In daily life, the word energy means the capacity to do work.

SCALAR PRODUCT(or multiplication of vector)-

  • There are 2 ways to multiplication of vector-
    • Vectors product- {WE STUDY IN CHAPTER 6}
    • Scalar product-
      • Also called dot product of two vectors.
      • It is denoted by A.B, and we read it that A dot B.
      • A.B = A B cosθ, where θ is angle between 2 vector, A and B are magnitude of vectors.
      • Each vector vector(like A and B) has direction but scalar product not have any direction.
      • The scalar product are always scalar.
      • If vector point in the same direction (θ = 0°), the scalar product is positive.
      • If the vector are perpendicular (θ = 90°), the scalar product is zero.
      • If vector point in the same direction(θ = 180°), the scalar product is negative.
      • The scalar product follow the distributive law:- A.(B+C) = A.B + A.C .

Work Energy Theorem-

  • After small derivation(derivation in question section), we get – 1/2mv2 – 1/2mu2 = m a . d = F . d.
  • Work Energy Theorem-
    • It state that the net work done on an object is equal to the change in its kinetic energy.
    • Wnet = Kf – Ki, where Wnet = total work done, K = Kinetic energy(1/2mv2.)

WORK-

  • Work- It is a product of component of force in direction of displacement and the magnitude of displacement.
  • W= F*s*cosθ 
  • If displacement(s) is zero, then no work done.
  • If force(F) is zero, then no work done.
  • If force(F) and displacement(s) both are perpendicular (90°), then no work done.
  • Work done can be positive, negative and zero-
    • Work done is positive when the value of cosθ is between 0° to 90°.
    • Work done is negative when the value of cosθ is between 90° to 180°.
    • Work done is zero when the value of cosθ is 90°.
  • Dimension of work is [M1L2T-2].
  • SI unit of work is Joule(J), on the name of famous physicist, James Prescott Joule(1811-1869).

THE KINETIC ENERGY(K.E.)-

  • It possessed by an object due to its motion.
  • K.E. = 1/2 mv2, where m is mass and v is velocity.
  • It is scalar quantity.
  • Its dimension is same as energy and work is [M1L2T-2].

WORK DONE BY DIFFERENT FORCES(variable force)-

  • It is the work done when force applied on an object changes in magnitude and direction during its motion.
  • It is calculated by integral of force over the displacement.
    • W =  ∫ F(x)dx, where F(x) is variable force, x is displacement.
  • The work depend on how forces change with position.
  • Mostly different forces act, rarely constant force work.
  • After small steps, we get finally.

POTENTIAL ENERGY(P.E.)-

  • Potential energy-
    • It is the energy an object has because of its position or configuration.
    • P.E. = mgh, where m is mass, g is gravity and h is height.
    • Its unit is Joule(J).
    • Its dimension is [M1L2T-2].

CONSERVATION OF MECHANICAL ENERGY-

  • Mechanical Energy(M.E.)-
    • It is the total energy of an object due to its motion (Kinetic Energy) and position (potential energy).
    • M.E. = K.E. + P.E.
  • Conservation of Mechanical Energy-
    • It means the total of kinetic energy and potential energy stays constant if only conservative force act.
    • K.E. + P.E. = Constant
  • The work done by conservative force is depend on only end point.

POWER-

  • Power- It is a rate of doing work or transferred of energy.
  • Its SI unit is Watt(W).
  • 1 watt is J/s or 1 J s-1 .
  • Dimension of power is [M1L2T-3].
  • Formula to find power is-
    • P = w / t
    • P = F * v, where F is force, v is instantaneous velocity.
  • Another unit of power is horse power (hp).
    • 1 hp = 746 W

THE COLLISIONS-

  • Collision- It is an event where 2 or more bodies interact for a short instant of time and exchanging energy and momentum.

ELASTIC COLLISION-

  • In collision, linear momentum is conserved.
    • Initial momentum(Pi) = Final momentum(Pf)
  • Total kinetic energy may be or conserved.
  • The major impact and deformation of collision is form heat and generate sound.
  • Types of collision-
    • Elastic Collision- Both momentum and kinetic energy are conserved.
    • Inelastic Collision- Momentum is conserved, but kinetic energy is not conserved.
    • Perfectly Inelastic Collision or Completely Inelastic Collision- Momentum is conserved, but the colliding bodies stick together, losing maximum kinetic energy.

COLLISION- 1D-

  • Collision in 1 Dimension or hear-on collision- When 2 object move along a same straight line before and after collision.

COLLISION- 2D-

  • Collision in 2 Dimension- When 2 objects collide and move in 2 perpendicular directions, involving both horizontal and vertical components of motion.

These all are the notes of chapter 1 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