Newton's Laws of Motion

Force

• Concept of force is central to all of physics whether it is classical physics,nuclear physics,quantum physics or any other form of physics
• So what is force? when we push or pull anybody we are said to exert force on the body
• Push or pull applied on a body does not exactly define the force in general.We can define force as an influence causing a body at rest or moving with constant velocity to undergo an acceleration.
• There are many ways in which one body can exert force on another body
  Few examples are given below
  (a)Stretched springs exerts force on the bodies attached to its ends
  (b)Compressed air in a container exerts force on the walls of the container
  (c) Force can be used to deform a flexible object
  There are lots of examples you could find looking around yourself
• Force of gravitational attraction exerted by earth is a kind of force that acts on every physical body on the earth and is called the weight of the body
• Mechanical and gravitation forces are not the only forces present infact all the forces in Universe are based on four fundamental forces
  (i) Strong and weak forces: These are forces at very short distance (10^-05 m) and are responsible for interaction between neutrons and proton in atomic nucleus
  (ii) Electromagnetic forces: EM force acts between electric charges
  (iii) Gravitational force -it acts between the masses
• In mechanics we will only study about the mechanical and gravitational forces
• Force is a vector quatity and it needs both the magnitude as well as direction for its complete description
• SI unit of force is Newton (N) and CGS unit is dyne where
  1 dyne= 10⁰⁵ N

Newton's First law of Motion

·       We have already stated Newton's First law of motion which says that a body would continue to be in state of rest or continue to move with constant velocity unless acted upon by a net external force

·       Here the net external force on the body is the vector sum of all the extenal forces acting on the body

·       When the body at rest or in a state of motion with uniform velocity then in both the cases acceleration is zero.This implies that
a=0 for F=0

·       When net forces i.e vector sum of all the forces acting on the body is zero.the body is said to be in equilbrium .When rotational motion is involved <,net torque on body should also be zero i.e their is no change in either translational or rotational motion

·       Since forces can be combined according to the rules of vector addition.Thus for a body to be in equilibrium
R=ΣF=0
or in component form
ΣF_x=0
ΣF_y=0
These are the condition for the body in translational equilibrium

·       We will discuss about rotational equilibrium while studying torque and rotational motion

·       Thus Newton's First law of motion quantitatively defines the concept of force as a influence that changes the state of motion of the body

·       It does not say anything about what has to be done to keep object moving that is once the body gains motion by the application of force would it always remains in the state of motion or it would come to rest

·       According to first law if we completely eliminates frictional forces, no forward force at all would be required to keep an object ( say a block on table) moving once it had been set in motion

Inertia and Mass

·       From First law of motion an object at rest would not move unless it is acted upon by a force

·       This inherent property of objects to remain at rest unless acted upon by a force is called intertia rest

·       Now consider the case of an object moving with uniform velocity along the straight line .Again from Newton's law it would continue to move with uniform

·       This inherent property by virtue of which a body in state of uniform motion tend to maintain its uniform motion is called inertia of motion

·       Combining these two statements 'The property of an object to remain in state of rest or uniform rectilinear motion unless acted upon by a force is called inertia'

·       Mass of any body is the measure of inertia .For example if we apply equal amount of force on two objects of different mass (say m₁ and
m₂ such that m₁ > m₂ ) then acceleration of both the object would be different (i.e , a₁ < a₂ )

·       Acceleration of object having larger mass would be lesser then the acceleration of object having smaller mass

·       Thus larger the mass of the body ,smaller would be the acceleration and larger would be the inertia

·       Newton's first law of motion revealing this fundamental property of matter i.e inertia is also known as law of inertia

Newton's second law of motion

• Newton's first law of motion qualitatively defines the concept of force and the principle of inertia
• For an body at rest, application of force causes a changed in its existing state and application of force on a body moving with uniform velocity would give the body under consideration as acceleration
• Newton's second law of motion is a relation between force and acceleration
• Newton's second law of motion says that
  " The net force on a body is equal to the product of mass and acceleration of the body"
  Mathematically
  F_net=ma                               (1)
  Where F_net is the vector sum of all the forces acting on the body
• Above equation -(1) can be resolved along x,y and z components .Thus in component form
  F_netx=ma_x
  F_nety=ma_y
  F_netz=ma_z
• Component of acceleration along a given axis is caused only by the net component of force along that axis only not by the components of force along other axis
• Newton's second law of motion is completely consistent with newton first law of motion as from equation (1) F=0 implies that a=0
• For a body moving under the influence of force, acceleration at any instant is determined by the force at that instant not by the previous motion of the particle
• Newton's second law of motion is strictly applicable to a single particle .In case of rigid bodies or system of particles, it refers to total external forces acting on the system excluding the internal forces in the system.

Newton's third law of motion

·       Statement of newton's third law of motion is " To every action there is always an equal and opposite reaction".

·       Thus,whenever a body exerts force on another then another object exert an equal force on previous body but in opposite direction

·       Force example motion of rocket depends on the third law of motion i.e, action and reaction .Rocket exerts action force on gas jet in backward direction

·       Force of action and reaction acts on different objects i.e,
Force object 1 exerts on object 2= Force object 2 exerts on object 1
i.e,
F₁₂=-F₂₁
Action=-(Reaction)

·       According to Newtonian mechanics force is always a mutual interaction between the bodies and force always occurs in pairs

·       Equal and opposite mutual forces between two bodies is the basic idea between Newton's third law of motion

·       While considering a system of particles ,internal force always cancel away in pairs i.e consider two particles in a body if F₁₂ and
F₂₁ are internal forces between particle system 1 and 2 then they add up to give a null internal force.Same way internal forces for the particles

 

Applying Newton's law of motion

·       Newton's law of motion ,we studied in earliar topics are the foundation of mechanics and now we look forward to solve problems in mechanics

·       In general, we deal with mechanical systems consisting of different objects exerting force on each other

·       While solving a problem choose any part of the assembly and apply the laws of motion to that part including all the forces on the chosen part of the assembly due to remaining parts of the assembly

·       Following steps can be followed while solving the problems in mechanics
1)Read the problem carefully
2) Draw a schematic diagram showing parts of the assembly for example it may be a single particle or two blocks connected to string going over pulley etc
3) Identify the object of prime interest and make a list of all the forces acting on the concerned object due to all other objects of the assembly and exclude the force applied by the object of prime interest on the other parts of the assembly
4) Indicate the forces acting on the concerned object with arrow and Label each force for example tension on the object under consideration can be labeled by letter T
5) Draw a free body diagram of the object of interest based on the labeled picture.Free body diagram for the object under consideration shows all the forces exerted on this object by the other bodies.Do not forget to consider weight W=mg of the body while labeling the forces acting on the body
6) If additional objects are involved draw separate free body diagram for them also
7)Resolve the rectangular components of all the forces acting on the body
8) Write Newton second law of equation for the body and solve them to find out the unknown quantities
9) Do not forget to employ Newton's third law of motion for action reaction pair which results in null resultant force

·       Following solved example would clearly illustrate how to apply Newton's laws of motion following the above given procedure