Kinetic and Potential Energy Overview

Kinetic Energy (Ek)

• Energy possessed by a moving object.
• Formula: Ek = 1/2 mv²
  • Where Ek is kinetic energy, m is mass, and v is velocity.
• Unit: Joules (J)
• Derivation:
  • Consider an object accelerated from rest by a constant force.
  • Work done by the force equals to the gain in kinetic energy: Ek = F × s
  • Using kinematics: v² = u² + 2as (initial velocity, u = 0)
  • Leads to Ek = 1/2 mv²

Gravitational Potential Energy (Ep)

• Energy due to an object's position above the Earth's surface.
• Formula: Ep = mgh
  • Where Ep is gravitational potential energy, m is mass, g is gravitational field strength, and h is height.
• Derivation:
  • Work done against gravity when an object is lifted: Ep = mgh

Energy Transformations

• Roller Coasters:
  • Initial lift gives high Ep, converted to Ek when descending.
  • Energy transformations occur with some loss due to friction and air resistance.
• Other examples:
  • Ski jump: Ep to Ek to maximize jump distance.
  • Thrown objects: Initial Ek transforms to Ep at peak height.
  • Pendulums: Continuous interchange between Ek and Ep.

Principles of Energy Conservation

• When an object falls:
  • Loss in Ep equals gain in Ek, assuming no energy loss.
  • Velocity of falling object: v = √(2gh)

Practice Questions

1. Calculate stopping distance of a motorcycle given Ek and braking force.
2. Determine increase in Ek when a vehicle accelerates from one speed to another.
3. Find velocity of a bullet given its mass and Ek.
4. Estimate kinetic energy for various objects (e.g., car, sprinter, jet).
5. Calculate energy loss and maximum height for a marble projected upwards.
6. Analyze transformations and energy losses in diverse scenarios (e.g., roller coasters, pendulums, ski jumps).

Homework and Application Problems

• Describe energy changes in cycling and pendulum motions.
• Analyze rock falling scenarios and skier velocity calculations.
• Solve problems involving kinetic and potential energy transformations on tracks and roller coasters.