PE KE Work Power Momentum Hooke's Law Study Guide

Study Guide Overview

  • Focus on the following concepts: Mechanical Energy, Potential Energy (PE), Kinetic Energy (KE), Work, Power, Momentum, and Hooke’s Law.

  • Utilize notes and worksheets for studying.

  • Access resources on Google Classroom for key answers and review material.

  • Understand how to rearrange formulas since original formulas will be on the test.

  • Familiarize yourself with units and abbreviations that correspond to specific terms and formulas.


Key Concepts

Work

  • Definition of Work: Work is done when a force causes displacement.

  • Example of Work Being Done: Pushing a box across the floor (force applied and movement occurs).

  • Example of No Work: Carrying a bag of groceries while walking horizontally (no displacement in the direction of the force).

  • Explanation: Work is considered to be done only when the force applied results in an object being moved.

Power and Work Relationship

  • Power (P): The rate at which work is done (measured in watts).

  • Example Calculation of Work: If Jan generates 450 watts in 6 seconds, then

    • Work (W) = Power (P) x Time (t) => W = 450 W x 6 s = 2700 J.

  • Minimum Power: A machine adds 5,000 J in 20 seconds. To find power, use

    • Power = Work / Time => P = 5000 J / 20 s = 250 W.


Energy Calculations

Kinetic Energy (KE)

  • Formula: KE = 1/2 mv^2.

  • Calculate KE for a volleyball with mass 2.0 kg and velocity 30 m/s:

    • KE = 1/2 x 2.0 kg x (30 m/s)^2 = 900 J.

Potential Energy (PE)

  • Formula: PE = mgh, where m is mass, g is gravitational acceleration (9.81 m/s²), and h is height.

  • An apple hanging 5.0 m with mass 0.2 kg:

    • PE = 0.2 kg x 9.81 m/s² x 5.0 m = 9.81 J.

  • A crane holding a concrete block weighing 2200 N at 10 m:

    • PE = Weight x Height = 2200 N x 10 m = 22000 J.

Height and Velocity Relationships

  • For a mass of 15 kg and PE of 200 J:

    • Use PE formula to find height: 200 J = 15 kg x 9.81 m/s² x h

    • Calculate height h = 200 J / (15 kg x 9.81 m/s²) = 1.36 m.

  • To find velocity of the previous mass when at PE of 200 J, use:

    • KE = PE (if no energy lost) => KE = 200 J, then find v using KE formula:

    • 200 J = 1/2 x 15 kg x v^2 => v = sqrt(200 J / (1/2 x 15 kg)) = 4.90 m/s.


Hooke’s Law and Momentum

Hooke’s Law

  • Spring Force: F = kx, where k is the spring constant and x is the extension.

  • For a spring constant of 10 N/m and extension of 0.3 m:

    • F = 10 N/m x 0.3 m = 3 N.

  • To find spring constant with a 6 N weight extended by 0.2 m:

    • k = F/x = 6 N / 0.2 m = 30 N/m.

Momentum

  • Momentum (p): p = mv, where m is mass and v is velocity.

  • Calculate momentum for 125.0 kg ball at 6.5 m/s:

    • p = 125.0 kg x 6.5 m/s = 812.5 kg·m/s.

  • For the falling rock with momentum 200 kg·m/s and velocity 5.0 m/s:

    • mass m = p/v = 200 kg·m/s / 5.0 m/s = 40 kg.

  • Find velocity for an 8.5 kg ball with momentum of 293 kg·m/s:

    • v = p/m = 293 kg·m/s / 8.5 kg = 34.47 m/s.


Energy Levels

  • Potential Energy (PE) is always highest at the top of a hill or structure.

  • Kinetic Energy (KE) is always highest when the object is in motion.

  • Where PE is Lowest? When the object is at the bottom or ground level.

  • Where KE is Lowest? When the object is at rest.

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