Newton's law of motion

 

 Newton's laws 

of motion 

There are following classification of forces 

1.   Gravitational force

2. Electromagnetic force

3. Nuclear force

4. Weak force

Another classification of forces-:

1. non - contact force

2. contact force  ( ex- frictional force, normal force, tension force)

Normal force-: Normal force is the component of  contact force in the direction perpendicular to the surface of contact. 

Normal force measure how strong two objects pressed against each other 

Tension -:  It is arises in a string when it is taught by some external force.

It always act along the string. 

It always have pulling tendency. 

For ideal string (massless , frictionless,) the tension is same throught out length of string .

What do you means by word " inertia" ?

The word inertia means that "avoid to change in state of body ". It is the property of the body.

simply ,we can say that if the object is in motion the body is continue to remain in uniform  motion unless no any external force is applied on it.also if the object is in rest then the continue to be in state of rest unless no any external force is applied on it . 

for ex -:  if ball is moving uniformly  on the road then it will continue to moving  unless  any frictional force is not act on it.

-: if any block is in rest on the table then it will maintain its state of rest unless we not apply external force on it.

What is newton's first law of motion?

Newton's first law of motion state that if the sum of  all forces acting on the particle is zero then and only then the particle remains at rest or moves with constant velocity(acceleration=0). 

What is frame of reference ?

 The reference from which observer measures the state of rest , motion and acceleration of the particle is called frame of reference.

 👉Also we can say that it define the position of a particle or an event in two or three dimensional space.  

There are two type of frame of reference - :

1. inertial frame of reference 

2.Non- inertial frame of reference

👉 inertial frame of reference - :  A  frame of reference in which newton's first law is valid is called an inertial frame of reference. 

 👉Non-inertial frame of reference -: A frame of reference in which newton's first law is not valid is called non-inertial frame of reference.

What is newton's second law of motion ?

According to second law the rate of change in linear momentum is directly proportional to external unbalanced forces ,this changes takes place in the direction of force. 

If p = linear momentum of a body , then from the second law 

F is  directly proportional to  dp/dt (rate of change of momentum)

F = kdp/dt = 1 --------(equation 1)

 so , F = 1   -------- equation 2 

 put the value of F in equation (1)

⇒1 = kdp/dt =1 

⇒1 = k*F = 1  ( F = dp/dt)

⇒1= k= 1  (F= 1  from equation 2 )

so k = 1 

from equation (1)

F = dp/dt 

but, p = m*v

 on differenciating both side , we get - 

dp/dt = m dv/dt  ( here m is constant  so taking outside while differenciating)

⇒F = ma  ( a= dv/dt)

∵ F = ma

What is newton's third law ?

For an isolated system of two bodies every action has an equal and opposite reaction and action and reaction take place on different bodies is called newton's third law . 

let us consider a system of two bodies A and B . 

F 12= force applied on 1 due to 2 . 

F 21= force applied on 2 due to 1. 

∴ F = F12 +F21

F12 = dp1/dt and F21 = dp2/dt 

F = dp1/dt +dp2/dt                                                                                    = d/dt(p1+p2)

∴  p1+p2 = total mometum of system. 

∴  p = dp/dt

but for isolated system external force 

F =0 

⇒  dp/dt = 0 

⇒ dp1/dt + dp2/dt =0 

 ⇒  F12 +F21 = 0 

  ⇒   F12 = -F21

principal of conservation of linear momentum  - :

According to this principle the total linear momentum of an isolated system remain constants. 

From newton 2nd law of , we know that , 

F = dp/dt 

for isolated system 

F= o 

dp/dt = 0 

dp = 0 

on integration both side , 

ഽ dp = ഽ0

  p = constant.

what is Impluse ?

When a large force is applied on body for very small time is called implusive force .the total effect of force on the body for a given time is called impluse. 

mathematically impulse is defined as the product of force and time 

Impluse = F*dt 

                = dp/dt*dt = dp

 Impluse = change in momentum 

generally impulsive force varies with time raises from 0 value to maximum value when the deformation is maximum . 

area under force-time graph with time axis = Impulse.

Impulse imparted to body 

I = ഽ Fdt

I = ഽma*dt

I =  ഽmdv/dt*dt

I = mഽdv  ,  lower limit (v= vi)  ,  upper limit (v= vf)

I = m 匚v］, lower limit (v= vi)  ,  upper limit (v= vf)

I = mvf-mvi

I = pf-pi  

                                      

Pseudo force -: It is made of two word pseudo and force. The word pseudo means false.i.e the force which is not real is called pseudo force. It is given by=  ao is the acceleration of    

acceleration of non - inertial frame of reference  and m is the mass of  body under consideration . 

👉 newton 's law is not valid for non-inertial frame of reference.To apply the newton 's law in non - inertial frame of reference we  have to apply pseudo force in the opposite direction of accleration of frame of reference.

👉Force is independent of frame of reference.

observer

A lift moving in upward direction and one observer is in lift and another is on the ground . find the tension in the wire of the lift when the observer is observing from lift and another observing outside the lift.

Soln-:  (1) for inertial frame of reference  (ground) 

  here block of mass M is taken as a system 

         Draw the free body diagram of block.                                                                                   

Along acceleration

Fnet = Ma

T-Mg = Ma

⇒T = mg+ma    ans.

For non - inertial frame of reference ( lift)

Draw the free body diagram of block when observing from lift. 

here a= 0

To apply the newton's law from the non- inertial frame of reference we have to  apply pseudo force in the opposite direction of frame of reference . 

now , fnet = 0  ( we have to stop the lift in order to apply newton's law of motion .so the acceleration of frame of reference become 0 .)

 

  T- (Ma+Mg) = 0 

T = (Ma+Mg)  ans.

💥    Equilibrium of forces

Those forces which has zero linear resultant and zero turning effect will not cause any change in the motion of  object to which they are applied  are called equilibrium of forces . 

👉 Resolution of force 

It is defined as a force is replaced by equivalent set of component.      In simple way we can say that forces is to break into x component and y component 

Note -: jiske sat theta sata rahega usko cos lenge or jiske sat theta hata rahega usko sin lenge. this is apply in any figure on which forces is acting. 

👉            coplanar forces in Equilibrium 

 When an object is in equilibrium under the action of a set of two or more coplanar  forces 

Each of three factors which comprise the possible movement of the object must be 0 

Simply we can say that ΣFx  = 0, ΣFy= 0 ,  Σ乙(torque)any axis = 0

💥   Equilibrium of concurrent coplanar forces

If the object is in equilibrium under two or more concurrent coplanar forces the algebraic sum of the components  of forces in any two mutually perpendicular direction should be zero. 

i.e. ΣFx  = 0 ,  ΣFy= 0 

{Summation of all forces along x axis and along y axis is 0 }

  

I hope this will helpful for you .

please share it so that many one got benefited .

Thank you 

   

SUMAN KUMAR