Power (Physics)
Power is the rate at which work is done or energy is transferred per unit time. It quantifies how quickly a system can perform work, making it essential for comparing engines, motors, and other energy-conversion devices. In practical applications, power determines the performance capacity of machines and biological systems alike.
Key Formula
P = W / t = F × v
LaTeX: P = \frac{W}{t} = F \cdot v
| Symbol | Meaning | Unit |
|---|---|---|
| P | Power | Watt (W) |
| W | Work done | Joule (J) |
| t | Time interval | Second (s) |
| F | Force applied | Newton (N) |
| v | Velocity of object | Metre per second (m/s) |
Worked Example
Problem
A motor lifts a 200 kg load vertically by 15 m in 30 seconds. Calculate the power output of the motor. (g = 10 m/s²)
Solution
Step 1: Calculate work done against gravity. W = mgh = 200 × 10 × 15 = 30,000 J Step 2: Divide work by time to get power. P = W / t = 30,000 / 30 = 1,000 W
Answer
P = 1,000 W = 1 kW
Power Units and Equivalents
| Unit | Symbol | Equivalent in Watts | Typical Application |
|---|---|---|---|
| Watt | W | 1 W | LED bulb |
| Kilowatt | kW | 1,000 W | Electric motor |
| Megawatt | MW | 1,000,000 W | Power plant |
| Horsepower | hp | 745.7 W | Car engine rating |
| Milliwatt | mW | 0.001 W | Bluetooth device |
Interactive Tools
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Related Terms
Work (Physics)
In physics, work is done on an object when a force causes a displacement of that object in the direction of the force. Work is a scalar quantity equal to the product of the force, the displacement, and the cosine of the angle between them. It represents the transfer of mechanical energy to or from an object and is measured in joules (J); no work is done if the force is perpendicular to the motion or if there is no displacement.
Kinetic Energy
Kinetic energy is the energy possessed by an object due to its state of motion. It depends on both the mass of the object and the square of its speed, meaning that doubling the speed quadruples the kinetic energy. Kinetic energy is transferred to objects through work and is a key quantity in collision analysis, transport safety, and the work-energy theorem.
Impulse
Impulse is the product of a force and the time interval over which it acts, and it equals the change in momentum of the object. It is a vector quantity that describes the total effect of a force applied over time rather than instantaneously. Impulse is widely used in collision analysis, sports biomechanics, and safety engineering to understand how forces affect motion.
From Latin "potere" meaning "to be able". The unit Watt is named after Scottish engineer James Watt (1736–1819), who developed the concept of horsepower to quantify steam engine output.