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Laws Of Motion

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Law of Motion PDF Notes, Important Questions and Formulas

FORCE

A pull or push which changes or tends to change the state of rest or of uniform motion or direction of motion of any object is called force. Force is the interaction between the object and the source (providing the pull or push). It is a vector quantity.

 

Effect of resultant force:

  • May change only speed
  • May change only direction of motion.
  • May change both the speed and direction of motion.
  • May change size and shape of a body

 begin mathsize 12px style table attributes columnalign left end attributes row cell Unit space of space force :  newton space and space fraction numerator kg. straight m over denominator straight S squared end fraction left parenthesis MKS space System right parenthesis end cell row cell dyne space and space fraction numerator straight g. cm over denominator straight S squared end fraction left parenthesis CGS space System right parenthesis end cell end table end style

1 newton =105

Kilogram force (kgf)

The force with which earth attracts a 1 kg body towards its centre is called kilogram force, thus

 begin mathsize 12px style kgf equals fraction numerator Force text  in newton end text over denominator straight g end fraction end style

Dimensional Formula of force: [MLT-2]

For full information of force we require

  • Magnitude of force
  • Direction of force
  • Point of application of the force
 

Electromagnetic Force

Force exerted by one particle on the other because of the electric charge on the particles is called electromagnetic force. 

Following are the main characteristics of

Electromagnetic force

  • These can be attractive or repulsive
  • These are long range forces
  • These depend on the nature of medium between the charged particles.
  • All macroscopic force (except gravitational) which we experience as push or pull or by contact are electromagnetic, i.e., tension in a rope, the force of friction, normal reaction, muscular force, and force experienced by a deformed spring are electromagnetic forces. These are manifestations of the electromagnetic attractions are repulsions between atoms/molecules.

 

Gravitational force:

It acts between any two masses kept anywhere in the universe. It follows inverse square rule

(F ∝ ) begin mathsize 12px style 1 over distance squared end style and is attractive in nature.

begin mathsize 12px style straight F equals fraction numerator GM subscript 1 straight M subscript 2 over denominator straight R squared end fraction end style

The force mg, which Earth applies on the bodies, is gravitational force.

Nuclear force:

It is the strongest force. It keeps nucleons (neutrons and protons) together inside the nucleus inspite of large electric repulsion between protons. Radioactivity, fission, and fusion, etc. result because of unbalancing of nuclear forces. It acts within the nucleus that too up to a very small distance.

 

1.4 Contact force:

Forces which are transmitted between bodies by short range atomic molecular interactions are called contact forces. When two objects come in contact they exert contact forces on each other.

 

1.4.1 Normal force (N):

It is the component of contact force perpendicular to the surface. It measures how strongly the surfaces in contact are pressed against each other. It is the electromagnetic force. A table is placed on Earth as shown in figure.

 

 

Here table presses the earth so normal force exerted by four legs of table on earth are as shown in figure.

 

Now a boy pushes a block kept on a frictionless surface.

 

Here, force exerted by boy on block is electromagnetic interaction which arises due to similar charges appearing on finger and contact surface of block, it is normal force.

 

A block is kept on inclined surface. Component of its weight presses the surface perpendicularly due to which contact force acts between surface and block.

 

Normal force exerted by block on the surface of inclined plane is shown in figure.

 

 

Force acts perpendicular to the surface

  • Normal force acts in such a fashion that it tries to compress the body
  • Normal is a dependent force; it comes in role when one surface presses the other.

 

Centripetal Force

  • Centripetal force is the force required to move a body uniformly in a circle. This force acts along the radius and towards the centre of the circle.
  • A continuous change in the direction of motion of the body, there is a change in velocity of the body and undergoes acceleration called centripetal acceleration or radial acceleration. The centripetal force is called as fictitious or pseudo force

Motion of a car on a level curved road

 

 

Forces acting on the car,

  • The weight of the car, mg, acting vertically downwards
  • Normal reaction R, of the road on the car acting vertically upwards
  • Frictional force f, along the surface of the road towards the centre of the turn

 

Free Body Problems

  • A diagram for each body of the system depicting all the forces on the body by the remaining part of the system is called free body diagram (FBD).

 

 

  • It is called free-body diagram because it will show the object without its surroundings i.e. the body is 'free" of its environment.


Friction

Friction is the force which develops at the surface of contract of two bodies and opposes (impedes) their relative motion.

 

 

 

  • Friction in liquids and gases is called viscosity.
  • The angle of friction between any two surfaces in contact is defined as the angle which the resultant of the force by virtue of limiting friction F and normal reaction R makes the direction of normal reaction R. It is represented by θ.

 

 

 

 

 begin mathsize 12px style tan text   end text straight theta text  = end text straight F over straight R equals straight mu end style

Hence,  m = tan θ

i.e. the limiting friction is equal to tangent of the angle of friction.

  • Angle of repose and angle of sliding is defined as the minimum angle of inclination of a plane with the horizontal, such that an object placed on the plane begins to slide.

 

 

 

Kinetic Friction / Dynamic Friction

  • Kinetic friction or dynamic friction is the opposing force which develops between the surfaces of contact of the two bodies, when one body is in relative motion over the surface of another body.

 

 

  • Kinetic friction is directly proportional to the normal reaction i.e.

            Fk R.

             Or Fk= mkR  

  • When the body moves with a constant velocity,

             Fk = F

 

Sliding Friction

  • The opposing force which comes into action when one object slides over the surface of another object is called sliding friction.
  • Sliding friction is smaller than static friction.


Rolling Friction

  • The opposing force which comes into action when an object rolls over the surface of another object is called rolling friction.

 

 

Momentum

  •  It is defined as the total quantity of motion contained in a body and is measured as the product of a body's mass and its velocity.
  • The momentum O' of a body is defined as the product of mass 'm' and velocity 'V of the body.

Momentum = Mass × Velocity

p=m × v

  •  The SI unit of momentum is Newton (N).

1 N = 1 kg. m/s

  •  The CGS unit of force is dyne.
    1 Newton =105 dyne
  • Every moving body possesses momentum.


Change in momentum

  • If Fx, Fy and Fz are components of force along X-axis, and Z-axis,

 begin mathsize 12px style table attributes columnalign left end attributes row cell straight F subscript straight x equals dp subscript straight x over dt equals ma subscript straight x end cell row cell straight F subscript straight y equals dp subscript straight y over dt equals ma subscript straight y end cell row cell straight F subscript straight z equals dp subscript straight z over dt equals ma subscript straight z end cell end table end style

 

Impulse

  • Impulse is the product of average force and time and equals the change in momentum. Impulse = Average force × Time = Change in momentum

 begin mathsize 12px style table attributes columnalign left end attributes row cell straight F with rightwards arrow on top equals fraction numerator dp with rightwards arrow on top over denominator dt end fraction end cell row cell straight F with rightwards arrow on top text  dt =  end text dp with bar on top end cell end table end style

  • Dimension: M1 L1 T-1
  • In SI, the unit of impulse is N s or kg m s-1 and in CGS the unit of impulse is dyn a or g cm e'.
  • Bogies of a train are provided with buffers because they avoid severe jerks during shunting of the train. Because of the presence of buffers, time of impact increases. Therefore, force during jerks decreases and hence the chance of damage decreases.
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