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Unit 3: Work, Energy, and Power

3.5: Power

Introduction

Power is the rate at which work is done or energy is transferred. In physics, power quantifies how quickly energy is used or transformed.

Understanding power is essential for solving problems involving engines, electrical circuits, and any system where energy conversion happens over time.

Key Concepts

  • Definition of Power: Power is defined as work done per unit time. The formula is: P = W/t.
  • SI Unit: The unit of power is the watt (W), where 1 W = 1 J/s.
  • Relationship with Work and Energy: If an engine does more work in a given time, it has a higher power output.
  • Instantaneous Power: Can be expressed as P = F · v when a force acts on an object moving at velocity v.
Tip: Ensure that when calculating power, work and time units are consistent (typically joules for work and seconds for time).

Graphical Representations

Power can be represented graphically by plotting work or energy versus time. The slope of a work vs. time graph gives the power.

Exam Strategy: When given a graph, look at the rate of change of work to determine power.

Mathematical Routines

To solve problems involving power, follow these steps:

  • Determine the work done (or energy transferred) in joules.
  • Identify the time interval in seconds over which the work is done.
  • Calculate power using P = W/t.
  • For problems involving force and velocity, use P = F · v, ensuring that the force and velocity are in compatible units.
Important: Double-check that all quantities are expressed in SI units (joules, seconds, newtons, and meters per second).

Practice Activities

Activity 1: Average Power Calculation

An engine does 5000 J of work in 10 s. Calculate its average power output.

Activity 2: Instantaneous Power

A car is moving at 25 m/s and a constant force of 400 N is applied. Calculate the instantaneous power.

Activity 3: Graphical Analysis

Given a work vs. time graph, determine the power output by finding the slope of the graph.

Summary & Exam Preparation Tips

Power is the measure of how quickly work is done or energy is transferred. Key takeaways:

  • Power is defined as P = W/t and is measured in watts (W).
  • Instantaneous power can be calculated using P = F · v.
  • Graphically, power is the slope of a work vs. time graph.
  • Ensure that all units are consistent when solving power problems.

Mastering power calculations will strengthen your understanding of energy transformations and improve your performance on the AP Physics exam.