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.