Worked physics examples
Real-world physics problems — cars, lifts, kettles, springs, skydivers — each solved with the formula, the substitution and the answer, by the same code as the calculators.
Newton's Second Law
Acceleration
- Acceleration of a car from 0 to 100 km/h in 8 s → 3.472 m/s²
- Acceleration from 0 to 60 mph in 6 s → 4.47 m/s²
- Deceleration braking from 50 km/h to 0 in 2.5 s → -5.556 m/s²
- A cyclist speeding up from 5 m/s to 10 m/s in 4 s → 1.25 m/s²
- A train going from 0 to 300 km/h in 5 minutes → 0.278 m/s²
- A sprinter reaching 10 m/s from 0 in 2 s → 5 m/s²
Momentum
- Momentum of a 1,500 kg car at 50 km/h → 20,833.33 kg·m/s
- Momentum of a 0.16 kg cricket ball at 140 km/h → 6.22 kg·m/s
- Momentum of an 80 kg runner at 5 m/s → 400 kg·m/s
- Momentum of a 40,000 kg truck at 90 km/h → 1,000,000 kg·m/s
- Momentum of a 0.057 kg tennis ball served at 200 km/h → 3.17 kg·m/s
Projectile Motion
Free Fall From Time
Torque
Terminal Velocity
Tension
- Cable tension lifting 500 kg at constant speed → 4,903.325 N
- Lift cable tension: 1,000 kg accelerating up at 1.2 m/s² → 11,006.65 N
- Lift cable tension: 1,000 kg accelerating down at 1.2 m/s² → 8,606.65 N
- Rope tension hauling a 20 kg bucket up at 0.5 m/s² → 206.133 N
Atwood Machine
- Atwood machine with 2 kg and 1 kg masses → 3.269 m/s²
- Atwood machine with 5 kg and 4.5 kg masses → 0.516 m/s²
- Atwood machine with 10 kg and 1 kg masses → 8.024 m/s²
- Atwood machine with 0.5 kg and 0.4 kg masses → 1.09 m/s²
Incline Tension
Two-Rope Tension
- Rope tension holding a 20 kg sign with ropes at 45° → 138.687 N
- Wire tension for a 5 kg lamp hung at 15° → 94.725 N
- Slackline tension: 70 kg with the line at 10° → 1,976.599 N
- Hammock rope tension: 100 kg with ropes at 30° → 980.665 N
Impact Force
- Average force on a 1,500 kg car stopping from 50 km/h in 0.6 m → 241,126.5 N
- Average force on a 70 kg person stopped from 30 km/h over 0.3 m → 8,101.9 N
- Average force of a 0.5 kg hammer at 10 m/s stopping in 5 mm → 5,000 N
- Average force catching a 0.43 kg football at 25 m/s over 0.2 m → 671.9 N
- Average force on a 60 kg gymnast landing at 6 m/s on a 0.15 m mat → 7,200 N
Horizontal Projectile
- Where a ball rolling off a 1.2 m table at 3 m/s lands → 1.48 m
- How far a stone thrown flat from a 20 m cliff at 15 m/s lands → 30.29 m
- Reach of a horizontal hose jet 1.5 m up at 8 m/s → 4.42 m
- Where a package dropped from 100 m at 50 m/s lands (no drag) → 225.8 m
- How far a skateboarder leaving a 0.5 m ledge at 4 m/s travels → 1.28 m
Kinetic Energy
- Kinetic energy of a 1,500 kg car at 100 km/h → 578,703.7 J
- Kinetic energy of a 1,500 kg car at 50 km/h → 144,675.9 J
- Kinetic energy of a 0.145 kg baseball at 145 km/h → 117.6 J
- Kinetic energy of a 90 kg cyclist and bike at 30 km/h → 3,125 J
- Kinetic energy of a 40,000 kg lorry at 80 km/h → 9,876,543.2 J
- Kinetic energy of an 80 kg runner at 6 m/s → 1,440 J
- Kinetic energy of a 1,500 kg car at 70 mph → 734,429.5 J
Potential Energy
