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📓 Quick Notes & Solutions

1. Density & Buoyancy Simulator

Mass ($m$): 5.0 kg

Volume ($V$): 4.0 L ($10^{-3}\text{m}^3$)

Mass ($m$) 5.0 kg

Volume ($V$) 4.0 L

Density ($\rho$) 1.25 kg/L

$$\rho = \frac{m}{V}, \quad m = \rho \cdot V, \quad F_A = \rho_{liquid} \cdot g \cdot V_{sub}$$

$$\rho$$: Body density ($\text{kg/m}^3$ or $\text{kg/L}$)
$$F_A$$: Archimedes buoyant force ($N$)
Floating condition: If $\rho \le 1.0 \, \text{kg/L}$ — the object floats in water.

🔗 Useful Resources on Density:

🧪 PhET Density Simulator 🌊 PhET Buoyancy Force

2. Speed & Uniform Motion Simulator

Speed ($v$): 15 m/s

Time ($t$): 4.0 s

Speed ($v$) 15 m/s

Time ($t$) 4.0 s

Distance ($s$) 60 m

$$s = v \cdot t, \quad v = \frac{s}{t}, \quad v_{avg} = \frac{s_{total}}{t_{total}}$$

$$v$$: Speed ($\text{m/s}$) | $$s$$: Distance covered ($\text{m}$)

🔗 Useful Resources on Kinematics:

🧪 PhET Moving Man 📖 Wikipedia: Speed

3. Pulleys & Simple Machines Simulator

Load Mass ($m$): 10 kg

Pulley Type: Movable Pulley (2x Mechanical Advantage)

Weight ($P = mg$) 98.1 N

Required Force ($F$) 49.0 N

Force Advantage 2x

$$F = \frac{m \cdot g}{2}, \quad W = F \cdot s, \quad \eta = \frac{W_{useful}}{W_{total}} \cdot 100\%$$

Fixed Pulley: Provides no force advantage, only changes the force direction.
Movable Pulley: Provides a 2x force advantage ($F = \frac{P}{2}$), but requires twice as much rope distance.

🔗 Useful Resources on Mechanics & Pulleys:

📖 Wikipedia: Simple Machines ⚖️ PhET Balancing Act

4. Wave Phenomena & Oscillations Simulator

Frequency ($f$): 1.5 Hz

Amplitude ($A$): 30 px

Period ($T = 1/f$) 0.67 s

Wavelength ($\lambda$) 133 px

$$v = \lambda \cdot f, \quad T = \frac{1}{f}, \quad x(t) = A \cdot \sin(\omega t + \phi_0)$$

$$\lambda$$: Wavelength ($\text{m}$) | $$f$$: Frequency ($\text{Hz}$)
$$T$$: Oscillation period ($\text{s}$) | $$A$$: Amplitude

🔗 Useful Resources on Waves:

🧪 PhET Wave on a String 🌊 PhET Wave Interference

5. Geometric Optics & Refraction Simulator

Angle of Incidence ($\alpha$): 45°

Refractive Index ($n_2$): 1.50 (Glass)

Angle of Incidence ($\alpha$) 45°

Angle of Refraction ($\beta$) 28.1°

$$n_1 \cdot \sin\alpha = n_2 \cdot \sin\beta, \quad \frac{1}{F} = \frac{1}{d} + \frac{1}{f_0}$$

Snell's Law: The ratio of the sines of the angles of incidence and refraction equals the ratio of the refractive indices.
Thin Lens Formula: Relates focal length $F$ with object distance $d$ and image distance $f_0$.

🔗 Useful Resources on Optics:

🧪 PhET Bending Light 🔍 PhET Geometric Optics

6. Electric Circuits & Ohm's Law

Voltage ($U$): 12 V

Resistance ($R$): 4 Ω

Voltage ($U$) 12 V

Current ($I$) 3.0 A

Power ($P$) 36 W

$$I = \frac{U}{R}, \quad P = U \cdot I, \quad W = U \cdot I \cdot t$$

$$I$$: Current ($A$) | $$U$$: Voltage ($V$) | $$R$$: Electrical resistance ($\Omega$)

🔗 Useful Resources on Electricity:

🧪 PhET Circuit Construction Kit ⚡ PhET Ohm's Law

📖 Expanded Physics Formula Reference

1. Kinematics & Density

$$\rho = \frac{m}{V}, \quad m = \rho \cdot V, \quad V = \frac{m}{\rho}$$

$$v = \frac{s}{t}, \quad s = v \cdot t, \quad a = \frac{v - v_0}{t}$$

2. Mechanics & Pulleys

$$F_{movable} = \frac{F_{gravity}}{2}, \quad M = F \cdot d, \quad \eta = \frac{W_{useful}}{W_{total}}$$

$$F_{elastic} = k \cdot \Delta x, \quad E_k = \frac{m \cdot v^2}{2}, \quad E_p = m \cdot g \cdot h$$

3. Waves & Geometric Optics

$$v = \lambda \cdot f, \quad T = \frac{1}{f}, \quad n = \frac{c}{v}$$

$$n_1 \sin\alpha = n_2 \sin\beta, \quad D = \frac{1}{F} = \frac{1}{d} + \frac{1}{f_0}$$

4. Electricity & Ohm's Law

$$I = \frac{U}{R}, \quad R = \rho_{conductor} \cdot \frac{l}{S}$$

$$P = U \cdot I = I^2 \cdot R = \frac{U^2}{R}, \quad Q = I^2 \cdot R \cdot t$$

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