310105e Energy 2025 TF

Energy Objectives

• Key Objectives:

  • Describe energy, potential energy, kinetic energy, and the units of energy.

  • Describe the forms of energy and their formulae.

  • Describe the relationship between potential energy and kinetic energy and the laws of conservation of energy.

  • Solve problems related to potential energy based on force and height data and kinetic energy based on mass and velocity data.

Kinetic Energy (EK)

• Definition:

  • Kinetic energy is the energy of motion associated with an object's mass and speed.

• Units:

  • Joule (J)

  • 1 Joule = 1 N/m = 1 kg m/s²

Example of Kinetic Energy Calculation

• Problem: Determine the kinetic energy of a 2000 kg bus moving at 35.0 m/s.

• Formula: EK = (1/2)mv²

• Calculation:EK = ( \frac{1}{2} \times 2000 , \text{kg} \times (35 , \text{m/s})^2 ) EK = 1,225,000 J or 1.225 MJ

Potential Energy (EP)

• Definition:

  • Gravitational potential energy is the energy stored due to an object's vertical position (height).

• Units:

  • Joule (J)

  • 1 Joule = 1 N/m = 1 kg × 9.81 m/s²

Example of Potential Energy Calculation

• Problem: A 1 kg object is 10 m in the air. What is its potential energy?

• Calculation: EP = mgh = 1 kg × 9.81 m/s² × 10 m = 98.1 J

Conversion of Potential Energy to Kinetic Energy

• When the 1 kg object starts falling, its potential energy is converted into kinetic energy just before it hits the ground.

• Kinetic Energy Calculation on Falling:

  • Using: EK = (1/2)mv²

  • Given potential energy (EP) = 98.1 J

  • EP = (1/2) × 1 kg × v²

  • Solving: 98.1 = (1/2) × 1 × v²v² = 196.2v =

Summary of Kinetic and Potential Energy Relationship

• Kinetic energy (EK) and gravitational potential energy (EP) are interconnected as energy transforms from one form to another, conserving total energy in a closed system.

Hooke’s Law

• Definition:

  • The force exerted by a spring is directly proportional to the distance compressed or stretched from its rest position.

• Formula: F = kx

  • Where:

    • F = Force exerted by/on the spring (N)

    • k = Spring constant (N/m)

    • x = Distance compressed or stretched (m)

Spring Potential Energy

• Formula: EP = ½kx²

• Units:

  • Joule (J)

• Note: A stiffer spring has a greater spring constant.

Example of Spring Potential Energy Calculation

• Problem: A ball of 13 kg mass is suspended at a height of 13 m. Calculate its potential energy:

• Calculation:EP = mgh = 13 kg × 9.81 m/s² × 13 m = 1.66 kJ

Spring Rate and Strength in Context

• Spring Strength:

  • Standardized in industry, expressed as spring rate (k) in newtons per meter (N/m).

• Formula for Spring Rate Calculation: k = F/x, where F is the force applied and x is the distance compressed or stretched.

Conservation of Energy

• Principle:

  • Energy is neither created nor destroyed but transferred between forms.

• Equation for Conservation: [ EP = EK ]

  • Just before hitting the ground, potential energy equals kinetic energy.

Self-Test

• End of Energy ILM 310105e