<h2>Checking Units</h2>
<p>According to the equation for kinetic energy, the unit should be $\text{kg·m·s$^{-2}$}$. We can prove that this unit is equal to the joule, the unit for energy.</p>
<p>\begin{align*} \left(\text{kg}\right){\left(\text{m·s$^{-1}$}\right)}^{2} &amp; = \left(\text{kg·m·s$^{-2}$}\right)·\text{m} \\ &amp; = \text{N·m} \left(\text{ because Force }\left(\text{N}\right) = \text{ mass }\left(\text{kg}\right) \times \text{ acceleration }\left(\text{m·s$^{-2}$}\right)\right) \\ &amp; = \text{J} \left(\text{ Work }\left(\text{J}\right) = \text{ Force }\left(\text{N}\right) \times \text{ distance }\left(\text{m}\right)\right) \end{align*}</p>
<p>We can do the same to prove that the unit for potential energy is equal to the joule:</p>
<p>\begin{align*} \left(\text{kg}\right)\left(\text{m·s$^{-2}$}\right)\left(\text{m}\right) &amp; = \text{N·m} \\ &amp; = \text{J} \end{align*}</p>
<div class="ns-school-emp">
<h2>Example: Mixing Units and Energy Calculations</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>
<p>A bullet, having a mass of $\text{150}$ $\text{g}$, is shot with a muzzle velocity of $\text{960}$ $\text{m·s$^{-1}$}$. Calculate its kinetic energy.</p>
</div>
<div>
<h3>Step 1: Analyse the question to determine what information is provided</h3>
<ul>
<li>
<p>We are given the mass of the bullet m = $\text{150}$ $\text{g}$. This is not the unit we want mass to be in. We need to convert to $\text{kg}$.</p>

\begin{align*} \text{Mass in grams } ÷ 1000 &amp; = \text{ Mass in kg} \\ \text{150}\text{ g} ÷ 1000 &amp; = \text{0.150}\text{ kg} \end{align*}</li>
<li>
<p>We are given the initial velocity with which the bullet leaves the barrel, called the muzzle velocity, and it is $v = \text{960}\text{ m·s$^{-1}$}$.</p>
</li>
</ul>
</div>
<div>
<h3>Step 2: Analyse the question to determine what is being asked</h3>
<ul>
<li>
<p>We are asked to find the kinetic energy.</p>
</li>
</ul>
</div>
<div>
<h3>Step 3: Substitute and calculate</h3>
<p>We just substitute the mass and velocity (which are known) into the equation for kinetic energy:</p>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{0.150}\text{ kg}\right){\left(\text{960}\text{ m·s$^{-1}$}\right)}^{2} \\ &amp; = \text{69 120}\text{ J} \end{align*}</div>
</div>
</div>

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

Checking Units

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.


Checking Units

Track Your Learning Progress