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Work and Power in Physics

Learning Competencies

• Learners will be able to calculate work done by an applied force and the power generated in practical situations like engineering and sports science.

Introduction to Work

• What is Work?

  • Definition: According to physics, work has a specific meaning that signifies a measurable change in a system induced by a force.

  • Work is defined as: a force acting upon an object, causing a displacement.

Key Terminology

• Symbols and Units:

  • Work (W): represents the work done.

  • Weight (w): represents the weight of an object.

  • Important Note: Do not confuse uppercase W (work) with lowercase w (weight); they represent different quantities.

Work Done by a Constant Force

• Formula for Work: The work (W) done by a constant force is defined as: W = F imes |\Delta x|

  • Where:

  • W = work done,

  • F = magnitude of the applied constant force,

  • |\Delta x| = magnitude of the displacement in the direction of the force (applicable for straight-line displacement).

Unit of Work

• Joule (J):

  • The unit of work or energy in the International System of Units (SI).

  • Defined as the work done by a force of 1 newton acting through a distance of 1 meter, symbolically expressed as: 1 J = 1 N·m.

  • The work done increases if either the force F or the displacement |\Delta x| increases.

Work at an Angle

• When a force is applied at an angle to the direction of displacement, the work done is given by the equation: W = F imes |\Delta x| imes cos( heta)

  • Where:

  • θ = angle between the direction of the force and the direction of displacement vectors.

Components of Force

• The component of the force in the direction of the displacement can be expressed as: F_x = F imes cos( heta)

  • Therefore, the work done can also be rewritten as:
    W = F_x imes |\Delta x|

Examples of Work Done

1. Work Done in Lifting Objects: When lifting an object, the work done can be calculated based on the direction of displacement and the applied force.

2. For perpendicular forces:

   • If θ = 90°, then F imes cos(90°) = 0, resulting in Work = 0.

3. For forces acting in the same direction:

   • If θ = 0°, then F imes cos(0°) = F.

   • The formula becomes: W = F imes |\Delta x|.

Sample Work Calculations

1. Basic Calculation Example:

   • Formula: W = F imes d

   • If d = 5m and F = 100N, then:

   • W = 100 N imes 5 m = 500 N·m or 500 Joules.

2. Calculation with Angle:

   • W = F imes d imes cos(30°)

   • Resulting values include various potential work outputs such as 413 N-m, 750 N-m depending on given scenarios.

Energy and Power

• Energy: In physics, energy is defined as the capacity to perform work.

  • All forms of energy are associated with motion.

• Power: Defined as the rate of doing work. It represents the amount of energy consumed per unit time.

  • The unit of power in SI is the Watt (W), which is equivalent to one joule of work performed per second (1 W = 1 J/s).

Work as a Scalar Quantity

• Work is classified as a scalar quantity, which means:

  • It can be either positive or negative but does not have a directional component (i.e., does not have direction).

  • Positive Work: Work done on a system increases energy.

  • Negative Work: Work done by a system decreases energy.

Practical Applications of Work

• Examples:

  • Total work can be computed in systems with multiple forces:

  • W{TOTAL} = F1 imes ext{Δ}x1 + F2 imes ext{Δ}x2 + F3 imes ext{Δ}x_3 + ext{…}

  • If the displacements of all forces acting on a system are equal, the formula can be simplified:

  • W{TOTAL} = (F1 + F2 + F3 + ext{…}) imes ext{Δ}x

Assignment Problems

1. Problem 1: A 4000 kg truck is lifted by a crane over a distance of 4.0 m. Calculate:

   • (a) Work done by the crane,

   • (b) Work done on the truck by gravity,

   • (c) Net work done on the truck.

2. Problem 2: Alex climbs 2.3 m up stairs, elevating his body weighing 80 kg. Determine the work done by Alex on the staircase.