What is Power in Physics?
In physics, power is the rate at which work is done or energy is transferred. It's a measure of how quickly a task is accomplished, not just whether it gets done. For example, two people can lift identical boxes up a flight of stairs, doing the same amount of work. However, the person who runs up the stairs does so with more power than the person who walks.
The Main Power Formula (P = W/t)
The most fundamental definition of power is work done divided by the time it took to do that work.
- Power (P): The rate of energy transfer, measured in Watts (W).
- Work (W): The energy transferred, measured in Joules (J).
- Time (t): The time over which the work is done, measured in seconds (s).
Units of Power: The Watt (W)
The SI unit for power is the Watt (W), named after the Scottish engineer James Watt. A Watt is defined by the formula for power:
1 Watt = 1 Joule per second (1 W = 1 J/s)
This means that if you do 1 Joule of work in 1 second, you are generating 1 Watt of power. A 100-Watt light bulb, for instance, converts 100 Joules of electrical energy into light and heat every second.
Alternative Formula: Power = Force × Velocity (P = Fv)
We can derive another useful formula for power. Since `Work = Force × Distance` (`W = Fd`), we can substitute this into the power equation:
P = W / t = (F × d) / t
Because velocity `v` is equal to `distance / time` (`v = d/t`), we can simplify this to:
This formula is extremely useful for calculating the power required to maintain a constant velocity against a constant opposing force (like air resistance or friction). To solve for the force, you can rearrange it to `F = P / v`.
Real-World Examples
- Lifting an Elevator: An elevator motor does 100,000 Joules of work to lift a car in 10 seconds. The power of the motor is `P = 100,000 J / 10 s = 10,000 W` (or 10 kW).
- Car Engine: A car traveling at a constant 20 m/s (72 km/h or 45 mph) must overcome 1,500 N of friction and air resistance. The power its engine must deliver to the wheels is `P = 1,500 N × 20 m/s = 30,000 W` (or 30 kW).
- Human Power: A person with a mass of 70 kg runs up a 4-meter high flight of stairs in 5 seconds. The work done against gravity is `W = Fd = (70 kg × 9.8 m/s²) × 4 m ≈ 2,744 J`. The power output is `P = 2,744 J / 5 s ≈ 549 W`.
For more on the concept of power, the Wikipedia article on Power in physics is a great resource.