🛡️ Archmere Physics

The Master Energy Equation Infographic

Mastering Work, Energy, and Conservation. Think of physics like an energy bank account: track what you start with, what you add or lose, and what you have left. Gravity is set to 10 m/s².

1. The Energy Audit

KEi + GPEi + EPEi + Wext = KEf + GPEf + EPEf

2. The Players

🏃‍♂️

Kinetic (KE)

½mv²

The energy of motion. If the object stops moving, this bank account drops to zero.

⛰️

Gravitational (GPE)

mgh

Energy of height. The higher you go relative to your 'zero' point, the more energy you store.

🏹

Elastic (EPE)

½kx²

Energy stored in a spring. Because distance (x) is squared, triple the stretch means 9x the energy!

⚙️

Work (W)

F · Δx||

Energy transfer. Only the force parallel to the motion counts towards changing the system's energy.

3. The Friction Workflow

Step 1

Find Normal Force

FN = mg · cosθ

Step 2

Find Kinetic Friction

fk = μk · FN

Step 3

Calculate Work

W = -(fk) · Δx

🏆 Spotlight: The Auk-a-pult Case Study

Tracking energy through a multi-stage environment.

The Challenge Narrative

Part 1: The Launch. A 2.0 kg block starts at rest, compressed 0.4m against a powerful spring. This is where all the system's "motion money" is initially stored.

Part 2: The Toll Booth. Upon release, the block crosses a 2.0-meter rough patch. Friction acts as a "toll booth," removing a specific amount of energy based on the block's weight and the surface roughness.

Part 3: The Peak. After the rough patch, the block enters a smooth ramp. It will continue to climb until it has spent every last Joule of its remaining energy. What is that final vertical height?

Scenario Specs

Block Mass (m)
2.0 kg
Spring Constant (k)
500 N/m
Compression (x)
0.4 m
Rough Patch Dist.
2.0 m
Friction (μk)
0.25

Physics Ledger (Audit)

Initial EPE +40.0 J
Work (Fric) -10.0 J
Net Energy 30.0 J
Final Height: h = 1.50 m

1 Stage 1: Launch

Energy Input: The spring is compressed. Formula: ½(500)(0.4)² = 40J. The block begins with 100% potential energy.

2 Stage 2: Rough Patch

Energy Loss: Friction does negative work. W = -(μkmg)·Δx = -(5N)(2m) = -10J. This energy is turned into heat.

3 Stage 3: The Climb

Final Conversion: 40J (Start) - 10J (Loss) = 30J remaining. At the peak of the ramp, all remaining energy becomes GPE. 30J = (2kg)(10m/s²)h, solving for h = 1.5m.

Energy State Transitions

3-4-5 Geometry

At 36.87°, we use the 3-4-5 triangle to simplify components without a calculator.

sin(36.87°)
0.6
cos(36.87°)
0.8

Quick Tip: Why EPE is powerful

Because the distance x is squared in the formula ½kx², double the compression doesn't just double the energy—it quadruples it.

Compress 10cm → 10 Joules
Compress 20cm → 40 Joules!