3.1 - Translational Kinetic Energy

Introduction

Welcome to the FiveHive article for AP Physics 1: Unit 3.1 - Translational Kinetic Energy!

This article will go over kinetic energy, an incredibly important concept that will be used in multiple other units. 

Kinetic Energy

Translational Kinetic energy is a form of energy that an object possesses as a result of its motion. As with all forms of energy, it is measured in Joules (J). Additionally, kinetic energy is a scalar quantity. While the object’s velocity has a direction, its kinetic energy does not.

The formula for kinetic energy is $K=\frac{1}{2}m{v}^2$, where $m$ is the mass of the object in kg and $v$ is the velocity of the object in $\frac{\mathrm{m}}{\mathrm{s}}$.  If you use the formula with the incorrect units, you will get the incorrect answer. 

Note that the velocity term is squared, meaning small changes in velocity can have a large impact on kinetic energy. For example, if an object’s velocity doubles, its kinetic energy will quadruple. 

Reference Frames

Recall in unit 1.4 you learned that motion is relative, and the velocity of an object depends on your frame of reference. Similarly, kinetic energy can also vary depending on the observer’s frame of reference, since it is dependent on velocity.

A $1000\text{ kg}$ car traveling at a speed of $5\frac{\mathrm{m}}{\mathrm{s}}$ relative to you has a kinetic energy of $K=\frac{1}{2}(1000\text{ kg})(5\frac{\mathrm{m}}{\mathrm{s}}{)}^2=12500\text{ J}$ from your frame of reference. 

However, if the same car is traveling at $30\frac{\mathrm{m}}{\mathrm{s}}$ relative to a stationary observer has a kinetic energy of $K=\frac{1}{2}(1000\text{ kg})(30\frac{\mathrm{m}}{\mathrm{s}}{)}^2=450000\text{ J}$ relative to their frame of reference.

Practice