Physics Capstone Modeling
Apply multiple physics models to a real-world system, justify assumptions, interpret data, and communicate evidence-based conclusions.
A lesson of Physics, in Fluids, Thermal Physics, and Modern Physics, about 10 minutes.
Physics Capstone: Modeling and Problem Solving
By the end of this lesson, you will be able to approach novel physics problems by identifying relevant principles, building models, making and testing predictions, and evaluating the limitations of your models.
The Big Idea
This capstone lesson synthesizes the year's work: every physics problem involves building a model, identifying which laws apply, making predictions, and testing them. The same skills — defining systems, drawing FBDs, choosing appropriate equations, checking units, estimating reasonableness — apply regardless of the specific topic.
The Physics Problem-Solving Framework
- Read carefully: what is asked? What is given?
- Draw a diagram: free-body diagram, energy diagram, circuit diagram, wave diagram — match to the type of problem.
- Identify the system and relevant principles:
- Kinematics? (Use kinematic equations)
- Forces? (Newton's Second Law)
- Energy? (Conservation; work-energy theorem)
- Momentum? (Conservation in isolated systems)
- Waves? (Wave equation, Snell's law, interference)
- Electricity? (Ohm's law, Kirchhoff's laws)
- Set up equations: list knowns, unknown, relevant equations.
- Solve: algebraically if possible before substituting numbers.
- Check: units correct? Order of magnitude reasonable? Does the answer make physical sense?
Multi-Concept Problem Examples
Example 1 — Energy + Kinematics
A roller coaster car (800 kg) starts from rest at the top of a 50 m hill. Using energy conservation (neglect friction), find the speed at the bottom. Then use kinematics to find how far it travels on a flat surface with friction ($\mu_k = 0.20$) before stopping.
Phase 1 (energy): $mgh = \frac{1}{2}mv^2 \implies v = \sqrt{2gh} = \sqrt{2(9.8)(50)} = 31.3$ m/s
Phase 2 (kinematics): deceleration from friction: $a = -\mu_k g = -1.96$ m/s²
$v^2 = v_0^2 + 2ad \implies 0 = 980 - 2(1.96)d \implies d = 250$ m
Example 2 — Waves + Optics
A laser beam ($\lambda = 632$ nm) passes from glass ($n = 1.5$) to air. Find the critical angle for total internal reflection.
$\sin\theta_c = n_2/n_1 = 1.00/1.50 = 0.667 \implies \theta_c = 41.8°$
Example 3 — Circuits + Energy
An electric motor (240 V, 5 A) runs for 2 hours. Find (a) power, (b) energy consumed, (c) cost at $0.12/kWh.
(a) $P = IV = 5 \times 240 = 1200$ W = 1.2 kW