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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson, and you will learn about the theory of special relativity and how it applies to you. Learn how you can use one of the most famous equations from this theory to calculate the power inside just one tiny object.

The world hasn't changed, but theories about the way the world works have changed over time. Our calculations are getting more and more accurate, and we are able to take into consideration things such as the speed of light. It is all thanks to Einstein's **special theory of relativity**, which tells us how objects appear to behave as they approach the speed of light and also how mass and energy are related to each other.

According to Einstein, as objects approach the speed of light, time seems to slow down for them when measured by an observer that is not moving. Also, when measured by an observer, objects traveling at a faster speed will measure shorter than if the objects weren't moving with respect to the observer. For example, I'm sitting on my front porch, and I'm watching cars drive by me. The faster the car is driving by, the shorter the car will look to me. Also, the faster the driver is driving, the slower time will seem to pass for him when compared to me. As an object gets close to the speed of light, time will seem to stop, and its length will seem to shrink to nothing.

The biggest equation to come out of Einstein's theory of special relativity is ** E = mc^2**, which tells us how

This special equation, *E* = *mc*^2, is called the **mass-energy equivalence equation** because the speed of light is a constant equal to 299,792,458 meters per second. This equation by Einstein allows us to calculate the amount of energy an object has inside of it. Because the speed of light is such a large number, you can see just how much power objects can possess. This energy is released when the mass of an object - its matter - is converted into energy. This conversion of mass to energy is what happens inside our sun. The units of this energy are *g* * (*m*/*s*)^2.

So think of our sun and its big size. Think about how far away it is. Even though it is so far away, because it is so huge, it has enough energy to heat up our Earth and grow all our plants, and we are only using just a tiny fraction of the energy the sun produces. We can see and feel the energy that is produced by our sun. We see it in the form of light, and we feel it in the form of heat.

We ourselves can calculate the amount of energy an object has by using Einstein's mass-energy equivalence equation. Let's see just how much energy a tiny object like a paper clip has inside of it. Now remember: we are calculating the *potential* energy the paperclip has. You can think of it as energy hidden inside an object. Once the right conditions are there, the object transforms itself into that energy. So now let's see how the equation works.

A paperclip has a mass of roughly one gram. So plugging this mass into our equation, we get *E* = 1 * *c*^2. Our *c*, the speed of light, is 299,792,458 meters per second. We can plug this in too and then evaluate for our energy to get *E* = 1 * 299,792,458^2 which is equal to **89,875,517,873,681,764 g x (m/s)^2**!

How much energy is this? A lot! Indeed, it *is* a lot. This is enough energy to power a really bright 100W light bulb for about 30,000 years!

What have we learned? We've learned that Einstein's **special theory of relativity** tells us how objects appear to behave as they approach the speed of light and also how mass and energy are related to each other. We learned that as objects approach the speed of light, an observer will notice that time slows down for the object, and its length will seem shorter. Einstein also related mass with energy and the speed of light when he introduced his now-famous mass-energy equivalence equation, ** E = mc^2**. This equation tells us how much energy can be released from an object if its mass were converted into energy. Our sun is an example of mass converting into energy. You can see and feel just how much energy is produced even though the sun is so far away.

The information in this lesson should prepare you to describe Einstein's special theory of relativity and mass-energy equivalence equation as well as understand their significance.

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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

- Theory of Relativity: Definition & Example 5:28
- The Value of e: Definition & Example 5:32
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