<h2>Using the Law of Conservation of Energy</h2>
<p>Mechanical energy is conserved (in the absence of friction). Therefore we can say that the sum of the ${E}_{P}$ and the ${E}_{K}$ anywhere during the motion must be equal to the sum of the the ${E}_{P}$ and the ${E}_{K}$ anywhere else in the motion.</p>
<p>We can now apply this to the example of the suitcase on the cupboard. Consider the mechanical energy of the suitcase at the top and at the bottom. We can say:</p>
<p><img alt="da9a09de47b91470d4b309983e987c81.png" src="https://data.ulearngo.com/assets/418e3e5d-c6a6-4286-8e61-e9eebef0a90d"/>\begin{align*} {E}_{M1} &amp; = {E}_{M2} \\ {E}_{P1} + {E}_{K1} &amp; = {E}_{P2} + {E}_{K2} \\ mgh + \frac{1}{2}m{v}^{2} &amp; = mgh + \frac{1}{2}m{v}^{2} \\ \left(\text{1}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{2}\text{ m}\right) + 0 &amp; = 0 + \frac{1}{2}\left(\text{1}\text{ kg}\right)\left({v}^{2}\right) \\ \text{19.6} &amp; = \frac{1}{2}\left({v}^{2}\right) \\ {v}^{2} &amp; = \text{39.2}\text{ m$^{2}$·s$^{-2}$} \\ v &amp; = \text{6.26}\text{ m·s$^{-1}$} \end{align*}</p>
<p>The suitcase will strike the ground with a velocity of $\text{6.26}$ $\text{m·s$^{-1}$}$.</p>
<p>From this we see that when an object is lifted, like the suitcase in our example, it gains potential energy. As it falls back to the ground, it will lose this potential energy, but gain kinetic energy. We know that energy cannot be created or destroyed, but only changed from one form into another. In our example, the potential energy that the suitcase loses is changed to kinetic energy.</p>
<p>The suitcase will have maximum potential energy at the top of the cupboard and maximum kinetic energy at the bottom of the cupboard. Halfway down it will have half kinetic energy and half potential energy. As it moves down, the potential energy will be converted (changed) into kinetic energy until all the potential energy is gone and only kinetic energy is left. The $\text{19.6}$ $\text{J}$ of potential energy at the top will become $\text{19.6}$ $\text{J}$ of kinetic energy at the bottom.</p>
<div class="ns-school-emp">
<h2>Activity: Conversion of Energy</h2>
<div class="ns-school-defn">
<section class="activity">
<h3>Materials</h3>
<p>A length of plastic pipe with diameter approximately 20 mm, a marble, some masking tape and a measuring tape.</p>
</section><section class="activity">
<h3>To do (1)</h3>
<p>First put one end of the pipe on the table top so that it is parallel to the top of the table and tape it in position with the masking tape.</p>
<p>Lift the other end of the pipe upwards and hold it at a steady height not too high above the table.</p>
<p>Measure the vertical height from the table top to the top opening of the pipe.</p>
<p>Now put the marble at the top of the pipe and let it go so that it travels through the pipe and out the other end.</p>
</section>
<section class="activity">
<h3>Questions</h3>
<ul>
<li>
<p>What is the velocity (i.e. fast, slow, not moving) of the marble when you first put it into the top of the pipe and what does this mean for its gravitational potential and kinetic energy?</p>
</li>
<li>
<p>What is the velocity (i.e. fast, slow, not moving) of the marble when it reaches the other end of the pipe and rolls onto the desk? What does this mean for its gravitational potential and kinetic energy?</p>
</li>
</ul>
</section>
<section class="activity">
<h3>To do (2)</h3>
<p>Now lift the top of the pipe as high as it will go.</p>
<p>Measure the vertical height of the top of the pipe above the table top.</p>
<p>Put the marble into the top opening and let it roll through the pipe onto the table.</p>
</section>
<section class="activity">
<h3>Questions</h3>
<ul>
<li>
<p>What is the velocity (i.e. fast, slow, not moving) of the marble when you put it into the top of the pipe, and what does this mean for its gravitational potential and kinetic energy?</p>
</li>
<li>
<p>Compared to the first attempt, what was different about the height of the top of the tube? How do you think this affects the gravitational potential energy of the marble?</p>
</li>
<li>
<p>Compared to your first attempt, was the marble moving faster or slower when it came out of the bottom of the pipe the second time? What does this mean for the kinetic energy of the marble?</p>
</li>
</ul>
</section>
</div>
</div>
<section class="activity"></section>
<section class="activity">
<p> </p>
<p> </p>
</section>
<p>The activity with the marble rolling down the pipe shows very nicely the conversion between gravitational potential energy and kinetic energy. In the first instance, the pipe was held relatively low and therefore the gravitational potential energy was also relatively low. The kinetic energy at this point was zero since the marble wasn't moving yet. When the marble rolled out of the other end of the pipe, it was moving relatively slowly, and therefore its kinetic energy was also relatively low. At this point its gravitational potential energy was zero since it was at zero height above the table top.</p>
<p>In the second instance, the marble started off higher up and therefore its gravitational potential energy was higher. By the time it got to the bottom of the pipe, its gravitational potential energy was zero (zero height above the table) but its kinetic energy was high since it was moving much faster than the first time. Therefore, the gravitational potential energy was converted completely to kinetic energy (if we ignore friction with the pipe).</p>
<p>In the case of the pipe being held higher, the gravitational potential energy at the start was higher, and the kinetic energy (and velocity) of the marble was higher at the end. In other words, the total mechanical energy was higher and and only depended on the height you held the pipe above the table top and not on the distance the marble had to travel through the pipe.</p>

1c4ddb66-ad36-4f81-90e7-4629f497d0b4

Using the Law of Conservation of Energy

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

Physics

Explore the concepts of mechanical energy, potential and kinetic energy, work, power, and conservation of energy through examples like pendulum, roller coaster, and inclined plane.


Using the Law of Conservation of Energy

Track Your Learning Progress