Video Transcript ExProb 1A-Units Conversion

Video Transcript ¨C ExProb 1A-Units Conversion

This problem covers unit conversion between weight and mass. So if the specific weight of brass is 520

lbs./cubic foot, find its density in SI units. So in essence we are given the specific weight of brass (520

lbs./ cubic foot.) And we are asked to find its density in SI units. So how do we begin?

Let¡¯s start by converting the 520 lbs./cubic foot to SI units. So given are 520 lbs./foot cubed. We need

to find a way to convert pounds to newtons. We have a relationship of 1 lb. is 4.4482 newtons. We also

need a way to get from cubic feet to cubic meters. We know that one foot is 0.3048 meters. But now

we need to cube each term so that we¡¯ll get cubic feet. A common error is to forget to cube your

conversion factor. So let¡¯s look at our units. Pounds will cancel. Cubic feet will cancel. And what we¡¯re

left with we multiply things out as 81685 newtons/meter cubed. We know we need to convert from

newtons, which is a force, to a mass. So let¡¯s look at some of the equations that we have available.

We know that weight is equal to M times G. Which means that if we are looking for mass we could take

weight and divide through by G. We also know that g is equal to 9.81 meters/second squared. Further

we know a relationship between newtons and kilograms. One newton is one Kilogram meter/second

squared. Given these relationships, beginning with our previous answer of 81685 newtons/meter

cubed. Let¡¯s divide through by G. Or multiple by the reciprocal, 9.81 meters/second squared. But none

of our units are going to cancel. So now let¡¯s use a relationship that one newton is equal to 1 kg

meter/second squared. Now let¡¯s see what has happened with our units. Newtons will cancel out.

Seconds squared will cancel out. One of the meters will cancel out. And this will leave us with 8327

kg/meters cubed. Well we¡¯re almost there. The only thing we may need now is to realize that in

general what we like to do is get our answer between one and a thousand. So if we begin with 8327

kg/meter cubed, we have a relationship between kg and mg. 1000 kg is equal to 1 mg. So simplifying

we have 8.33 mg/meters cubed. This is our final answer.

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