🫴Physical Science Unit 9 – Work, Energy, and Power

Key Concepts and Definitions

• Energy the capacity to do work or cause change
• Kinetic energy energy of motion determined by an object's mass and velocity
• Potential energy stored energy due to an object's position or configuration
  • Gravitational potential energy energy due to an object's height above a reference point
  • Elastic potential energy energy stored in a deformed elastic object (spring)
• Work force applied over a distance in the direction of the force
• Joule (J) SI unit of energy and work equivalent to applying 1 Newton of force over a distance of 1 meter
• Power rate at which work is done or energy is transferred measured in Watts (W)
• Conservation of Energy principle stating that energy cannot be created or destroyed only converted from one form to another

Types of Energy

• Mechanical energy sum of an object's kinetic and potential energy
  • Kinetic energy ($KE = \frac{1}{2}mv^2$) depends on mass and velocity
  • Potential energy ($PE = mgh$) depends on mass, gravity, and height
• Thermal energy internal energy of a substance due to the random motion of its particles
• Chemical energy potential energy stored in chemical bonds (fossil fuels, batteries)
• Electrical energy energy associated with electric charges and their movement (current)
• Electromagnetic energy energy in the form of electromagnetic waves (light, radio waves)
• Nuclear energy energy released during nuclear reactions (fission, fusion)
• Sound energy energy associated with the vibration of particles in a medium (air, water)

Work and Its Relationship to Energy

• Work ($W = Fd\cos\theta$) product of force and displacement in the direction of the force
  • Positive work done when force and displacement are in the same direction ($0° < \theta < 90°$)
  • Negative work done when force and displacement are in opposite directions ($90° < \theta < 180°$)
  • No work done when force is perpendicular to displacement ($\theta = 90°$)
• Work-Energy Theorem states that the net work done on an object equals the change in its kinetic energy ($W_{net} = \Delta KE$)
• Work can be represented by the area under a force-distance graph
• When work is done on a system, energy is transferred or converted
  • Lifting an object increases its gravitational potential energy
  • Compressing a spring increases its elastic potential energy
• Energy is required to perform work overcoming friction, air resistance, or gravity

Conservation of Energy

• Energy cannot be created or destroyed only converted from one form to another
• In a closed system, the total energy remains constant
• Mechanical energy is conserved in the absence of non-conservative forces (friction, air resistance)
  • $KE_i + PE_i = KE_f + PE_f$ (initial energy equals final energy)
• Energy can be dissipated as heat due to non-conservative forces
• Law of Conservation of Energy applies to all forms of energy (mechanical, thermal, chemical, etc.)
• Energy transformations occur in many real-world scenarios (power plants, vehicles, ecosystems)

Power: Energy Transfer Rate

• Power ($P = \frac{W}{t}$) rate at which work is done or energy is transferred
  • Measured in Watts (W) equivalent to 1 Joule per second (1 J/s)
• Instantaneous power ($P = Fv$) product of force and velocity at a given instant
• Average power ($P_{avg} = \frac{W}{t}$) total work done divided by the time interval
• Power output determines the efficiency of machines and devices
  • Higher power implies faster energy transfer or work done
• Comparing power ratings helps assess the performance of engines, appliances, and electronic devices
• Power generation and transmission are crucial aspects of modern infrastructure (power plants, electrical grids)

Equations and Calculations

• Kinetic Energy: $KE = \frac{1}{2}mv^2$
  • $m$: mass (kg)
  • $v$: velocity (m/s)
• Gravitational Potential Energy: $PE = mgh$
  • $m$: mass (kg)
  • $g$: acceleration due to gravity (9.8 m/s²)
  • $h$: height (m)
• Work: $W = Fd\cos\theta$
  • $F$: force (N)
  • $d$: displacement (m)
  • $\theta$: angle between force and displacement
• Power: $P = \frac{W}{t}$ or $P = Fv$
  • $W$: work (J)
  • $t$: time (s)
  • $F$: force (N)
  • $v$: velocity (m/s)
• Conservation of Mechanical Energy: $KE_i + PE_i = KE_f + PE_f$
  • Subscripts $i$ and $f$ denote initial and final states

Real-World Applications

• Roller coasters demonstrate the conversion between kinetic and potential energy
• Hydroelectric power plants harness the potential energy of water to generate electricity
• Solar panels convert electromagnetic energy (sunlight) into electrical energy
• Hybrid and electric vehicles utilize the interplay between chemical, electrical, and kinetic energy
• Biomechanics applies principles of work and energy to analyze human movement (sports, rehabilitation)
• Energy-efficient technologies (LED lights, insulation) aim to minimize energy waste and optimize power usage
• Renewable energy sources (wind, solar, geothermal) rely on energy transformations to produce usable power

Common Misconceptions and FAQs

• Misconception: Energy is a substance or material that can be used up
  • Reality: Energy is a property that can be transferred or converted but not created or destroyed
• Misconception: An object at rest has no energy
  • Reality: An object at rest may have potential energy due to its position or configuration
• Misconception: Work is done whenever a force is applied
  • Reality: Work is only done when the force causes a displacement in the direction of the force
• FAQ: Can energy be recycled?
  • Energy cannot be recycled in the same sense as materials, but it can be continuously converted from one form to another
• FAQ: Is it possible to create a perpetual motion machine?
  • No, perpetual motion machines are impossible due to the law of conservation of energy and the presence of non-conservative forces
• FAQ: How does the concept of energy relate to the concept of force?
  • Force is an interaction that can cause a change in an object's energy by doing work on the object