What is kinetic energy and what is its formula?
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Kinetic energy is the energy an object has due to its motion. KE = 1/2 m v^2, where m is mass and v is velocity.
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What is kinetic energy and what is its formula?
Kinetic energy is the energy an object has due to its motion. KE = 1/2 m v^2, where m is mass and v is velocity.
Calculate the kinetic energy of a 1500 kg car moving at 20 m/s.
Using KE = 1/2 m v^2: KE = 1/2 × 1500 × 20^2 = 300,000 J.
What is potential energy (gravitational) and its formula?
Gravitational potential energy is stored energy due to an object's height. PE = m g h, where m is mass, g is gravity, and h is height.
If 5 kg ball is dropped from 10 m (ignore air resistance), what is its potential energy at the top?
PE = m g h = 5 × 9.8 × 10 = 490 J (this is the energy at the top before it falls).
For the same 5 kg ball dropped from 10 m, what is its kinetic energy just before it hits the ground?
Ignoring losses, mechanical energy is conserved, so KE (just before impact) = PE (initial) = 490 J.
How do you find the velocity of the 5 kg ball just before impact from 10 m?
Use KE = 1/2 m v^2 = initial PE. Solve v = sqrt(2 g h) = sqrt(2 × 9.8 × 10) = ≈14.0 m/s.
What is elastic potential energy in a spring and its formula?
Elastic potential energy stored in a spring is given by PE_spring = 1/2 k x^2, where k is the spring constant and x is displacement from equilibrium.
A spring has k = 200 N/m and x = 0.1 m. Calculate its stored energy.
PE_spring = 1/2 × 200 × (0.1)^2 = 1 J.
If you triple the extension x of an elastic spring (within elastic limit), how does the stored energy change?
Since PE_spring ∝ x^2, tripling x increases energy by 3^2 = 9 times.
What is the SI unit of energy and give three intuitive examples of a joule.
The Joule (J) is the SI unit of energy. Examples: energy to lift a 102 g apple 1 m, ~1 J; small heat produced by a quiet person every 0.01 s; energy equivalent of 0.00028 Wh.
Convert 1 Wh to joules and list common multiples used for electrical energy.
1 Wh = 3600 J. Common multiples: 1 kWh = 1000 Wh, 1 MWh = 1000 kWh, 1 GWh = 1000 MWh.
Name other common energy units used for heat and fuels.
Heat units: BTU, therm, quad. Fuel units: barrel of oil equivalent (boe), tonne of oil equivalent (toe), tonne of coal equivalent (tce).
What is power and what is its SI unit?
Power is the rate of energy conversion per unit time. The SI unit is the Watt (W), equal to 1 J/s.
How are energy and power different?
Energy is a quantity (how much), power is a rate (how fast energy is used or converted). Watt-hours measure energy; watts measure power.
State Ohm’s Law and identify the units of V, I, and R.
Ohm's Law: V = I × R. Voltage V in volts (V), current I in amperes (A), resistance R in ohms (Ω).
Give three equivalent forms relating power, voltage, current and resistance.
P = I × V, P = V^2 / R, and P = I^2 × R. These follow by substituting Ohm's Law.
Express electrical energy E in terms of power and time and list equivalent forms using V, I, R.
E = P × t. Equivalently: E = I V t, E = V^2 / R × t, E = I^2 R × t.
A microwave runs at 10 A and 230 V for 1 hour. What is its power (kW), energy (kWh), and cost at 30p/kWh?
Power P = I×V = 10×230 = 2300 W = 2.3 kW. Energy E = P×t = 2.3 kWh. Cost = 2.3×£0.30 = £0.69 (69 pence).
How would you calculate the monthly cost of running a 30 A, 230 V heater for 2 hours/day over 30 days at 30p/kWh?
First find power: P = I×V = 30×230 = 6900 W = 6.9 kW. Daily energy = 6.9×2 = 13.8 kWh. Monthly (30 days) = 13.8×30 = 414 kWh. Cost = 414×£0.30 = £124.20.
What is energy conversion and what law governs it?
Energy conversion is transforming energy from one form to another. It follows the law of conservation of energy: energy cannot be created or destroyed, only converted.
In an energy conversion, how is input split between useful output and waste?
Energy input = useful energy output + waste energy (waste often as unusable thermal energy).
Define energy efficiency and provide the formula.
Energy efficiency (η) measures useful output relative to input: η = (Useful Energy Output) / (Energy Input). Typically expressed as a percentage.
Give two system-level measures to improve PV (solar) system efficiency.
Use photovoltaic-thermal (PVT) hybrid collectors to capture electricity and heat, and optimize installation to reduce losses; PVT recovers waste heat to increase total energy output.
What is a Combined Cycle Gas Turbine (CCGT) and how does it improve efficiency?
A CCGT uses gas and steam turbines with a heat recovery steam generator to use exhaust heat to produce additional power, improving overall efficiency compared to single-cycle plants.
What does a Mechanical Ventilation with Heat Recovery (MVHR) system do for a building?
An MVHR system recovers heat from exhaust air to pre-warm incoming fresh air, reducing heating demand, lowering energy consumption, and maintaining indoor air quality.
How do you compute overall efficiency of a multi-stage plant (e.g., coal power plant)?
Multiply the efficiencies of each stage: η_plant = (η_boiler × η_turbine × η_generator) × 100%.
A coal plant burns 5000 MJ and produces 1500 MJ electrical energy. What is its efficiency?
η = Useful output / Input = 1500 / 5000 = 0.3 = 30%.
For the 8-hour coal plant example: total energy input (kWh) from coal and total electrical output?
Total energy input = 20,000 kg × 2800 kWh/kg = 56,000,000 kWh. Total electrical output = 1,500,000 kW × 8 h = 12,000,000 kWh.
Using the numbers above, what is the plant efficiency and one recommended improvement?
η = 12,000,000 / 56,000,000 = 0.2143 = 21.43%. Recommendation: implement Combined Heat and Power (CHP) to capture waste heat and raise overall energy utilization.
