3.1 Translational Kinetic Energy
Energy is a scalar quantity that represents a system's ability to produce change. The most straightforward form of energy to observe is the energy of motion, known as Kinetic Energy.
Translational Kinetic Energy (K): The energy an object possesses due to its translational (straight-line) motion.
Translational Kinetic Energy Formula
- m = mass of the object (kg)
- v = speed of the object (m/s)
- Unit = Joules (J)
⚠️ Remember: Because velocity is squared, kinetic energy is a scalar quantity and can never be negative. A car moving at -10 m/s has the exact same kinetic energy as a car moving at +10 m/s!
3.2 Work
In physics, Work is not about physical effort; it is the mechanical transfer of energy into or out of a system due to a force acting over a displacement.
Work (W): The product of the component of force parallel to the displacement and the magnitude of the displacement.
- F = magnitude of the force (N)
- d = magnitude of the displacement (m)
- θ = angle between the force vector and displacement vector
Sign of Work
Positive Work (+W)
Force and displacement point in the same direction (θ < 90°). Energy is added to the system (it speeds up).
Negative Work (-W)
Force and displacement point in opposite directions (θ > 90°). Energy is removed from the system (it slows down).
Zero Work (W=0)
Force is perpendicular to displacement (θ = 90°). No energy is transferred. Examples include Normal force or Centripetal force.
Work from a Graph
If a force is not constant, you cannot simply use $W = Fd$. Instead, you must use graphical analysis.
The Area under a Force vs. Position (F-x) graph equals the Work done.
3.3 Potential Energy
Potential energy is the energy "stored" in a system due to the relative positions of its interacting parts. A single object cannot have potential energy; it requires a system of at least two objects.
| Gravitational Potential Energy (Ug) | Elastic Potential Energy (Us) |
|---|---|
| Energy stored in the Earth-Object system based on height. | Energy stored in a spring-object system based on compression or stretch. |
|
ΔUg = mgΔy
|
Us = ½kx2
|
| Height (Δy) is relative. You can choose any horizontal level to be y=0! | Displacement (x) is measured from the spring's natural, relaxed length. |
3.4 Conservation of Energy
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred or transformed. The way we write this mathematically depends on our choice of system boundary.
Closed/Isolated System: No external forces do work on the system. Total mechanical energy is perfectly conserved.
Open System (Work-Energy Theorem): External forces (like friction or an applied pull) act on the system, changing its total energy.
🎯 Solving Energy Problems:
- Define your system (e.g., Block + Earth + Spring).
- Identify the initial state and final state.
- Set a reference point for zero potential energy (usually the lowest point).
- Determine if any external forces are doing work.
- Set up the conservation equation and solve!
3.5 Power
While Work tells us how much energy is transferred, Power tells us how fast that energy is transferred.
Power (P): The rate at which work is done or the rate at which energy is transferred into or out of a system.
If a constant force moves an object at a constant velocity, power can also be expressed as:
Thought Experiment: The Stair Climb
Walking up a flight of stairs and sprinting up the same flight of stairs requires the exact same amount of Work (your change in potential energy, mgΔy, is the same). However, sprinting takes less time (Δt), so it requires far more Power!
Unit 3 Key Takeaways
Kinetic energy is a scalar and is never negative.
Forces perpendicular to motion (like centripetal force) do ZERO work.
The Area under a Force-Position graph equals Work done.
Potential Energy requires a system (e.g., Object-Earth).
Energy is conserved in isolated systems: Ki + Ui = Kf + Uf.
Power is the rate of doing work (Watts = Joules per second).
End of Unit 3 Study Guide.