- Potential energy gained climbing 3 m of stairs at 75 kg → 2,206.5 J
- Energy stored lifting 1,000 kg of water 100 m → 980,665 J
- Potential energy of a 20 kg suitcase lifted 1.5 m → 294.2 J
- Potential energy of a 2 kg book on a 2 m shelf → 39.2 J
- Potential energy an 80 kg hiker gains climbing 1,000 m → 784,532 J
Work
- Work pushing a trolley 50 m with 30 N → 1,500 J
- Work pulling a sled 100 m with 80 N at 30° → 6,928.2 J
- Work pushing a car 10 m with 400 N → 4,000 J
- Work towing a suitcase 200 m with 25 N at 45° → 3,535.53 J
Power
- Power delivering 336 kJ in 2 minutes → 2,800 W
- Power climbing stairs: 2,200 J in 5 s → 440 W
- Power of 90 kJ in 1 minute → 1,500 W
- Power of a 1,800 J lift done in 1.2 s → 1,500 W
- Average power putting 580 kJ into a car in 8 s → 72,500 W
Watts to Joules
- Energy used by a 60 W bulb in 1 hour → 216,000 J
- Energy used by a 2,000 W kettle in 3 minutes → 360,000 J
- Energy used by a 10 W LED in 8 hours → 288,000 J
- Energy used by a 1,500 W hair dryer in 10 minutes → 900,000 J
- Energy delivered by a 5 W phone charger in 2 hours → 36,000 J
Ohm's Law
Wavelength
- Wavelength of 5 GHz Wi-Fi → 0.059958 m
- Wavelength of FM radio at 100 MHz → 2.997925 m
- Wavelength of a 440 Hz note in air (343 m/s) → 0.779545 m
- Wavelength of AM radio at 1 MHz → 299.792458 m
- Wavelength of 5 MHz ultrasound in soft tissue (1,540 m/s) → 0.000308 m
- Wavelength of 1 kHz sound in water (1,480 m/s) → 1.48 m
Lens Equation
Pressure
- Pressure under a person weighing 70 kgf on 0.05 m² of shoe → 13,729.3 Pa
- Pressure under a heel carrying 60 kgf on 1 cm² → 5,883,990 Pa
- Tyre contact pressure: 1,500 kgf on 0.06 m² → 245,166.3 Pa
- Pressure of a 500 N push on a 2 mm² pin tip → 250,000,000 Pa
Watts to Amps
Density
- Density of 1 L of milk weighing 1.03 kg → 1,030 kg/m³
- Density of a 0.5 kg block of wood of 0.0008 m³ → 625 kg/m³
- Density of a 50 g stone that displaces 20 cm³ → 2,500 kg/m³
- Density of a 2.7 kg block with a volume of 1 L → 2,700 kg/m³
Specific Heat
- Heat to warm 1.5 kg of water by 85 °C → 533,715 J
- Heat to warm 150 kg of bath water by 25 °C → 15,697,500 J
- Heat to warm a 1 kg aluminium pan (c = 900) by 180 °C → 162,000 J
- Heat to warm 0.5 kg of olive oil (c = 1,970) by 150 °C → 147,750 J
Thermal Expansion
Ideal Gas Law
- Pressure of 1 mol of gas at 25 °C in 24.5 L → 101,181.9 Pa
- Pressure of 2 mol of gas in a 10 L tank at 20 °C → 487,476.9 Pa
- Pressure of 200 mol of gas in a 50 L cylinder at 15 °C → 9,583,249.6 Pa
- Pressure of 0.5 mol of gas in a 1 L bottle at 100 °C → 1,551,270.9 Pa
- Pressure of 1 mol of gas at 300 K in 1 m³ → 2,494.3 Pa
Snell's Law
Hooke's Law
Electricity Cost
- Yearly cost of a 2,000 W heater, 4 h a day at €0.25/kWh → 730.5 €
- Yearly cost of a fridge averaging 150 W, 24 h a day at €0.30/kWh → 394.47 €
- Yearly cost of a 10 W LED, 5 h a day at €0.20/kWh → 3.65 €
- Yearly cost of a 7,000 W EV charger, 2 h a day at €0.25/kWh → 1,278.38 €
- Yearly cost of a 100 W TV, 4 h a day at €0.25/kWh → 36.53 €