Crash Course — Unit 3: Work, Energy, and Power

• Translational Kinetic Energy (K)
  €” The energy an object has because it's moving. It depends on mass and speed, and since speed is squared, doubling your speed quadruples your kinetic energy.
• Work (W)
  €” The transfer of energy into or out of a system by a force. It's only done when a force causes displacement in its own direction.
• Work-Energy Theorem
  €” The net work done on an object is equal to its change in kinetic energy (W_net = ΔK). This is a powerful bridge between forces and energy.
• Gravitational Potential Energy (Ug)
  €” Stored energy an object has due to its height in a gravitational field. You must define a h=0 reference point to calculate it.
• Elastic Potential Energy (Us)
  €” Stored energy in a spring that is stretched or compressed. The further you stretch it, the more energy it stores.
• The System
  €” The object or group of objects you choose to analyze. This choice is critical: it determines which forces are "external" (doing work) versus "internal" (changing potential energy).
• Conservation of Mechanical Energy
  €” In an isolated system (no friction or outside pushes/pulls), the total mechanical energy (K + U) remains constant. It just changes form, like from potential to kinetic.
• Non-Conservative Work
  €” Work done by forces like friction or air resistance. This work removes mechanical energy from the system, usually converting it into thermal energy (heat).
• Power (P)
  €” The rate at which work is done or energy is transferred. It’s not about how much energy, but how fast it's transferred.

Key Formulas / Terms

• Kinetic Energy
  K = ½mv²
• Work Done by a Force
  W = Fd cos(θ) (where θ is the angle between the force and the displacement)
• Work-Energy Theorem
  W_net = ΔK = K_f - K_i
• Gravitational Potential Energy
  ΔUg = mgh
• Elastic (Spring) Potential Energy
  Us = ½kx²
• Conservation of Energy (Isolated System)
  E_i = E_f which expands to K_i + Ug_i + Us_i = K_f + Ug_f + Us_f
• Conservation of Energy (with External Work)
  E_i + W = E_f
• Power (as a rate)
  P = ΔE / Δt or P = W / Δt
• Power (from force and velocity)
  P = Fv cos(θ)

Exam Traps

• Trap
  Confusing "work" with "effort." The prompt says Carlos holds a 50-pound box perfectly still for two minutes and asks for the work done. · Counter: Remember the formula: W = Fd cos(θ). If there is no displacement (d=0), no mechanical work is done. The answer is zero, even though Carlos's muscles are tired.
• Trap
  Forgetting the angle in the work formula. A wagon is pulled by a handle at a 45° angle to the ground. You're tempted to just multiply the force by the distance. · Counter: Work is only done by the component of the force that is parallel to the motion. Always use W = Fd cos(θ). If a force is perpendicular to motion (like the normal force on a block sliding horizontally), it does zero work.
• Trap
  Incorrectly defining the "system." A question asks for the work done by gravity on a falling ball. You might say "zero" because you know energy is conserved. · Counter: Read the prompt carefully! If the "system" is just the ball, then gravity is an external force that does positive work on it, increasing its kinetic energy. If the "system" is the ball and the Earth, then energy is conserved, and the change is described as a decrease in the system's potential energy, not as work.
• Trap
  Assuming energy is always conserved. A block slides down a ramp with friction and you set mgh = ½mv². · Counter: Mechanical energy is only conserved in the absence of non-conservative forces like friction. Friction does negative work, removing energy. The correct equation is E_initial + W_friction = E_final, or mgh - F_f * d = ½mv².
• Trap
  Treating energy as a vector. An object moves left at -10 m/s, so you calculate a negative kinetic energy. · Counter: Energy is a scalar. It has magnitude, but no direction. Kinetic energy depends on speed squared (v²), so it's always positive or zero. K = ½m(-10)² = ½m(100).