"Force and Law of Motion"

 Force and law of motion

• Topics to be covered :- 
• Introducing
• What causes motion
• Force
• Balanced and unbalanced forces
• Galileo's idea of force and motion
• Newton's first law of Motion
• Newton's second law of motion
• Mass Vs inertia
• Newton's third law of motion
• Conservation of momentum

Introduction:- What causes motion?

• External force is needed to make a stationary body move 
• External force is needed to stop a moving body

Balanced and unbalanced forces:-

Balanced force:- 

• Equal and opposite forces
• Do not cause any change in motion
• Example:- Tug of war

Unbalanced forces:- 

• Unequal forces 
• Can be in the same or opposite direction
• Causes a change in motion

Law of motion:- 

• Aristotle's law of uniform motion:- An external force is required to keep a body in uniform motion.

Aristotle's fallacy:-

• He didn't discuss about opposite forces like frictional forces

Conclusion:-

• An external force is required to keep a body in motion, only if resistive forces like frictional and viscous force are present.

Galileo's Law :-

• A body moving on a frictionless surface should move with constant velocity.

Conclusion:- 

• Aristotle law was falsified by Galileo.
• A body at rest or in uniform motion experience zero net force.

Newton's first law of motion:- 

• A body at rest tends to remain at rest and a body in uniform motion tends to remain in the state of motion until and unless an external / unbalanced force is applied on it.
• Example:- Ball at rest , Ball in uniform motion

What is inertia?

• Inertia is the resistance of a body. To change its state of motion.
• Or
•  tendency of the body at rest tends to stay at rest  and tendency of the body in motion to keep in motion is called inertia.
• Example:-Jerk experienced when brakes applied suddenly.
• Tendency to bend on one side on a bike during sharp turn.

Newton's second law is about 

• Newton's first law was for scenario where net force is zero
• Newton's second law is for scenario with net force not equal to zero 

What is momentum ?.

• Momentum is product of mass of a body and it's velocity
• It is a vector quantity
• It is denoted by 'p'
• Mathematical expression is p=mv
• SI unit = kgm/s
• Dependency of force on mass 
• Force required to push object with same velocity 
• Greater the mass,more the force required to set the body in motion

Dependency of force on change in velocity

• Greater the velocity of moving object , more the force is required to stop the object
• Dependency of force on change in momentum in a  given time, greater is the force that needed to be applied.

Mathematical formulation of second law of motion:-

• Let an object of mass , m is moving along straight line with initial velocity, u
• It is uniformly accelerated to velocity, v in time t
• So initial momentum p(initial) = mu
• final momentum p(final) = mv
• Change in momentum, 
• dp = p(final) - p(initial) 
• = mv-mu = m(v-u)
• Change in momentum w.r.t time, dp/dt =m(v-u)/t
• Or, the applied force , F = km(v-u)/t = kma
• When k=1 
• F= ma 
• This is second law of motion

Newton's second law of motion:-

• The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts
• F  is directly proportional to (rate of change of momentum) 
• F = k(dp)/dt 
• When k=1 

• F = dp/dt

Alternatively:- 

• The relationship between an object's mass m, it's acceleration a , the applied force F is F=ma the direction of force is the same as the direction of acceleration.
• Another way of derivation :-
• F= dp/ dt

• F = d(mv)/dt
• F = m(dv)/dt
• F = ma 
• Where F= force applied,  m= mass of object , a= acceleration of an object
• Unit of force = Kgm/s^2
• S.I unit of force is newton (N)

Consistency of second law with first law:- 

• According to second law, F= ma
• If F = 0 then a=0 (m cannot be zero)

• Also acceleration is zero if the body is at rest or in uniform motion

According to first law, 

If a= 0 , F=0 

So two laws are consistent with each other.

Impulse:-

• Impulse is defined as a force multiplied by time it acts over. 
• Example :- Tennis racket striking the ball 
• Impulse = change in momentum.
• Because as per definition , I = F×t = dp

Newton's third law of motion:-

• To every action ,there is always an equal and opposite reaction
• Example:- Tonie holding ball
• He exerts force on ball to hold it - action
• The ball exert force back on his hand :- reaction
• Apple falling down the tree.
• Apple is pulled by earth due to gravitational force- action 
• Earth is pulled by Apple also - reaction 
• But mass of earth is very large as compared to Apple . So for e exerted by earth on Apple is also very large .so net force is acting on Apple and apple  down

Action and reaction forces :- 

• Action and reaction forces always act on different bodies 
• Action and reaction forces occurs at the same instant 
• There is no cause effect relation between them 

Conservation of momentum:-

• In an isolated system, the total momentum is conserved (does not mean zero) 

Example1:-

• Bullet from rifle 
• Initial momentum:- zero and kinetic energy = zero
• After fire :- momentum of bullet + momentum of rifle = zero but KE   increase
• So momentum is conserved 
• Momentum before collision = momentum after collision