# Work, Energy, Power

Daniel Weibel
Created 1 Feb 2016
Last updated 1 Jun 2016

Explanation of the concepts work, energy and power known from physics.

# Work (Arbeit)

• Unit: J (joule), Nm (newton-metre), cal (calorie), Ws (watt-second), kWh (kilowatt-hour)
• “Moving a mass over a distance”
• $W = F \, s$ (work is force times distance)
• Example:
• Force: $F = 10 \text{N}$
• Distance: $s = 2 \text{m}$
• Work: $W = F \, s = 20 \text{Nm} = 20 \text{J}$
• Equivalences: $1 \text{J} = 1 \text{Nm} = 1 \text{Ws}$
• Analogy with distance (120 km)

# Energy (Energie)

• Unit: J (joule), Nm (newton-metre), cal (calorie), Ws (watt-second), kWh (kilowatt-hour)
• “Capacity to do work”
• Equivalent to work

# Power (Leistung)

• Unit: W (watt), hp (horsepower), dBm (decibel-milliwatt)
• “Amount of work done per time”
• “Rate of doing work”
• “Energy consumed per time”
• “Light bulb wattage: rate at which the light bulb converts electrical energy into light and heat”
• $P = \frac{W}{t}$ (power is work divided by time)
• Examples:
• Doing 500 Nm work in 5 sec.: $P = \frac{500\text{Nm}}{5\text{s}} = 10\text{W}$
• Doing 500 Nm work in 1 hour: $P = \frac{500\text{Nm}}{3600\text{s}} = 0.134\text{W}$
• 40 W light bulb: amount of energy used in 1 hour: $E = 40\text{W} \cdot 3600 \text{s} = 144000 \text{J}$
• Equivalences:
• $W = \frac{\text{J}}{\text{s}}$
• $1 \text{hp} \approx 740 \text{W}$
• Analogy with speed (30 km/h)