Applications of Laws of Motion

1.0Introduction to Laws of Motion

Laws of motion, formulated by Sir Isaac Newton, form the foundation of classical mechanics. They describe the relationship between forces acting on a body and its motion. Understanding these laws is essential for JEE students, as they appear in numerical problems, conceptual questions, and real-life scenarios.

The three laws of motion are:

1. First Law: Law of inertia $(F=ma)$
2. Second Law: Force equals mass times acceleration
3. Third Law: Action-reaction law

The applications of these laws are observed in both microscopic and macroscopic phenomena, from planetary motion to the motion of vehicles and machinery.

2.0Newton’s First Law and Its Applications

Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.

  Or

To change the state of motion of a body an external force is necessary. There are two states of motion of a body.

(1) State of rest $(v=0,a=0)$

(2) State of uniform motion $(v0,a=0)$

  Or

If the vector sum of all the forces acting on a particle is zero, then and only then the particle remains unaccelerated (i.e., remains at rest or moves with constant velocity).

The first law is also known as the law of inertia.

Inertia: The resistance of a particle to change its state of rest or of uniform motion along a straight line. It could be of three types:

• Inertia of rest
• Inertia of motion
• Inertia of direction

Note:

1. Force is the cause of changes in motion

• Force does not cause motion. We can have motion in the absence of force, as described in Newton’s first law. Force is the cause of change in motion as measured by acceleration.

2. ma is not a force

• Equation 2 does not say that the product $ma$ is a force. All forces on an object are added vectorially to generate the net force on the left side of the equation. This net force is then equated to the product of the mass of the object and the acceleration that results from the net force

Applications:

• Seat belts in vehicles: Prevent passengers from continuing forward motion during sudden braking.
• Vehicle design: Understanding inertia helps in designing shock absorbers and brakes.
• Objects at rest: Heavy objects on a table remain stationary until an external force moves them.

3.0Newton’s Second Law and Its Applications

The rate of change of linear momentum of a body is equal to net force acting on the body.

$F=dpdt=ddtmv$ (Mass is constant)……..(1)

$F=mdvdt=ma$ …….(2)

• Acceleration of a particle as measured from an inertial frame (ground) is given by the vector sum of all the forces acting on the particle divided by its mass.

4.0Newton’s Third Law and Its Applications

Newton’s Third Law of Motion

If a body A exerts a force F on another body B, then B exerts a force $-F$ on A ,the two forces acting along the line joining the bodies

These two forces in Newton’s third law are known as Action-Reaction pairs.

Third law of motion : 

To every action, there is always an equal and opposite reaction. Newton’s law from an 1803 translation from Latin as Newton wrote.

Important points about the Third Law

(a) The terms ‘action’ and ‘reaction’ in the Third Law mean nothing else but ‘force’. A simple and clear way of stating the Third Law is as follows: Forces always occur in pairs. Force on a body A by B is equal and opposite to the force on the body B by A.

(b) The terms ‘action’ and ‘reaction’ in the Third Law may give a wrong impression that action comes before reaction i.e. action is the cause and reaction the effect. There is no such cause-effect relation implied in the Third Law. The force on A by B and the force on B by A act at the same instant. Any one of them may be called action and the other reaction.

(c) Action and reaction forces act on different bodies, not on the same body. Thus, if we are considering the motion of any one body (A or B), only one of the two forces are relevant. It is an error to add up the two forces and claim that the net force is zero.

However, if you are considering the system of two bodies as a whole, FAB force on A due to B) and FBA (force on B due to A) are internal forces of the system (A + B). They add up to give a null force. Internal forces in a body or a system of particles thus cancel away in pairs. This is an important fact that enables the Second Law to be applicable to a body or a system of particles.

Example

Tension at 'A' is force applied by string on (1) 

Tension at 'B' is force applied by string on (2)

(d) String is assumed to be massless unless stated, hence tension in it everywhere remains the same and equal to applied force.

However, if a string has a mass, tension at different points will be different being maximum (applied force) at the end through which force is applied and minimum at the other end connected to a body. (eg.)

(e) Every string can bear a maximum tension, i.e. if the tension in a string is continuously increased it will break if the tension is increased beyond a certain limit. The maximum tension which a string can bear without breaking is called "breaking strength". It is finite for a string and depends on its material and dimensions.

Applications:

• Rocket launch: Gases expelled downward produce upward motion.
• Swimming: Pushing water backward propels a swimmer forward.
• Walking: Feet push backward, ground pushes forward enabling motion.
• Jet engines: Reaction of exhaust gases moves the plane forward.

Applications in Everyday Life

• Braking systems: Applying Newton’s laws to design brakes in vehicles.
• Safety features: Helmets, airbags, and safety harnesses use principles of inertia and force.
• Elevator motion: Acceleration and force calculations ensure smooth operation.
• Furniture and objects: Understanding friction and motion helps in ergonomics.

What is the system? 

Any group of objects which we decide to study together can be taken as a system.

Internal and external forces 

If the action-reaction pair exists in the considered system, then it is known as internal force, otherwise it is known as external force.

Free-Body Diagram (FBD) 

The diagrammatic representation of a body that is isolated from its surroundings, showing all the external forces acting on it, is known as the free-body diagram (FBD).

Steps for drawing the FBD

1. Isolate the free body.
2. Draw the external forces.
3. Choose the axes and resolve the forces.

5.0Solved Problems on Laws of Motion

Illustration-1:Draw the free body diagram and find tension in each string and acceleration of the system.

Solution: 

acceleration $=$ Net Pulling Force Total Mass to be pulled $=3010=3m/s^2$

$T1=3a$

$N3-3g=30$

$N3=30N$

$T2-T1=2a$

$N2-2g=20$

$N2=20N$

$30-T2=5aN5-5g=50N5=50N$

Note:

Here NAB and NBA are the action-reaction pair(Newton’s third Law)

Illustration-2:A block of mass 50 Kg is kept on another block of mass 1 kg as shown in fig. A horizontal force of 10 N ia applied on the 1 kg block(All surface are smooth).Find

$g=10m/s^2$            

1. Acceleration of Block A AND B
2. Force exerted by B on A

Solution

1. F.B.D of 50 kg

$N2=50G=500N$

Along the horizontal direction there is no force $aB=0$

(b)  F.B.D of 1  kg block

                   $10=1aA$

              $aA=10m/s2$

Along vertical direction

$N1=N2+1g=500+10=510N$

Illustration-3:Find Tension and acceleration

Solution

$T1-T2-2g=25$                               

$T1-T2=30$

$T1-45=30$

$T1=7$

$T2-3g=35$

$T2=15+30$

$T1=45N$