Usually, Students struggle with the concept of Newton’s Third Law of Motion. This is not as simple as it looks to be. One must have a command on the very concept before one dive in the questions of past papers regarding Newtonian physics (dynamics).
(Sir Muhammad Abdullah Shah)
Generally, the 3rd law of newton is defined as to every action there is an equal and opposite reaction, or every action is an equal and opposite reaction. Now, this is often wrongly interpreted.
The entire concept of Newtons 3rd law revolves around 4 important points:
In Newtonian physics, forces always exist in a pair: action and reaction. They are usually termed as third law pair forces.
The pair of forces are always in opposite direction and of equal magnitude. They are always in the same lie of action.
This very pair of force acts on two different bodies.
And, the action and reaction pair of forces are always of the same type of force.
Let us now comprehend each of them separately.
What do action and reaction mean?
First of all, this action and reaction mean nothing but forces. This same law can also be written in a different way and in a more understandable meaning as this is a better explanation of Newton's 3rd law of motion. ‘’When a mass exerts a force on the other mass, the other mass exerts a force on the first mass which is equal in magnitude but opposite in direction.’’ For example. If a student exerts some force on wall, the student also feel some pain. Now what actually happens here is a system of two bodies. The wall and the student’s hand. So, when student’s hand hits the wall, it exerts a force on the wall; simultaneously, the wall exerts the same force on the student’s hand. This is why the student also feels pain. So, if the student hits the wall harder, the student would also experience a harder force. Remember, we also call the action and reaction forces as the Third Law Pair. One more thing, these pair of forces exist simultaneously, not in a way that one force causes the other. It would be unfair to say that force exerted by the student’s force existed first and then wall exerted the force. Action and reaction forces always exist simultaneously or at the same time.
The action and reaction forces of equal magnitudea must act in opposite directions
It is simple that the relationship of action and reaction is of equal magnitude but in opposite directions. They can’t be in the same direction.
The action and reaction forces acts on two different bodies, never on a same body.
The third law pair always act on two different objects. Have a look at the figure below :……. In figure a there are two forces acting on it; they are equal in magnitude and opposite in direction. For sure, they will cancel out each other. But, now consider figure b the two forces act on two separate masses. On one mass there is a force of 100 Newton acting in upward direction and on the other mass there is a force of 100 Newton acting in downward direction. There is no point that they will cancel out each other because these two forces are not on the same object. So action reaction can never cancel out each other.
The third law pair forces are always of the same type
Remember, the third pair forces (action and reaction) are always of the same type. If one is gravitational force, the other has to be a gravitational force as well. It can never be like one is a gravitational force and the other force is electrostatic. And this is where the tricky questions are mostly asked in the question papers.
Exam Question # 01: [AQA GCSE/Physics Specimen/2018/Q9(i)]
Figure 15 shows the forces acting on a child who is balancing on a pogo stick.
The child and pogo stick are not moving.
The downward force of the child on the spring is equal to the upward force of the spring on the child. This is an example of which one of Newton’s Laws of motion? [1 mark]
Tick one box.
First Law
Second Law
Third Law
Solution
Now, the question itself tells us about the forces. It says the one force acts by the child on the spring, which is in the downward direction, and the other force acts by the spring on the child in the upward direction. Let us check those 4 points one by one:
Is there a pair of forces? | Yes, the one force is exerted by the child on the spring and the other force is exerted by the spring on the child. |
Are the two forces equal in magnitude and opposite in directions? | Yes, both are equal in magnitude and the direction of the force exerted by the child on the spring is downwards whereas the force exerted by the spring on the child is in upward direction. |
Are these two forces acting two different masses? | Yes, the one is exerted on spring and the other on the child. a |
Re they of the same type? | Yes, they are the same type. They both are contact forces. |
So, now its is evident that the two forces are the third pair forces, and therefore this is a 3rd law of newton example. So, the answer is
Third Law
Exam Question # 02: [Edexcel IAL]
Complete the table below by giving one example of each type of force.
Type of force | Example |
Gravitational |
|
Electromagnetic |
|
Nuclear |
|
(3)
The diagram shows forces acting on the Sun and the Earth. These forces form a Newton’s third law pair.
State three properties of these forces which are necessary for them to be a Newton’s third law pair.
(3)
Solution
For its first part, one must have knowledge of Types of Forces.
Type of force | Example |
Gravitational | Weight or force of attraction between two masses |
Electromagnetic | Electrostatic force between the two stationary point masses |
Nuclear | The force between the protons which make them reside in the nucleus though they have alike charges |
In the second part, the examiner asks us about the three conditions necessary for the forces to be a Newton third law of pair. So, they are 4 in total, student may write any three of them.
The forces must be of equal magnitudes.
They must be in opposite directions.
The forces should act on two different or separate masses like in this case one force acts on the sun and the ither acts on the earth.
