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Work and Mechanical Energy

Joseph Brown

Joseph Brown

10 min read

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Study Guide Overview

This AP Physics 1 study guide covers work and energy. It explores different types of energy, including kinetic, gravitational potential, elastic potential, and thermal energy. The guide explains the work-energy theorem and the law of conservation of energy. It also includes practice questions and exam tips.

AP Physics 1: Energy Review - The Night Before 🚀

Hey! Let's get you feeling confident about energy for tomorrow's exam. We're going to break this down, make it super clear, and get you ready to rock! 💪

1. Work and Energy: The Big Picture

What is Energy? 🤔

Energy is the ability to do work. It comes in many forms, and it's all about how things move and interact. Let's dive into the main types you need to know for AP Physics 1. ### Work: The Energy Transfer Mechanism

  • Definition: Work is the process of transferring energy into or out of a system by applying a force over a distance.
  • Key Idea: Work is done when a force has a component parallel to the displacement of the object. If the force is perpendicular to the motion, no work is done.
Key Concept

Work is a scalar quantity (no direction) and is measured in Joules (J). Remember: Work = Force x Distance x cos(θ), where θ is the angle between the force and displacement vectors.

Exam Tip

Always check if the force and displacement are parallel. If they aren't, use the cosine of the angle between them to find the component of the force that does the work. This is a common spot where students lose points!

2. Types of Energy

Kinetic Energy (K): The Energy of Motion

  • Definition: Energy an object possesses due to its motion.

  • Formula: K=12mv2K = \frac{1}{2}mv^2 where m is mass and v is velocity.

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  • Key Point: Kinetic energy is always positive because velocity is squared.

  • Change in Kinetic Energy: ΔK=Kf−KiΔK = K_f - K_i. This change occurs when work is done on an object.

Memory Aid

Think of a car: the faster it goes, the more kinetic energy it has. Doubling the speed quadruples the kinetic energy!

Deriving Kinetic Energy from Work

Here's how work leads to changes in kinetic energy:

  1. Start with Work: W=FdW = Fd

  2. Newton's Second Law: F=maF = ma

  3. Kinematics: vf2=vi2+2adv_f^2 = v_i^2 + 2ad which can be rearranged to a=vf2−vi22da = \frac{v_f^2 - v_i^2}{2d}

  4. Substitute: W=mad=m(vf2−vi22d)d=12mvf2−12mvi2=ΔKW = mad = m(\frac{v_f^2 - v_i^2}{2d})d = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 = ΔK

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Gravitational Potential Energy (Ug): Energy of Position

  • Definition: Energy stored in an object due to its position in a gravitational field.
  • **Formula...