FORCE AND MOTION

 as in mdcat physics, the theory is not the most important and only we have to learn the tips and tricks to solve the numerical problems. However, some theoretical key points which I write on every post, and also write the important formula and example of the question to solve it. 

Displacement:

The shortest distance between any two points is called displacement. In the case of a straight line, the distance and displacement are equal to each other. while in a circular path, the displacement is zero and the distance is 2pi r and the ratio of distance to displacement is equal to infinity.

velocity: The rate of change of displacement is called velocity. 

    v= ▲d/▲t

• Average velocity does not tell us about the motion of the body between any two points along which the body moves.
• if a ball hits the floor and comes back to its initial position, its displacement is zero and its average velocity is zero.
• Non-Uniform velocity:  If the body covers equal displacement in unequal intervals of time r cover the unequal displacement in equal intervals of time, then it has non-uniform velocity.
• If the displacement is zero, then the average velocity is zero but the average speed has some value.
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• If the body covers an equal distance in unequal intervals of time then:
•                                      v=  2v1v2/v1+v2
• If the body covers an unequal distance in equal intervals of time then:
•                                         v= v1+v2/2
• if a body covers 1/3rd of distance with v1, second 1/3rd of distance with v2, and third 1/3rd of the distance with v3, then:
•                                  v= 3v1v2v3/v1v2+v2v3+v3v1

 When the object moves along a straight line, and its direction of motion does not change, then all the vectors can be manipulated as scalers.

If a body covers unequal displacements in unequal intervals of time, then

                                v= d1+d2/ t1+t2

Acceleration: The rate of change of velocity is called acceleration.

The negative acceleration is called deceleration or retardation.  a=▲v/▲t.

Force: its SI unit is Newton and its absolute unit is dyne.

             1N= 100000 dyne 

Newton's law of motions:

     These laws are valid only in the inertial frame of reference and for those bodies whose speed is lower than the speed of light.

   According to newton's third law action and reaction never act on the same body and never cancel or balance each other.

Momentum: The quantity of the motion which is equal to the product of the mass and velocity of the body is called the momentum of the body.

                                           p=mv

If two bodies of different masses and velocities have the same momentum then:

                 m1v1=m2v2 or m1/m2=v2/v1 

When a large force acts on a body for a short time an impulse is produced which is equal to the product of force and time.

              Fx t = MVf-MVi   

for the freely falling body, the rate of change of momentum is equal to :

         F= ▲p/t or mg= MVf-MVi  / t

law of momentum:

      In an isolated system, the rate of change of momentum is: m1v1+m2v2=m1v'1+m2v'2

 Elastic collision:  In this collision, the total energy, momentum, and K.E energy are conserved.  So no heat or sound energy is produced in an elastic collision. In an elastic collision, the speed of approach is equal to the speed of separation.

while in an inelastic collision, the momentum and total energy only remain conserved. And heat or sound may be produced. in an inelastic collision, the speed of approach is greater than the speed of separation.

as v1+v'1=v2+v'2 or  v1-v2= v'2-v'1

and v'1= (m1-m2)v1/m1+m2  +  2m2v2/m1+m2     

  v'2= 2m1v1/m1+m2  +  (m2-m1)v2/m1+m2          

  Projectile Motion:  The two-dimensional motion of the body under constant acceleration due to gravity. 

      the body moves along the x-axis as well as along y- the axis.    Motion along the x-axis is completely independent of the motion along the y-axis.

Types:

1. Inclined projectile
2. oblige projectile 
3. Horzintilal projectile

Oblique projectile: this projectile makes an elliptical path when it moves with high velocity and under the nonuniform gravity acceleration and makes a parabolic path when moves with low velocity and under constant 'g'. In the absence of air friction, the projectile makes a parabolic path.  At the highest point of the projectile when the angle is zero along the x-axis the angle between velocity and gravitational acceleration G is 90 degrees and at the maximum height, the range is half of its value.                                                                 The maximum height attained by the projectile during projectile motion is h= Vi^2 sin^2Θ/ 2g.                                                            Time taken by the projectile from its point of projection to its point of landing is:   T= 2VisinΘ/g                                                               The maximum horizontal distance covered by the projectile during its projectile motion is called Range: R= Vi^2 sin2Θ/g