They both must be of the same type as in this case both forces are gravitational forces.
Exam Question # 03: [Edexcel IAL]
(a) Complete the following statement of Newton’s third law of motion.
“If body A exerts a force on body B, then body B … ‘’
(2)
(b) A man checks the weight of a bag of potatoes with a newton meter. Two of the forces acting are shown in the diagram
The table below gives these forces. For each force there is a corresponding force, the ‘Newton’s third law pair force’. In each case state
• the body that the Newton’s third law pair force acts upon
• the type of force (one has been done for you)
• the direction of the Newton’s third law pair force
Force | Body the Newton’s third law pair force acts upon | Type of force | Direction of the Newton’s third law pair force |
Weight of potatoes |
|
|
|
Push of ground on man |
| Normal contact force |
|
Solution
If body A exerts a force on body B, then body B would exert equal and opposite force on body A. (This is what third law of newton tells us.)
Force | Body the Newton’s third law pair force acts upon | Type of force | Direction of the Newton’s third law pair force |
Weight of potatoes | Earth (When potatoes’ weight acts on the bag of potatoes, so its reaction force – the other force of a pair – would act on earth.) | Gravitational force (Weight is example of gravitational force.) | Upwards (As we know that the pair of forces are always in opposite direction, so when weight acts downwards, the direction of reaction force should be upwards.) |
Push of ground on man | Ground (The reaction force would be the push of man on ground.) | Normal contact force | Downwards (Since both the forces in the pair are opposite in direction.) |
Exam Question # 04: [Edexcel IAL/U1/Jan 2019/Q5]
According to Newton’s third law, when two objects interact, they exert forces on
each other.
Which of the following statements is not a correct description of these forces?
A) The forces act at the same time.
B) The forces act in the same direction.
C) The forces act on different objects.
D) The forces have the same magnitude
Solution
The 4 assumptions that are considered while discussing Newton 3rd law of motions are as follow
The forces must be of equal magnitudes.
They must be in opposite directions.
The forces should act on two different or separate masses
They both must be of the same type
So, the option B is not a correct description of these forces. The forces must act in opposite directions.
Exam Question # 05: [Cambridge IAL 9709/P1/Jan 2016/Q12]
A box is shown resting on the ground. Newton’s third law implies that four forces of equal magnitude are involved. These forces are labelled P, Q, R and S.
Forces P and Q act on the box. Forces R and S act on the Earth.
For clarity, the forces are shown slightly separated
Which statement about the forces is correct?
A) P is the equal and opposite force to Q and both are forces of contact.
B) Q is the equal and opposite force to P and both are gravitational forces.
C) R is the equal and opposite force to S and both are forces of contact.
D) S is the equal and opposite force to Q and both are gravitational forces.
Solution
Let us first understand which force does each arrow represents.
P is the Normal Contact Force (the force exerted by the ground on the box). It is an example of contact force. The easiest way to know is the force a contact force or not is that this force only occurs at the point of contact and the very arrow of P is also been starting from the point of contact – the ground.
R is the force exerted by the ground on the box in reaction. So here P & Q are equal in magnitude, opposite in directions, and of the same type, meaning thereby they both are contact forces.
Q is the weight of the box, and weight is gravitational force. The arrow of weight always generates from the centre of gravity.
S is the force exerted by the earth on the box. It is also gravitational force. So, the forces Q & S are equal in magnitude and opposite in direction.
To sum up, P & R and Q & S are the third pair forces.
So, the correct option is D: S is the equal and opposite force to Q and both are gravitational forces.
The correct answer is B because:
Newton's third law of motion states that when two bodies interact, the forces they exert on each other are
Equal in size
Opposite in direction
The same type of force
The person exerts force Q on the trolley
The trolley exerts force R on the person
Therefore, Q and R are the third law pairs
This is answer B
Remember that for third law pairs, you are looking for a pair of objects exerting a force on one another that is equal in magnitude but opposite in direction, and of the same type
Force P is the normal contact force of the floor on the trolley
Force S is the total drag force of friction and air resistance on the trolley
Both of these forces are acting on the trolley so they cannot be third law pairs
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.
The SI unit of momentum is .
Sometimes you may be asked too derive the unit of momentum as
Multiply ‘
As we know,
Hence, the derived unit of momentum is
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,
On combining both proportionalities we get
On removing proportionality sign, we get
On considering
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.
And we have learned above that the product of mass and velocity is known as momentum. So the formula would be
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.
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.
Now, using the formula
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 (
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
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.
The maximum possible resultant force may be when all three forces act in the same direction.
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.
An object at rest will remain at rest and a body in motion will continue its uniform motion unless acted upon by a resultant or net force.
It is important to note that in physics the uniform motion means the body is in same speed and direction.
By this, it can be deduced that a body may experience resultant force equal to zero in two conditions.
