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Unit 3: Work, Energy, and Power

3.2: Work

Introduction

Work is a measure of energy transfer that occurs when a force causes an object to move. In physics, work is defined as the product of the force applied to an object, the displacement of the object, and the cosine of the angle between the force and displacement vectors.

Unlike force, work is a scalar quantity. Understanding how to calculate work is fundamental to solving energy problems in AP Physics.

Key Concepts

  • Definition of Work: Work is done when a force causes displacement. It is given by the formula:
    W = F d cosθ
  • Force (F): The applied force (in newtons, N).
  • Displacement (d): The distance over which the force is applied (in meters, m).
  • Angle (θ): The angle between the force vector and the displacement vector.
  • Positive vs. Negative Work:
    • Positive work is done when the force has a component in the direction of displacement.
    • Negative work is done when the force has a component opposite to the direction of displacement.
Tip: If the force is applied perpendicular to the direction of motion (θ = 90°), no work is done.

Graphical Representations

Work can also be visualized on a force vs. displacement graph. The area under the curve represents the work done on the object.

  • For a constant force, the area is a rectangle: W = F d (if θ = 0°).
  • For variable forces, the area under the curve can be determined using integration.
Exam Strategy: When given a graph, calculate work by finding the area under the force vs. displacement curve.

Mathematical Routines

To solve work problems, follow these steps:

  • Identify the force applied and its direction relative to the displacement.
  • Determine the displacement over which the force acts.
  • Calculate the work done using the formula W = F d cosθ.
  • For variable forces, use integration: W = ∫ F(x) dx.
Tip: Ensure that all quantities are in SI units before performing calculations.

Practice Activities

Activity 1: Constant Force

A force of 10 N is applied to move an object 5 m in the direction of the force. Calculate the work done.

Activity 2: Inclined Force

A 20 N force is applied at an angle of 30° to the horizontal to push a box 4 m along a flat surface. Calculate the work done by the force.

Activity 3: Variable Force

A force that varies with displacement is given by F(x) = 2x (in N) for x between 0 and 3 m. Determine the work done on the object.

Summary & Exam Preparation Tips

Work is a key concept in energy analysis. Key points include:

  • Work is a scalar quantity defined as W = F d cosθ.
  • Only the component of force in the direction of displacement does work.
  • Graphically, work is the area under the force vs. displacement curve.
  • For variable forces, integration is used to determine work.

Mastering work calculations is essential for understanding energy conservation and solving AP Physics problems.