Motion, Heat, and Thermodynamics
Key Takeaways
- Velocity is speed with direction; acceleration is the rate of change of velocity.
- The three kinematic equations solve most motion problems: v = v₀ + at, d = v₀t + 1/2at², v² = v₀² + 2ad.
- Projectile motion combines constant horizontal velocity with vertical acceleration due to gravity.
- Heat transfers via conduction (direct contact), convection (fluid circulation), and radiation (electromagnetic waves).
- Temperature and heat are different: temperature is average molecular kinetic energy; heat is energy transfer between objects.
Motion, Heat, and Thermodynamics
Linear Motion (Kinematics)
Key Definitions
| Term | Definition | Unit |
|---|---|---|
| Displacement | Distance with direction | meters (m) |
| Speed | How fast (no direction) | m/s |
| Velocity | Speed with direction | m/s |
| Acceleration | Rate of velocity change | m/s² |
The Kinematic Equations
For constant acceleration:
| Equation | Variables | Use When |
|---|---|---|
| v = v₀ + at | v, v₀, a, t | No distance needed |
| d = v₀t + 1/2at² | d, v₀, a, t | No final velocity needed |
| v² = v₀² + 2ad | v, v₀, a, d | No time needed |
| d = (v₀ + v)/2 × t | d, v₀, v, t | No acceleration needed |
Where:
- v₀ = initial velocity
- v = final velocity
- a = acceleration
- t = time
- d = displacement
Free Fall
Objects in free fall accelerate at g = 9.8 m/s² (≈ 10 m/s²) downward, regardless of mass (ignoring air resistance).
Example: A ball is dropped from rest. What is its velocity after 3 seconds? v = v₀ + at = 0 + (10)(3) = 30 m/s downward
Example: How far does it fall in those 3 seconds? d = v₀t + 1/2at² = 0 + 1/2(10)(9) = 45 m
Projectile Motion
A projectile has two independent motions:
| Direction | Acceleration | Velocity |
|---|---|---|
| Horizontal | 0 (constant velocity) | v_x = v₀ cos(θ) |
| Vertical | g = 9.8 m/s² downward | v_y = v₀ sin(θ) - gt |
Key facts:
- Horizontal and vertical components are independent
- At the peak, vertical velocity = 0 (horizontal velocity unchanged)
- Time up = Time down (for level launch and landing)
- Maximum range occurs at 45° launch angle
Example: A ball is thrown horizontally at 20 m/s from a cliff 80 m high. How long until it hits the ground?
Only vertical motion matters for time: 80 = 1/2(10)t² → t² = 16 → t = 4 seconds
Horizontal distance: d = 20 × 4 = 80 m
Momentum
p = m × v (momentum = mass × velocity)
Conservation of Momentum
In any collision or interaction (no external forces):
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
(Total momentum before = Total momentum after)
Types of Collisions
| Type | Momentum Conserved? | KE Conserved? | Example |
|---|---|---|---|
| Elastic | Yes | Yes | Billiard balls |
| Inelastic | Yes | No | Car crash (objects deform) |
| Perfectly inelastic | Yes | No (maximum KE loss) | Objects stick together |
Example: A 2 kg ball moving at 5 m/s hits a stationary 3 kg ball. They stick together. What is the final velocity?
2(5) + 3(0) = (2 + 3)v → 10 = 5v → v = 2 m/s
Heat and Temperature
Temperature Scales
| Scale | Water Freezes | Water Boils | Conversion |
|---|---|---|---|
| Fahrenheit (°F) | 32°F | 212°F | °F = 9/5 × °C + 32 |
| Celsius (°C) | 0°C | 100°C | °C = 5/9 × (°F - 32) |
| Kelvin (K) | 273 K | 373 K | K = °C + 273 |
Heat Transfer Methods
| Method | Mechanism | Example |
|---|---|---|
| Conduction | Direct contact between molecules | Touching a hot pan handle |
| Convection | Fluid circulation (hot rises, cold sinks) | Warm air rising from a heater |
| Radiation | Electromagnetic waves (no medium needed) | Heat from the Sun reaching Earth |
Conductors vs. Insulators
| Material Type | Heat Conduction | Examples |
|---|---|---|
| Good conductors | Fast heat transfer | Metals (copper, aluminum, steel) |
| Good insulators | Slow heat transfer | Wood, foam, air, rubber, fiberglass |
Specific Heat
Q = mcΔT
Where:
- Q = heat energy (Joules)
- m = mass (kg)
- c = specific heat capacity (J/kg·°C)
- ΔT = temperature change (°C)
Water has a very high specific heat (4,186 J/kg·°C), meaning it takes a lot of energy to change its temperature. This is why oceans moderate coastal climates.
Example: How much heat is needed to raise 2 kg of water from 20°C to 70°C? Q = 2 × 4,186 × 50 = 418,600 J ≈ 419 kJ
Thermal Expansion
Most materials expand when heated and contract when cooled.
- Solids: expand slightly in all directions
- Liquids: expand more than solids
- Gases: expand the most (significant volume changes)
This is why bridges have expansion joints, thermometers work, and hot air balloons float.
Laws of Thermodynamics (Simplified)
| Law | Statement | Practical Meaning |
|---|---|---|
| Zeroth | If A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C | Thermometers work |
| First | Energy cannot be created or destroyed | Total energy is conserved |
| Second | Heat flows from hot to cold naturally | Entropy always increases |
| Third | Absolute zero (0 K) cannot be reached | There is a minimum possible temperature |
An object starts from rest and accelerates at 5 m/s² for 6 seconds. What is its final velocity?
A ball is dropped from a 45-meter building. How long does it take to reach the ground? (Use g = 10 m/s²)
Which heat transfer method does NOT require a medium (material) to travel through?
A 5 kg object moving at 4 m/s collides with and sticks to a 15 kg stationary object. What is the combined velocity after the collision?
Convert 68°F to Celsius.