One when body is at rest (v=0)
Second, when the body is moving at a constant velocity (same speed and direction).
Moreover, the definition of mass can be defined with the help of 1st law of motion.
Mass (inertia) is the property of an object that resists any change in its current state of rest or uniform motion.
Let’s now consider some examples below to learn how 1st law of newton works in our daily life.
Example 1: Sliding Book
Scenario: Imagine a book placed on a table. The table is suddenly pulled out from under the book.
Explanation: When the table is pulled out, there's no horizontal force acting on the book. According to Newton's First Law, the book will remain at rest in its position in the air. It will continue to float momentarily until gravity pulls it down.
Example 2: Car Braking Incident
Scenario: The man inside the car was not wearing a seatbelt. The car was moving at a speed of 100 kmph.
Explanation: When the car suddenly applied the brakes, the car experienced a decelerating force. However, the man inside the car was still moving at 100 kmph due to inertia (property of an object that resists any change in its current state). Since there was no force acting specifically on the man, he continued to move forward at 100 kmph. Without a seatbelt to stop his forward motion, he was propelled out of the windscreen when the car stopped abruptly.
Example 3: Bus Braking Incident:
Scenario: A person standing inside a bus loses balance and falls backward when the bus suddenly starts moving.
Explanation: When the bus is at rest, the person and everything inside the bus are at rest. When the bus suddenly starts moving forward, the lower portion of the person's body, which is in contact with the bus (meaning it has a contact force acting on its lower part of body in the form of friction force by the floor of the bus on him), starts moving along with the bus. However, the upper portion of the person's body tends to stay at rest due to inertia. Since there is no force applied to keep the upper body in motion with the bus, the person loses balance and falls backward.
In all these examples, the concept of inertia, which is a fundamental aspect of Newton's First Law of Motion, is clearly demonstrated. Objects tend to maintain their state of motion (whether at rest or in motion at a constant velocity) unless acted upon by a resultant/net force.
Is it necessary for a body to be at rest, the polygon of forces acting on it must be closed?
When a body is at rest, the concept of the "polygon of forces" refers to the graphical method used to represent multiple concurrent forces acting on an object. In equilibrium (which includes the state of rest), the vector sum of all the forces acting on the object is equal to zero. This condition ensures that the object is not accelerating and remains at rest.
The "polygon of forces" method involves drawing vectors to scale, representing all the forces acting on the object. These vectors are placed head-to-tail in a sequence. If the object is in equilibrium, the polygon formed by these vectors must be closed. In other words, the starting point of the first vector should meet the ending point of the last vector, forming a closed geometric shape, typically a polygon.
The closure of the polygon signifies that the forces are in balance and that the object is in equilibrium. If the polygon does not close, it indicates that the forces are not balanced, and the object would be in a state of motion or acceleration, not at rest. Therefore, a closed polygon of forces is a visual representation of the balance of forces in an object at rest or in equilibrium.
Q1: 9702 Mar 23/P12/Q12, M/J 14/P11/Q11, O/N 09/P12/Q11, O/N 09/P11/Q12
The diagrams show two ways of hanging the same picture.
In both cases, a string is attached to the same points on the picture and looped symmetrically
over a nail in a wall. The forces shown are those that act on the nail.
In diagram 1, the string loop is shorter than in diagram 2.
Which information about the magnitude of the forces is correct?
A
B
C
D
QUESTION BREAKDOWN
Context: Two picture frames are being hung on a wall using strings looped symmetrically.
Focus: Identify the correct information about the magnitude of forces involved (specifically, normal reaction force and tension in the strings).
SOLUTION
How to know this question is about the application of 1st Law of Newton?
The question says that the frame is hanging, a condition which aligns with the principles of Newton's First Law.
Understanding the Forces
Normal Reaction Force (R): This force is exerted by the wall on the nail and supports the weight of the picture frame. For both frames to remain stable, the normal reaction force (R) must balance the weight of the frame (W). Therefore,
Tension in Strings (
Consider a frame hanging, we are considering a general scenario here.
Since the frame is hanging, meaning it is in equilibrium, not moving vertically or horizontally, the sum of forces acting on a body along the y – axis is zero.
By this expression, it may be concluded that
When
When
Comparison of Picture Frames:
Picture 1: The string loop is shorter, resulting in smaller angles. The higher tension (T1) is required to balance the smaller vertical component.
Picture 2: The string loop is longer, leading to larger angles. The lower tension (T2) is needed because of the significant vertical component.
Correct Option:
Eliminating Options: By understanding that normal reaction force must equal the weight of the frame
Correct Answer: The correct answer is option B, where tension
Q2: 9702 M/J 23/ P11/ Q13
The diagram shows a ball of weight W hanging in equilibrium from a string.
The string is at an angle
Which relationship between the magnitudes of T, P and W is correct?
