​​ Law of Newton?

The question says that the box moves at an increasing speed, a condition which aligns with the principles of Newton's Second Law.

  • Understanding the Forces

Considering the forces acting in the car horizontally, there are two forces: driving force and resistive force.​​ 

Using the formula​​ 

Fnet=ma

forward force-backward force=ma

driving force-resistive force=ma

2000-F=750×2

F=2000-1500

F=500 N

F=0.5 KN

  • Correct Answer

The correct​​ answer is option A; the resistive force is 0.5KN.​​ 

Q3: MJ 22/ P13/ Q5

Forces of magnitudes 2N, 4 N and 7 N combine to produce a resultant force.

The magnitudes of the three forces are fixed, but the forces may act in any direction in the same

plane.

What is not a possible magnitude of the resultant force?

A​​ 0 N  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ ​​ 

B​​ 5 N  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ ​​ 

C​​ 8 N  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

D​​ 13 N

QUESTION BREAKDOWN

Context:​​ Three forces combine to give a resultant force.​​ 

Focus:​​ Calculate possible resultant forces acting in different arrangements.​​ 

SOLUTION

  • How to know this question is about the application of 2nd​​ Law of Newton?

Though this question doesn’t directly says about the resultant force isn’t equals to zero but by carrying the calculation it is deduced here the principles of Newton's Second Law applicable.​​ 

  • Understanding the Forces

Let’s check out the minimum and maximum possible value of resultant force on the combination of three forces. You may draw in any direction. ​​ 

  • The minimum possible resultant force may be when 7N force acts in opposite direction to 2N & 4N.

R=7-2+4

R=7-6

R=1N

  • The maximum possible resultant force may be when all three forces act in the same direction.​​ 

R=7+4+2

R=13N

Therefore, the resultant force must value from 1N to 13N.​​ 

  • Correct Answer

The​​ correct option is A​​ as we have found above that the resultant force can’t be smaller than 1N and not more​​ than 13N. and among all the options, A stands incorrect because it is less than 1N.​​ 

Q4: Edexcel IAL U1/Oct/2020/Q7

Two forces, X and Y, act at a point. Which of the following vector diagrams shows the magnitude and direction of the resultant of the two forces?

 

QUESTION BREAKDOWN

Context:​​ Two forces combine to give a resultant force.​​ 

Focus:​​ Identify the vector diagram showing the correct direction of a resultant force. ​​ 

SOLUTION

  • How to know this question is about the application of 2nd​​ Law of Newton?

In identifying the resultant force direction, the 2nd​​ law of newton is applied as resultant force isn’t equals to zero. ​​ 

  • Understanding the Forces

Resultant force is the sum of vectors. In the vector diagram, the resultant force must be arranged in a way that its head must coincide with head of the one vector, and former’s tail with the tail of the other vector. In other words, resultant force arrow starts from the first vector tail and end at the head of the second vector.​​ 

  • Correct Answer

The​​ correct option is C​​ as we it represents the correct direction of resultant force. Whereas the option A & B are incorrect as vectors have not been added. ​​