Work

Types of Energy

  • Various forms of energy exist in science:

    • Kinetic Energy (K)

      • Formula: K = ½mv²

      • Includes rotational and vibrational forms.

    • Gravitational Potential Energy (Ug)

      • Formula: Ug = mgh

    • Elastic Potential Energy (Us)

      • Formula: Us = ½kx²

    • Internal or Thermal Energy (ETH)

    • Chemical Energy (Echem)

    • Mass Energy

      • Formula: E = mc²

Energy Units

  • Energy is measured using the unit Joule (J)

    • 1 Joule = 1 kg-m²/s²

Scientific Inquiry

  • Has science identified all forms of energy?

    • Likely not, especially regarding concepts like dark energy.

    • Dark Energy:

      • Causes the universe's accelerating expansion.

      • Its true nature remains largely unknown.

Energy Transformations

  • Energy transformations occur within a system, while interactions with the environment are crucial in understanding energy transfer.

Basic Energy Model

  • Energy is transferred between the environment and the system:

    • Work (W) and heat (Q) are energy transfers into/out of the system.

Isolated Systems

  • An isolated system maintains a constant total energy (E).

    • Total Energy (E) = K + Ug + Echem + ETH = constant

Heat and Work

  • Heat (Q) flows from hot to cooler bodies.

  • Work (W) is done when an external force moves a system.

  • Internal forces do not result in work.

  • Work is a scalar quantity, dependent on force orientation and path.

Calculating Work by a Constant Force

  • The effectiveness of work done depends on force direction relative to displacement.

  • Different orientations yield different impacts on kinetic energy (K) and energy transfer.

Work and Displacement

  • Work done by a force is calculated using:

    • W = F·d·cos(θ)

  • Forces that do not result in displacement do not constitute work.

Energy and Friction

  • Friction arises from interactions between surfaces.

    • Internal energy is often converted to heat due to these interactions.

  • Although work done may appear zero during resistance (e.g., holding a weight), internal energy conversion occurs.

Energy Expressions

  • Several formulas relate work done to energy in a system:

    • Wext = ΔEsys

    • ΔEsys = m½(vf² − v0²)

Potential Energy in Specific Scenarios

Gravitational Potential Energy

  • Change in gravitational potential energy (GPE) when height changes can be calculated:

    • ΔEsys = Wext = mg(hf – h0)

  • GPE is conservative, path-independent.

Spring Potential Energy (SPE)

  • Elastic potential energy in springs is represented as:

    • Uspring = ½Kx²

  • The area under the force vs. displacement graph provides the energy change.

Work-Energy Method

  • Use this method to analyze system changes:

    • Identify the system and the exerting forces.

    • Note that internal forces do no work.

Biological Systems and Work

  • Constant energy supply is required for muscle engagement.

  • Skeleton acts as support but relies on muscle alignment.

  • Utilizing body weight minimizes energy expenditure.

Internally Powered Objects

  • Such objects perform complex functions and generate heat during movement.

  • E.g., a person or vehicle moving at a constant speed may not do mechanical work but still expends energy.

Energy and the Body: Food

  • Food provides chemical energy; it converts during metabolic processes to usable energy forms (e.g., ATP).

  • Metabolism rates and oxygen consumption correlate with energy use.

Energy Output: Metabolic Power Use

Common Activities (Table Example)

  • Categorizes energy expenditure during various activities (e.g., weightlifting, cycling).

  • Specific metabolic power values highlighted for practical understanding.

Power

  • Power (P) is the rate of energy change:

    • P = ΔE/Δt = W + Q/Δt

  • Definitions diverge for mechanical systems and conserved energy scenarios.

    • Units: 1 Watt = 1 Joule/second, 1 Horsepower = 745 W

Specific Power Calculation

  • Specific Power measures output concerning agent mass:

    • E.g., if 140 W is consumed by a 70 kg individual, specific power = 2 W/kg.

Efficiency

  • Efficiency relates output work to energy consumed:

    • Efficiency (e) = mechanical work done/energy consumed.

    • Typically less than 1 due to heat dissipation.

Real-World Example Problems

  • Many examples illustrate calculating mechanical work and comparing energy use during different activities (e.g., badminton, weightlifting).

  • Efficiency factors important in determining total energy needs versus mechanical work output.