Physics: Mechanics and Force

• Physics is a natural science that studies matter, its motion, and behavior through space and time, and that studies the related entities of energy and force.

Mechanics

• Mechanics is the branch of physics concerned with the motion of bodies under the action of forces, including the special case of bodies at rest.
• Mechanics can be divided into:
  • Classical mechanics: Deals with the motion of macroscopic objects at speeds much less than the speed of light.
  • Quantum mechanics: Deals with the behavior of matter at the atomic and subatomic levels.
  • Relativistic mechanics: Deals with the motion of objects at speeds comparable to the speed of light.

Force

• Force is an interaction that, when unopposed, will change the motion of an object.
• A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
• Force can also be described intuitively as a push or a pull.
• Force is a vector quantity, meaning it has both magnitude and direction.
• The SI unit of force is the Newton (N).
• Examples of forces include:
  • Gravitational force: The force of attraction between objects with mass.
  • Electromagnetic force: The force between electrically charged objects.
  • Strong nuclear force: The force that holds protons and neutrons together in the nucleus of an atom.
  • Weak nuclear force: The force responsible for radioactive decay.

Work

• In physics, work is said to be done when a force acting on an object causes a displacement of the object.
• Work is a scalar quantity, meaning it has magnitude but no direction.
• The SI unit of work is the joule (J).
• The work done by a constant force is calculated as:
  • W = F * d * cos(θ)
    • Where:
      • W is the work done
      • F is the magnitude of the force
      • d is the magnitude of the displacement
      • θ is the angle between the force and displacement vectors.
• If the force and displacement are in the same direction, the work done is positive.
• If the force and displacement are in opposite directions, the work done is negative.
• If the force is perpendicular to the displacement, no work is done (e.g., moving horizontally while holding a weight).

Power

• Power is the rate at which work is done.
• Power is a scalar quantity.
• The SI unit of power is the watt (W).
• Power is calculated as:
  • P = W / t
    • Where:
      • P is power
      • W is work done
      • t is the time taken to do the work.
• Power can also be expressed as:
  • P = F * v
    • Where:
      • F is the force
      • v is the velocity of the object on which the force is acting, both in the same direction.

Energy

• Energy is the capacity to do work.
• Energy is a scalar quantity.
• The SI unit of energy is the joule (J).
• Different forms of energy:
  • Kinetic energy: The energy of motion.
    • KE = (1/2) * m * v^2
      • Where:
        • KE is kinetic energy
        • m is mass
        • v is velocity
  • Potential energy: Stored energy due to position or condition.
    • Gravitational potential energy: PE = m * g * h
      • Where:
        • PE is potential energy
        • m is mass
        • g is the acceleration due to gravity
        • h is height above a reference point
    • Elastic potential energy: PE = (1/2) * k * x^2
      • Where:
        • k is the spring constant
        • x is the displacement from the equilibrium position
  • Thermal energy: Energy associated with the temperature of an object.
  • Chemical energy: Energy stored in chemical bonds.
  • Electrical energy: Energy associated with electric charge.
  • Nuclear energy: Energy stored within the nucleus of an atom.

Work-Energy Theorem

• The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
  • W_net = ΔKE = KE_f - KE_i
    • Where:
      • W_net is the net work done
      • KE_f is the final kinetic energy
      • KE_i is the initial kinetic energy

Conservation of Energy

• The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another.
• In a closed system, the total energy remains constant.
• This principle is fundamental to many areas of physics.