Asked by g
The energy of a moving object.
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Answered by
GPT-5 mini
AI
You’re referring to kinetic energy — the energy an object has because of its motion. Key points and formulas:
1. Classical (non‑relativistic) kinetic energy
- Formula: KE = 1/2 m v^2
- m = mass (kg), v = speed (m/s)
- Unit: joule (J) where 1 J = 1 kg·m^2/s^2
- Derived from the work–energy theorem: work done to accelerate an object from rest to speed v equals the change in kinetic energy.
- Alternative form using momentum p = mv: KE = p^2 / (2m).
- Example: A 1500 kg car at 20 m/s has KE = 0.5 × 1500 × 20^2 = 300,000 J.
2. Rotational kinetic energy
- For a rotating rigid body: KE_rot = 1/2 I ω^2
- I = moment of inertia, ω = angular speed (rad/s).
3. Relativistic kinetic energy (when v is a significant fraction of c)
- Total energy: E = γ m c^2, where γ = 1 / sqrt(1 − v^2/c^2).
- Kinetic energy: KE = (γ − 1) m c^2.
- For small v (v << c) this reduces to the classical 1/2 m v^2.
4. Notes
- Kinetic energy is a scalar (non‑directional) but depends on the reference frame — different observers moving relative to the object measure different KE.
- Energy can be converted to other forms (e.g., potential energy, heat) but total energy is conserved in an isolated system.
If you want, I can show a step‑by‑step derivation of KE from Newton’s laws, compute KE for a specific example, or explain how KE relates to stopping distance. Which would you prefer?
1. Classical (non‑relativistic) kinetic energy
- Formula: KE = 1/2 m v^2
- m = mass (kg), v = speed (m/s)
- Unit: joule (J) where 1 J = 1 kg·m^2/s^2
- Derived from the work–energy theorem: work done to accelerate an object from rest to speed v equals the change in kinetic energy.
- Alternative form using momentum p = mv: KE = p^2 / (2m).
- Example: A 1500 kg car at 20 m/s has KE = 0.5 × 1500 × 20^2 = 300,000 J.
2. Rotational kinetic energy
- For a rotating rigid body: KE_rot = 1/2 I ω^2
- I = moment of inertia, ω = angular speed (rad/s).
3. Relativistic kinetic energy (when v is a significant fraction of c)
- Total energy: E = γ m c^2, where γ = 1 / sqrt(1 − v^2/c^2).
- Kinetic energy: KE = (γ − 1) m c^2.
- For small v (v << c) this reduces to the classical 1/2 m v^2.
4. Notes
- Kinetic energy is a scalar (non‑directional) but depends on the reference frame — different observers moving relative to the object measure different KE.
- Energy can be converted to other forms (e.g., potential energy, heat) but total energy is conserved in an isolated system.
If you want, I can show a step‑by‑step derivation of KE from Newton’s laws, compute KE for a specific example, or explain how KE relates to stopping distance. Which would you prefer?
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