Lesson_4_-_Conservation_of_Energy

Conservation of Energy

Overview

• Energy is defined as the ability to do work.

• Energy is measured in joules (J).

Key Concepts

• Total Mechanical Energy: The sum of potential energy (PE), kinetic energy (KE), and internal energy (Q).

• Conservation of Energy Principle: Energy cannot be created or destroyed. The total energy before motion equals the total energy during and after motion.

Definitions

• Energy: The ability to do work; Unit: Joules (J).

• Total Mechanical Energy (ET):

  • Formula: ET = KE + PE + Q

• Conservation of Energy:

  • Formula: E_before = E_after

  • KE_initial + PE_initial + Q_initial = KE_final + PE_final + Q_final

Application: Skate Park Simulation

• Observe potential and kinetic energy changes as a skater moves:

  • Half-Pipe:

    • As the skater ascends, potential energy increases while kinetic energy decreases.

    • As the skater descends, potential energy decreases while kinetic energy increases.

  • Loop:

    • Explore energy changes as the skater goes up and comes down the loop.

    • Discuss total energy change in the system.

Example: Free Falling Rock

• Isolated System Principle: The total energy remains constant; energy may only change form.

• Hypothetical scenario of a 5kg rock free-falling from rest:

  • Calculate potential energy (PE) at different heights (10m, 5m, 0m).

  • Discuss how PE decreases as the rock falls and how kinetic energy (KE) increases.

  • Analyze total energy at different heights.

Kingda Ka Energy Transfer

• Model Kingda Ka roller coaster with parameters:

  • Mass (m): 5 kg

  • Spring constant (k): 1000 N/m

  • Compression (x): 0.5 m

• Calculate energies at points A, B, and C, noting total energy and speed at B.

• Determine max height at C; if height is 2 m, calculate work done against friction.

Conceptual Question

• Car Brake Shoes:

  • The material must tolerate high temperatures due to energy transfer during braking.

Problem Solving

Problem #1

• Concrete block (8.0 kg) dropped from 60 meters:

  • Find gravitational PE at release.

  • Calculate KE at impact speed (30 m/s).

  • Analyze mechanical energy loss; determine energy conversion.

Problem #2

• Steel block (55 kg) slides down 2 m incline:

  • Calculate energy dissipated as heat (velocity at bottom = 3.5 m/s).

Problem #3

• Potato sack (120 kg) dropped 15 meters:

  • Calculate energy lost to air friction with final velocity (13 m/s).

Problem #4

• Steel block (45 kg) on frictionless incline:

  • Calculate velocity at the base (height = 3 m).

Problem #5

• Tossing a ball (100 g) to hit ceiling 10 m high:

  • Determine minimum speed required.

Pendulums

Definition

• A pendulum is a weight suspended from a pivot allowing it to swing freely.

Characteristics

• Period: Time to complete one cycle. Affected by string length:

  • Longer string = higher period

  • Shorter string = shorter period

• Use the same formulas to evaluate KE and PE at various points during swings.

Pendulum Energy Changes

• Analyze energy transitions as the pendulum swings from positions A to D and D to G.

Pendulum Problem

• Given mass of ball on string (7 kg) with speed at D (3 m/s):

  • Calculate KE at D.

  • Determine height at A.

  • Calculate speed at point C (height C = 0.23 m).