⚡ Mechanical Energy

Kinetic Energy (Eₖ): 0 J
Pot. Energy (Eₚ): 0 J

📈 Efficiency & Power

Efficiency: 0%
Power Loss: 0 W

The Physics of Energy Transfer

Energy is defined as the capacity to do work. The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. In AS Level Physics, we focus primarily on mechanical energy transfers.

Work Done (W) = Force (F) × displacement (s) × cos(θ)

1. Mechanical Energy Forms

  • Kinetic Energy (Eₖ): The energy an object possesses due to its motion. Eₖ = ½mv².
  • Gravitational Potential Energy (Eₚ): The energy stored by an object due to its position in a gravitational field. Eₚ = mgh.
  • Elastic Potential Energy: The energy stored in a deformed material. E = ½Fx = ½kx².

2. Power and Efficiency

Power is the rate at which work is done or energy is transferred. For a moving object subject to a constant force, Power can also be calculated as the product of force and velocity (P = Fv).

Power = Work / Time = Energy / Time
Exam Tip: When calculating work done against gravity (e.g., a person climbing stairs), the displacement is the vertical height, not the diagonal distance traveled.

Deep Dive: Worked Examples

✅ Example 1: Energy Transformation (Free Fall)

A 0.5kg ball is dropped from a height of 10m. Calculate its velocity just before hitting the ground.

Step 1: Conservation of Energy Loss in GPE = Gain in KE
Step 2: Equate and simplify mgh = ½mv² → gh = ½v² → v = √(2gh)
Step 3: Solve v = √(2 × 9.81 × 10) ≈ 14.0 m/s

✅ Example 2: Power to Overcome Friction

A car travels at a constant 30 m/s. If the total resistive forces are 800 N, find the engine's power output.

Step 1: Formula selection At constant velocity, Driving Force = Drag Force = 800 N. Use P = Fv.
Step 2: Calculate Power = 800 × 30
Step 3: Solve Power = 24,000 W (or 24 kW)

✅ Example 3: System Efficiency

An electric motor lifts a 200kg crate 5 meters in 10 seconds. If the motor consumes 1500W of electrical power, what is its efficiency?

Step 1: Work done against gravity W = mgh = 200 × 9.81 × 5 = 9810 J
Step 2: Output Power P_out = Work / Time = 9810 / 10 = 981 W
Step 3: Efficiency Eff = (981 / 1500) × 100 = 65.4%

✅ Example 4: Work Done at an Angle

A child pulls a sled 10m with a force of 50N at 30° to the horizontal. Calculate the work done.

Step 1: Use W = Fs cos(θ) W = 50 × 10 × cos(30°)
Step 2: Solve W = 500 × 0.866 = 433 J

✅ Example 5: Kinetic Energy of a Proton

A proton (m = 1.67 × 10⁻²⁷ kg) is accelerated to 2 × 10⁶ m/s. Find its KE.

Step 1: Formula E_k = 0.5 × m × v²
Step 2: Calculate E_k = 0.5 × 1.67e-27 × (2e6)²
Step 3: Solve E_k = 3.34 × 10⁻¹⁵ J