Laws of Motion Notes: Newton’s First, Second and Third Law of Motion with Example In the grand tapestry of the cosmos, where celestial bodies dance through the vast expanse of space and objects on Earth move with a rhythm of their own, there exists a set of fundamental principles that govern the motion of all things. These principles were first articulated by one of the greatest scientific minds in history: Sir Isaac Newton. Newton’s Laws of Motion revolutionized our understanding of the physical world and laid the groundwork for classical mechanics, shaping the way we perceive motion and interact with our environment.
Laws of Motion are the brainchild of Issac Newton. The entire branch of classical mechanics is based on Newton’s Laws of Motion. We have studied the types of motions in Motion in a Straight Line and in Motion in Two and Three Dimensions. We know the different physical quantities we require to define motion: displacement, velocity and acceleration. Further, we also discussed the different types of motion: Projectile, Circular, Uniform and Non-uniform. Now, we know that a uniform motion does not have acceleration but in a non-uniform motion, the body accelerates.
Let’s go through the Definitions
- Velocity: The rate of change of displacement of a body is called velocity. It is denoted by V. The SI unit of velocity is m/s.
- Uniform velocity: The velocity of a body that does not change with time is called uniform velocity.
- Acceleration: The rate of change in velocity of the body is called acceleration. It is denoted by a. The SI unit of acceleration is m/s2.
- Force: The interaction that after applying to a body changes or tries to change the state of rest or a state of uniform motion of the body is called force. It is generally denoted by F.
Sir Isaac Newton gave the laws of motion regarding the motion of objects. There are various activities in our daily life in which we encounter the laws of motion in various forms. For this topic, we need to understand both conceptual as well as mathematical/numerical aspects of the events.
For example, We know that if we kick a football with the help of our foot, it moves. The movement of the football is due to force. When you kick a wall then instead of moving, it also applies some opposite force on your foot and you feel bad. We will see that all these activities are based on the laws of motion.
Newton’s Laws of Motion
Newton gave us three laws of motion that can be applied to all macroscopic objects in motion. Let’s study them in detail.
Newton’s First Law of Motion
According to the First Law of Motion, “An object at rest will remain at rest and the object moving with uniform velocity will continue the uniform velocity until we apply some external force.”
For example, a car moving with some velocity will be moving until we apply the brakes to stop it. A ball kept on the road will remain at rest until we apply some force to move it.
The state of rest or state of uniform motion of any object implies zero acceleration. Thus according to the first law of motion, when the net external force on a body is zero then the acceleration of the body will be zero. The acceleration of the body will be non-zero only when there is some external force on the system.
Newton’s first law of motion gives the definition of force. It also gives the definition of inertia of a body.
Inertia and Mass
A body, either in a state of rest or in a state of motion, always tries to resist change. So if an external force is applied to the body, the body will try to resist the force. This inbuilt ability of the body is equal to the mass of the body. It is called inertia.
Unbalanced and Balanced Force
When two opposing forces of the same magnitude act on an object, the forces get balanced. For example, A box lying on the floor has a downward force due to weight. At the same time, the floor exerts an equal upward thrust.
When one force exceeds another, the system becomes unbalanced. For example, when we lift the box, we apply an extra upward force.
Finding Net Force
Considering the above example, let the box have a weight of 30N.
In the first case of balanced force, the floor will also exert 30 N upwards on the box.
Therefore,
Net force = weight of the box + upward thrust = -30+30=0
In the second case of an unbalanced force.
Let’s apply a force of 40N to lift the box.
Therefore,
Net force = weight of the box + upward thrust + external force = -30+30+40= 40N
The Big Misconception
Students often think that an object at rest has no forces acting on it. However, it is not true. An object at rest also experiences forces. However, the forces are at equilibrium or balance. The forces are not zero, the net force or resultant force is zero.
Newton’s Second Law of Motion
According to Newton’s second law of motion, “The rate of change of momentum of any object is directly proportional to the force applied on the object in the direction of the force.”
F α dPdt
F =K d(mv)dt
F =K mdvdt
Since, acceleration (a)=dvdt
F =Kma
Where K is a constant, m is the mass of the object, V is velocity, t is time and a is acceleration.
If m=1, a=1 and F =1 then k =1 for unit measures
Thus force (F) = ma
Unit of force: kg.m/s2 or Newton (N)
Newton: The force required to create the acceleration of 1 m/s2 for a 1 kg mass is called 1 Newton force in the direction of the force.
Mass (m) = 1 kg, acceleration (a) = 1 m/s2
Force (F) = m a = 1 × 1 = 1 kg.m/s2 = 1 Newton (N)
Newton’s second law of motion gives the formula of the force. It also gives the formula of the impulse of a body.
Impulse
The change in momentum of an object is called impulse. It is denoted by J.
Impulse (J) = Change in momentum (ΔP)
F = ΔPΔt
Δ P = F. Δ t
Thus Impulse (J) = Δ P = F.Δ t
Q. A ball of mass 3 kg is moving with an acceleration of 2 m/s2. Find the force on the ball.
Ans.
