Energy II, or Conservation of Energy

by Jacob Spindel, January 1998

Table of Contents

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New Quantities

Here's the quantities you can know:

All of these are defined on other pages except for restoring force, spring constant, and spring potential energy, which are explained below.

Defining Spring Constant and Restoring Force

Springs spring. That is, they push back when they're compressed. When the spring "pushes back", it is exerting a force, which can be measured in Newtons. We can calculate how much a spring will push back. To do this, use the following formula:


where F is the force, k is something called the spring constant, and x is the distance the spring has been compressed (not the length of the spring!). What's the deal with that "spring constant" thing, anyway? It's just a characteristic of the spring. Not every spring pushes back the same amount, so the spring constant of a spring, measured in N/m, is how we calculate information based on the specific spring.

Defining Spring Potential Energy

How exactly does a spring push back when it has been compressed? No, not magic dwarves. A compressed spring has energy stored in it. You know, energy. That thing we measure in Joules (J). Our other new formula tells us exactly how much energy.



So now we have all the formulas we need for solving spring force and energy problems with:

1. PE=m*g*h

2. PES=1/2*k*x2

3. KE=1/2*m*v2

4. W=F*s

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General Problem Solving Strategy:

The most important thing to remember in this lesson is that energy is CONSERVED. You can't create energy or get rid of it. Energy can change forms, but it cannot appear or disappear. All of these problems will involve a "before" and an "after." In other words, something will happen in the problem, like an object speeding up or slowing down, that will cause energy to change forms. However, at the beginning of the problem and at the end of the problem, the total amount of energy will remain the same because energy is CONSERVED. Your job will be to know when energy changes from one form to another. Possible forms of energy include potential energy, spring potential energy, kinetic energy, and work. An object can have all four kinds of energy simultaneously. If you add all the different kinds of energy the object has together, you will find its total energy. If the object changes in some way (for example, it falls, it speeds up, or it slows down), it may have less of one type of energy and more of a different type of energy than it had before. However, the total energy will be the same throughout the problem.