WEBVTT
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A volume of air moving through a wind turbine has a mass of 1.5 times 10 to the power of six kilograms.
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If the air is moving at five meters per second, what is the kinetic energy of the volume of air?
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Give your answer in megajoules to two significant figures.
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Okay, so in this question, we’ve been told that we’ve got a volume of air moving through a wind turbine.
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And we know that this volume of air has a mass of 1.5 times 10 to the power of six kilograms.
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We’ve also been told that the air is moving at five meters per second.
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And given all of this information, we need to work out the kinetic energy of the volume of air.
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We’ve also been told to give our answer in megajoules to two significant figures.
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Okay, so here’s this wind turbine that has a volume of air is going to be moving through and here’s our volume of air actually coming up to the turbine.
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We know that it’s gonna go through the turbine at a speed of five meters per second and we know that it has a mass of 1.5 times 10 to the power of six kilograms.
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Now, we need to calculate the volume of air’s kinetic energy.
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To do this, we can recall that the kinetic energy of an object 𝐸 sub 𝑘 for energy sub kinetic is given by half multiplied by the mass of the object multiplied by the velocity of the object squared.
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So in this case, our object is the volume of air that’s gonna be moving through the turbine.
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And so the air has a kinetic energy of half multiplied by the mass of the volume of air multiplied by the square of the velocity of the air.
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And when we evaluate this product, we find that the kinetic energy is 18,750,000 joules.
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And the reason that it’s in joules is because we use the standard unit for mass which is kilograms and the standard unit for velocity which is meters per second.
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So the kinetic energy is gonna come out in its standard unit, which is joules.
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However, we need to give our answer firstly in megajoules and secondly to two significant figures.
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Let’s worry about the megajoules bit first.
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We can recall that one megajoule is the same as 10 to the power of six joules.
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Therefore, if you want to find out the number of megajoules in 𝐸 sub 𝑘, then we divide this by 10 to the power of six because that’s the number of joules per megajoule.
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In other words, every megajoule has 10 to the power of six joules in it.
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And so when we conduct this division, we find that 𝐸 sub 𝑘 is 18.75 megajoules.
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So now that we have our answer in megajoules, we need to find it to two significant figures.
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So here’s the second significant figure.
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Is the one after that — the third one — that will tell us what happens to the second one.
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Now, this third significant figure is a seven.
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That value is larger than five.
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Therefore, our second significant figure is going to round up.
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And so 18.75 is going to round to 19 megajoules.
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And at this point, we have our final answer, the kinetic energy of the volume of air is 19 megajoules to two significant figures.