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Energy Definition

  • Defined as the capacity of a system to perform work.

  • Exists in various forms: heat, kinetic, potential, and electrical energy.

  • Can be converted from one form to another.

  • According to the principle of conservation of energy:

    • Energy can never be created or destroyed.

  • SI unit is Joule (J).

Work Done

  • No work is done when energy is not transferred to an object.

  • Work is done when energy is transferred to an object in motion (e.g., a person pushing a box).

  • Work is essentially a transfer of energy between an object and its surroundings.

    • Example: Changing the speed of an automobile involves work.

Kinetic Energy (KE)

  • Kinetic energy is the energy associated with an object's motion.

    • Formula: KE = 1/2 mv² (where m = mass, v = velocity).

    • Same mass and speed but different directions result in the same kinetic energy.

    • If mass doubles (2m) while speed remains the same, kinetic energy doubles (KE = 2 × KE).

    • If speed doubles, the kinetic energy increases by four times (KE = 4 × KE).

Work and Kinetic Energy Relationship

  • When a block slides on a frictionless surface:

    • If pushed in the same direction of motion, total work done is positive (W_total > 0), causing the block to speed up.

    • If no net force acts (push straight down), total work done is zero (W_total = 0), and speed stays constant.

    • If pushed against the direction of motion, total work done is negative (W_total < 0), slowing the block.

  • Work-energy theorem:

    • The net work done on an object equals the change in kinetic energy (W_total = ΔKE).

Potential Energy (PE)

  • Related to an object's position in a gravitational field.

    • Example: PE increases as an object is lifted (PE = mgh).

  • Gravitational potential energy depends on the height (h) above a reference point—calculation involves work done against gravity.

    • Work by external forces (Wext) and gravitational work (Wg) derived from changes in height.

Elastic Potential Energy

  • Associated with the deformation (stretching or compressing) of objects like springs.

  • Velocities upon release of a compressed spring convert elastic potential energy into kinetic energy.

    • Formula: PE_elastic = 1/2 kx² (where k = spring constant, x = displacement from equilibrium).

  • Work done on or by the spring equals the change in elastic potential energy.

Conservative vs Nonconservative Forces

  • Conservative forces: The work done is independent of the path taken.

    • Example: Gravity feeds into conservation of total mechanical energy.

  • Nonconservative forces: Change the mechanical energy; work done by forces like friction doesn't result in potential energy transfer.

Conservation of Mechanical Energy

  • Total mechanical energy (E = KE + PE) remains constant if only conservative forces act.

  • In systems affected by nonconservative forces, such as friction, mechanical energy is not conserved (e.g., trampoline vibration dissipates mechanical energy).

Power and Efficiency

  • Power is the rate of doing work:

    • Unit of power: Watt (W), 1 W = 1 J/s.

  • Efficiency is the ratio of useful energy output to total energy input:

    • Example: Calculate power output based on work done over time (P = W/t).

Practical Examples and Applications

  • Problem-solving involving kinetic and potential energies using conservation principles:

    • Analyze energy transformations in systems with springs and blocks (frictionless scenarios).

    • Applications in calculating speeds of blocks and objects on inclines, accounting for energy losses from friction.

("Department of Physics / Mindanao State University / Iligan Institute of Technology")