Power in Physics Lecture Notes

Introduction

• Topic: Power in Physics
• Instructor: Chad from Chad's Prep
• Objective: Understanding power, its formula, SI units, and calculations
• Resources: Comprehensive playlists and premium master courses on Chad's Prep.

Definition of Power

• Power: The rate at which work is done.
• Formula:
  • ( P = \frac{W}{\Delta t} )
  • ( P ) is power, ( W ) is work, ( \Delta t ) is change in time.

SI Units for Power

• Unit: Watt (W)
  • ( 1 \text{ Watt} = 1 \text{ Joule/second} )
  • Alternative expressions:
    • ( \text{Newton meter/second} )
    • ( \text{Kilogram meter}^2/\text{second}^3 )

Relationships in Power

• Proportional Relationships:
  • Power ( \propto ) work
  • Power ( \propto \frac{1}{\text{time}} )
• Inverse Relationship:
  • If work is doubled, power doubles.
  • If time is doubled, power is halved.

Calculating Power

• Work: Force times displacement ( W = F \cdot \Delta x )
• Alternate Power Formula: Power can also be calculated as force times velocity ( P = F \cdot v ).

Example Problems

Problem 1: Elevator

• Scenario: Calculate average power to raise a 2000 kg elevator 30 m in 10 s.
• Solution Steps:
  • Use ( P = \frac{W}{\Delta t} )
  • Calculate force: ( F = mg = 2000 \times 9.8 \text{ m/s}^2 = 19600 \text{ N} )
  • Use displacement ( \Delta y = 30 \text{ m} )
  • Power ( = \frac{F \cdot \Delta y}{\Delta t} = \frac{19600 \cdot 30}{10} = 58800 \text{ W} )

Problem 2: Elevator at Constant Speed

• Scenario: Power to raise elevator at 3 m/s.
• Solution Steps:
  • Use ( P = F \cdot v )
  • Given ( F = 19600 \text{ N}, v = 3 \text{ m/s} )
  • Power ( = 19600 \cdot 3 = 58800 \text{ W} )
  • Final answer rounded to two sig. figs: 59000 W

Problem 3: Motorcycle Horsepower

• Scenario: Calculate horsepower from 1500 N force and 25 m/s velocity
• Solution Steps:
  • Use ( P = F \cdot v )
  • Power ( = 1500 \cdot 25 = 37500 \text{ W} )
  • Convert to horsepower (1 hp = 746 W)
  • Horsepower ( = \frac{37500}{746} \approx 50.3 )
  • Rounded to two sig. figs: 5.0 x 10^1 hp

Conclusion

• Power: Understand power as a fundamental concept in physics with real-world applications like elevators and engines.
• Use of SI Units: Importance of understanding different units and conversions.