Given that:
Mass (m) = 3 kg
Acceleration (a) = 2 m/s2
According to Newton’s second law:
Force (F) = m a = 3 × 2 = 6 N
Q. A bullet of mass 0.5 kg is moving with a velocity of 40 m/s enters a wooden block and comes to rest after 10 sec. find the average force applied by the wooden block on the bullet.
Ans.
Given that:
Initial velocity (u) = 40 m/s
Final velocity in rest position (V) = 0
Mass (m) = 0.5 kg
Time take (Δ t) = 10 sec
Initial momentum (P1) = m u = 0.5 × 40 = 20 kg m/s
Final momentum (P2) = m V = 0.5 × 0 = 0
Change in momentum (Δ P) = Impulse (J) = (P1–P2) = 20 – 0 = 20 kg. m/s
Since impulse (J) = Force (F) × time (Δ t) = 20
F × 10 = 20
Force (F) = 20/10 = 2 N
Q. The velocity of a particle varies as V = 2 t2. Find the force on the particle at the time (t) = 5 seconds. The mass of the particle is 2 kg.
Ans.
Given that:
Mass (m) = 2 kg
Velocity (V) = 2 t2
Time (t) = 5 sec
Since,
Acceleration (a)= dVdt= d(2t2)dt=4t
Force (F) = m a = 2 × 4 t = 8 t
At time (t) = 5 sec
Force (F) = 8 t = 8 × 5 = 40 N
Average force: The net force applied to a body over a time interval is called average force. The average force is a force acting on a body for a period of time.
Newton’s Third Law of Motion
Newton’s third law of motion states that: “To every action, there is always an equal and opposite reaction”
Important points
- Forces always occur in pairs force on a body A by B is equal and opposite to force on the body B by A
Fab = -Fba
- The force on A by B and the force on B by A act at the same time instant, so there is no cause-effect relation
- Action and reaction forces act on different bodies not on the same body
Fab = -Fba
Force on A by B = – Force on B by A
Q. A man applies a 40 N of force on a wall. Find the force applied by the wall on the man.
Ans.
Given that:
Force by the man on the wall (F) = 40 N
According to Newton’s third law:
Action force = Force by man on wall (F) = 40 N
Force applied by wall on the man = reaction force = action force = 40 N
Why is Newton’s Second Law Called Real Law?
Both the first and third laws can be proved by the second law of motion.
Proof Of First Law By Second Law:
Force (F)= dpdt
As we know by the second law,
If there is no external force applied then F=0 so
dpdt=0
Δ p = 0 So, Δ V = 0
No change in velocity if there is no net external force is applied. Hence the first law was proved.
Proof Of Third Law By Second Law:
If there is no external force then
Fnet=0
dpdt=0
dpAdt+dpBdt=0
FAB+FBA=0
FAB=−FBA
Hence the third law also stands proved.
Conservation of Momentum
The product of mass and velocity is called momentum. It is denoted by P.
Momentum (P) = mass (m) × Velocity (V)
The Law of Conservation of Momentum can be stated as— “If there is no net external force on the system then the total momentum of the system of interacting particles is conserved.”
The initial momentum of the system = Final momentum of the system
When two particles collide with each other then there is no external force on the two-particle system. So the momentum of the system of two particles before and after the collision will remain the same.
m1u1+m2u2=m1v1+m2v2p1+p2=p′1+p′2
Q. A body of mass 0.25 kg is projected with muzzle velocity 100m/s from a tank of mass 100 kg what is the recoil velocity of the tank?
A. Given that: Mass of tank (mt) =100kg and mass of object (mo) =0.25kg
(Vo) = 100 m/s, then Vt =?
As we know that initially both are at rest so u0 = 0 and ut =0
So total momentum before collision = mtuo+mout=0
Total momentum after collision should also be equal to zero, so mtVt+moVo=0,
100 x Vt + 0.25 x100 = 0 Hence Vt = – 0.25 m/s
Equilibrium of a Particle
Equilibrium of a particle is the situation when the net external force on the particle is zero.
If two forces F1 and F2, act on a particle, equilibrium requires F1=−F2orF1+F2=0
i.e. the two forces on the particle must be equal and opposite.
The resultant of any two forces say F1 and F2, obtained by the parallelogram law of forces must be equal and opposite of the third force, F3
Q. A mass of 6 kg is suspended by a rope of length 2 m from the ceiling. A force of 50 N in the horizontal direction is applied at the midpoint P of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium? (Take g = 10 m/s2). Neglect the mass of the rope.
Ans.
Ans.
T2 = 6 × 10 = 60 N,
T1 cos θ = T2 = 60 N
T1sinθT1cosθ=5060
T1 sin θ = 50 N
So,
tanθ = 5/6
Types of Forces
Common Forces in Mechanics are friction force, drag force, tension, central force, spring force, and pseudo force. They are seen in most of our daily life problems. Hence, we call them Common Forces in Mechanics Study them here.
Hope this helped you to understand the important concept of the Laws of Motion. Do practice it now on the Testbook through the free mock tests.