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