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Explanation of the Relationship between Work and Kinetic Energy - Succeed in Physical Science. Also refer to physics, force, distance, mass acceleration, velocity, equation, newton, kilogram, joule, Ron Kurtus, School for Champions. Copyright © Restrictions Relationship between Work and Kinetic Energyby Ron Kurtus (revised 13 October 2007) There is a relationship between work and kinetic energy. Work is defined in Physical Science as the result of a force moving an object a distance and is stated by the equation W = Fd. But the result of the force being applied on the object also means that the object is moving with some given velocity, according to the equation for force as F = ma. From those two equations, it can be shown that work is equivalent to kinetic energy KE = ½mv². Questions you may have include:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Useful tools: Metric-English Conversion | Scientific Calculator. Work is force times distanceThe definition of work is that it equals force times the distance traveled while that force is being applied or W = Fd where:
Thus, if you would apply a force of F = 3 newtons (3 N) to move an object d = 5 meters (5 m), the work done would be W = Fd = 15 joules (15 J). The force required to do some work is determined from the equation F = W/d. Force is mass times accelerationWe know that a force will accelerate an object according to the equation F = ma where:
Rewriting the equation, the acceleration is a = F/m. Thus, if F = 3 N and m = 2 kg, then the acceleration would be a = 1.5 m/s². Work is kinetic energyWork is related to kinetic energy. This can be shown by examining the force and time it takes to travel a distance. AccelerationAcceleration is defined as the change in velocity over a time period. Suppose you start with an object at rest and accelerate it up to some end velocity v. The change in velocity is (v − 0) = v. Thus, the acceleration in such a case is a = (v − 0)/t = v/t where:
If we substitute a = v/t into the equation F = ma, we get F = mv/t. DistanceSince the velocity went from 0 to v, then v/2 is the average velocity for the motion. The distance traveled equals the average velocity times the time, so we get d = ½vt for the distance traveled when the force is applied. Kinetic energyNow let's take all of the equations together. Since W = Fd and F = mv/t, we get W = mvd/t. And since d = ½vt, we substitute it into the equation and get W = mv(½vt)/t. Since t/t = 1, the equation becomes W = ½mv², which is the equation for kinetic energy. KE = ½mv². Pretty clever! SummaryIt can be shown that there is a relationship between work and kinetic energy. Work is the result of a force moving an object a distance and is stated by the equation W = Fd. The result of the force being applied on the object means that the object is moving with some given velocity, according to the equation F = ma. From those two equations, it can be shown that work is equivalent to kinetic energy KE = ½mv². Physical Science rules ResourcesThe following resources provide information on this subject: WebsitesBooks
Top-rated books on the Science of Work MiscellaneousMini-quiz to check your understanding1. If the work done to move a 2 kg object 1 m was 10 J, how much would the force be? 2. If an object started at 2 m/s and accelerated to 8 m/s in 3 seconds, what would the acceleration be? 3. If a force of 3 N moved a 6 kg object 4 m, what would its kinetic energy be? If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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