Work, Energy, and Power

Robert Jones

12 min read

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Study Guide Overview

This study guide covers Work, Energy, and Power in AP Physics C: Mechanics. Key topics include the work-energy theorem, connecting work and kinetic energy; potential energy (gravitational and elastic) and its relationship with forces; the conservation of energy principle; and power as the rate of work/energy transfer. It also provides practice questions and exam tips focusing on problem-solving strategies and key concepts.

#AP Physics C: Mechanics - Unit 3 Study Guide: Work, Energy, and Power 🚀

Hey there, future physics pro! This guide is your go-to resource for acing Unit 3. We'll break down work, energy, and power, making sure you're not just memorizing formulas, but truly understanding the concepts. Let's get started!

#1. Work-Energy Theorem

#What it is:

The work-energy theorem is your secret weapon for connecting work and kinetic energy. It states that the net work done on an object equals the change in its kinetic energy. Think of it as the energy transfer in motion. 💡

Formula: $W_{net} = \Delta KE = KE_f - KE_i$ where $KE = \frac{1}{2}mv^2$
- $W_{net}$ is the net work done
- $\Delta KE$ is the change in kinetic energy
- $KE_f$ is the final kinetic energy
- $KE_i$ is the initial kinetic energy

Key Concept

The work-energy theorem is a scalar equation, meaning it doesn't involve direction. It's all about the magnitude of energy transfer.

#Key Ideas:

Work: Work is done when a force causes a displacement. If the force and displacement are in the same direction, the work is positive. If they're opposite, the work is negative. If they are perpendicular, work done is zero.
- Formula: $W = F \cdot d \cdot cos(\theta)$ where $\theta$ is the angle between the force and the displacement.
Kinetic Energy (KE): The energy of motion. The faster an object moves, the more KE it has.

Memory Aid

Remember: Work is like the 'push' that changes an object's motion (kinetic energy).

#Example:

Imagine pushing a box across a floor. The work you do increases the box's kinetic energy, making it move faster. If you push in the opposite direction of motion, you are doing negative work, slowing it down.

Practice Question

Multiple Choice Questions:

A 2 kg block is pushed along a horizontal surface with a force of 10 N over a distance of 5 m. If the coefficient of kinetic friction is 0.2, what is the net work done on the block? (A) 50 J (B) 40.4 J (C) 10 J (D) 9.6 J
A 1 kg ball is dropped from a height of 10 m. What is the kinetic energy of the ball just before it hits the ground? (Assume no air resistance) (A) 98 J (B) 49 J (C) 196 J (D) 0 J

Free Response Question:

A 0.5 kg block is initially at rest on a horizontal surface. A force of 20 N is applied at an angle of 30 degrees above the horizontal. The block moves 2 meters along the surface. The coefficient of kinetic friction between the block and the surface is 0.1. (a) Draw a free body diagram for the block. (b) Calculate the work done by the applied force. (c) Calculate the work done by the frictional force. (d) Calculate the net work done on the block. (e) Calculate the final speed of the block using the work-energy theorem.

Answer Key:

Multiple Choice:

(B) 40.4 J. Net work = Work by applied force - Work by friction. Work by applied force = 10 N * 5 m = 50 J. Frictional force = μ * normal force = 0.2 * 2 kg * 9.8 m/s^2 = 3.92 N. Work by friction = 3.92 N * 5 m = 19.6 J. Net work = 50 J - 19.6 J = 40.4 J
(A) 98 J. The potential energy at the top is converted to kinetic energy at the bottom. Potential energy = mgh = 1 kg * 9.8 m/s^2 * 10 m = 98 J.

Free Response:

(a) Free body diagram should include: gravity (downward), normal force (upward), applied force (at 30 degrees), and friction (opposite to motion). (b) Work by applied force = F * d * cos(θ)...

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