A P = T cos and W = T sin
B T = P + W
C T2 = P2 + W2
D W = P tan and W = T cos
QUESTION BREAKDOWN
Context: Ball is hanging in equilibrium by the string attached and metal rod.
Focus: Identify the correct equations defining the relationship between forces T, P, & W.
SOLUTION
How to know this question is about the application of 1st Law of Newton?
The question says that the ball is equilibrium, a condition which aligns with the principles of Newton's First Law.
Understanding the Forces
Tension in the spring causes forces two act on the ball in two directions. One is upwards, and the second is leftwards.
Force P is the force applied by the metal rod on the ball horizontally (along the positive x- axis).
Whereas, weight always acts vertically downward, acting towards the centre of the Earth.
Since ball is in equilibrium, the sum of forces acting on the ball horizontally and vertically are equal to zero.
It is important to note that the angle
Let us first consider the forces acting vertically.
Now, considering the forces acting on the ball horizontally.
We may write the above values as
Since
OR
Correct Option:
By comparing the values of
Q3: 9702 MJ 22/ P11/ Q7
An object is moving along the ground in a straight line at a constant speed.
Which statement about the resultant force acting on the object is correct?
A The resultant force acting on the object is equal to its weight.
B The resultant force acting on the object is equal to the product of its mass and its velocity.
C The resultant force acting on the object is equal to the resistive force.
D The resultant force acting on the object is equal to zero.
QUESTION BREAKDOWN:
Context: An object is moving along the ground in a straight line at a constant speed.
Focus: Determine the correct statement about the resultant force acting on the object.
SOLUTION
Analysing the Options
Option A: The resultant force acting on the object is equal to its weight.
Evaluation: This statement does not necessarily hold true when the object is moving at a constant speed. Weight is the force due to gravity, but if the object is not accelerating vertically, the vertical forces are balanced.
Conclusion: Incorrect.
Option B: The resultant force acting on the object is equal to the product of its mass and its velocity.
Evaluation: This statement describes the formula for calculating momentum (
Conclusion: Incorrect.
Option C: The resultant force acting on the object is equal to the resistive force.
Evaluation: This option is closer to the correct concept. When an object moves at a constant speed, the resistive force (like friction) is equal in magnitude but opposite in direction to the applied force, resulting in a balanced situation.
Conclusion: Partially correct but not the best choice.
Option D: The resultant force acting on the object is equal to zero.
Evaluation: This option accurately represents the scenario. When an object moves at a constant speed, it experiences no acceleration. According to Newton's first law of motion, the object is in a state of equilibrium, with the net force being zero.
Conclusion: Correct choice.
Correct Answer:
The correct option is D. The resultant force acting on the object is equal to zero.
Q4: MJ 22/ P13/ Q13
A street lamp is fixed to a wall by a metal rod and a cable.
Which vector triangle could represent the forces acting on the end of the rod at point P?
QUESTION BREAKDOWN:
Context: The street lamp is held stable/fixed by a metal rod and cable.
Focus: Determine the correct vector diagram of the given options.
SOLUTION
How to know this question is about the application of 1st Law of Newton?
The question says that the lamp is fixed, a condition which aligns with the principles of Newton's First Law.
Understanding the Forces
Tension in the string as it supports the lamp.
On the other hand, the weight acts in downwards direction as the earth attracts it to the centre of the earth.
Remember, to form a vector triangle, it is necessary that the vectors, forces in this case, must be combined with each head’s coinciding with other vector’s tail. In other words, there should be no resultant vector. If the bottom vector is drawn with its direction leftward, tension in the cable would become resultant force, which is not the case in this question. Recall that it is must for the body to be equilibrium that the polygon of forces is closed, otherwise the resultant force would exist, acting on a body.
Hence, the correct vector diagram/triangle is shown below.
Correct Answer
The correct option is D, as the weight acts downwards, not upwards as shown in option A. other than options A and D, there has been a resultant vector forming therefore, they cant be the correct options.
Q5: Edexcel IAL U1/Oct/2021/Q6
A block of wood is stationary on a frictionless ramp as shown. The block is held in place by a string. The weight of the block is W. The force applied to the block by the string is F.
A triangle of forces can be used to determine the magnitude and direction of the normal contact force N acting on the block.
Which of the following triangles is correct?
QUESTION BREAKDOWN
Context: A block is held by the string on an inclined surface.
Focus: Identify the vector diagram showing the polygon of forces closed.
SOLUTION
How to know this question is about the application of 1st Law of Newton?
The question says that the block is stationary, a condition which aligns with the principles of Newton's First Law.
Understanding the Forces
For an object to be stationary, it is necessary that the polygon of forces acting on the object is closed that is the starting point of the first vector should meet the ending point of the last vector, forming a closed geometric shape, typically a polygon.
Correct option
The correct option is A that the normal force mut act in upward direction.