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# Density word problem: blimp

## Video transcript

a helium-filled blimp stays aloft since helium is less dense than regular air so helium will rise above regular air that was a strangely phrased first sentence but they're just saying helium is less dense so helium will rise relative to regular air the density of helium is about 1.1 kilograms per meter cubed less than regular air which means a cubic meter of helium can lift about 1.1 kilograms because it has because the density of helium so forget 4 cubic meter of helium so this is a cubic meter of helium so this is a cubic meter of helium and here is a cubic meter of regular air they're saying they're saying that the mass of this cubic meter of helium is going to be 1.1 kilograms less than the mass of this cubic meter of regular air and that's what allows it because of the buoyancy that what that's what allows a cubic meter of helium that be able to lift about 1.1 kilograms a blimp with the mass of 2.1 one times 10 to the 5th kilograms can carry as much as as much as two times 10 to the 5th cubic meters of helium if the average mass of a person with luggage is 10 to the 2nd kilograms what is the number of passengers the blimp couldn't carry so I encourage you to pause this video and I'll give you a little structure for this think about how much mass 2 times 10 to the 5th meter cubic meters of helium can carry and then just realize it has to carry the blimp and then what's left over is what's what we can use to carry people so I'm assuming you've given a go at it so the first step is to say look we have 2 times 10 to the 5th cubic meters of helium and helium he a cubic meter of helium can lift one point one killer one point one kilograms so we could say that we can lift we can lift 1.1 kilograms per cubic metre per cubic metre so what is this going to give us well our units cancel nicely this gives us the number the the mass of kilograms that we can lift meters cubes cancelling with meters cube you'd have a meter cubed in the numerator meter cubed in the denominator our dimensional analysis allows our units to cancel just like numbers would in fractions and so we're left with 2 times 10 to the fifth times 1.1 well 2 times 1.1 is 2 point 2 so this is going to give us 2.2 times 10 to the 5th kilograms is how much we can lift so this is how much how much we can lift once again this is probably the most important step this is our mass of helium in terms of cubic meters and this is how much how many kilograms we can lift per cubic meter so you multiply those two we get the in kilograms how much mass we can lift so now let's subtract out the things that we need to lift we need to subtract out the mass of the actual blimp the actual structure that is holding the helium so let's subtract that so let's subtract 2.1 one times 10 to the 5th kilograms and so after lifting the blimp what do we have left over well let's see 2.2 and maybe I should well let me make it 2 point 2 minus 2 point 1 1 we might be able do that in our heads that's the same thing as 2 point 2 0 minus 2 point 1 1 20 minus 11 is 9 so we could think of it that way it's 0.09 or if you want you could say well 0 minus 1 well let's do a little bit of regrouping here 10 minus 1 is 9 1 minus 1 is 0 2 minus 2 is 0 so this gives us this gives us 0 point 0 9 kilograms of lifting capacity after we've netted out the mass of the blimp after netting out the mass of the blimp oh actually let me be careful 0.09 times 10 to the 5th times 10 to the 5th kilograms that we can lift after netting out the of the blimp this is what we can use to lift the people and their luggage with so they tell us that the people and luggage that each person plus that person's luggage is 10 to the 2nd kilograms so let's divide this by 10 to the 2nd divided by 10 to the 2nd and we could I guess we could say kilograms per person kilograms per person and then what do we end up with well this is going to be equal to 10 to the 5th divided by 10 squared is going to be 10 to the 3rd so that's going to be this is going to simplify to 10 to the 3rd so we get 0.09 times 10 to the third and then kilograms divided by kilograms per person if we just think about the dimensional analysis this is the same thing as kilograms times the reciprocal of this of people of person persons or person per kilogram kilogram gets cancelled out and you're just left with people or persons so this is how many people when we say people were saying the people plus their luggage so what is 0.09 times 10 to the third well that's just this times that's 0.09 times 1,000 so let's multiply it if we start with 0.09 we multiply it by 10 once we get to 0.9 multiply it by 10 again we get to 9 multiply it by 10 again we get to 90 so this right over here is the same thing as 90 people so we can lift we can the maximum load for this blimp is 990 people and their luggage