Physics: Potential Energy

• Physics is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force
• Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light
• Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed
• The joule (J) is the standard unit of energy in the International System of Units (SI)

Potential Energy

• Potential energy is energy that is stored in an object due to its position or configuration
• It can be transformed into other forms of energy, such as kinetic energy
• Potential energy is associated with forces that depend on the configuration (position) of a body
• The potential energy represents the work done by these forces when the body changes from a reference configuration to a given configuration
• Common types of potential energy include:
  • Gravitational potential energy: The energy an object has due to its height above a reference point
  • Elastic potential energy: The energy stored in a deformed elastic object, such as a stretched spring
  • Electric potential energy: The energy a charge has due to its location in an electric field
  • Chemical potential energy: The energy stored in the chemical bonds of molecules

Gravitational Potential Energy

• Gravitational potential energy is the energy an object possesses because of its position in a gravitational field
• The gravitational potential energy of an object near the Earth's surface is given by:
  • U = mgh
  • Where:
    • U is the potential energy (measured in joules)
    • m is the mass of the object (measured in kilograms)
    • g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
    • h is the height of the object above a reference point (measured in meters)

Elastic Potential Energy

• Elastic potential energy is the energy stored in a deformable object, such as a spring or rubber band, when it is stretched or compressed
• The elastic potential energy stored in a spring is given by:
  • U = (1/2)kx²
  • Where:
    • U is the potential energy (measured in joules)
    • k is the spring constant (measured in newtons per meter)
    • x is the displacement from the spring's equilibrium position (measured in meters)

Power

• Power is the rate at which energy is transferred, used, or transformed
• It is a scalar quantity
• Power is commonly measured in watts (W), where one watt is equal to one joule per second (1 W = 1 J/s)
• Power can be calculated using the following formulas:
  • P = W/t
  • P = Fv
  • Where:
    • P is power (measured in watts)
    • W is work done (measured in joules)
    • t is time taken (measured in seconds)
    • F is the force applied (measured in newtons)
    • v is the velocity of the object (measured in meters per second)

Efficiency

• Efficiency is a measure of how much of the input energy or power is converted into useful output energy or power
• It is a dimensionless quantity, often expressed as a percentage
• Efficiency is always less than or equal to 1 (or 100%), due to energy losses from heat, friction, and other factors
• Efficiency is calculated as the ratio of useful output energy or power to the total input energy or power:
  • Efficiency = (Output Energy / Input Energy) x 100%
  • Efficiency = (Output Power / Input Power) x 100%
• Example: If a motor consumes 100 J of electrical energy and produces 80 J of mechanical energy, its efficiency is 80%

Energy Conservation

• The law of conservation of energy states that the total energy of an isolated system remains constant
• Energy cannot be created or destroyed but can be transformed from one form to another or transferred from one object to another
• In any process, the total energy remains the same; energy is neither gained nor lost
• For example, in a closed system, potential energy can be converted into kinetic energy, and vice versa, but the total energy of the system remains constant