Dimensional Analysis – convert mph to m/s
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Let’s do another dimensional analysis example
that’s slightly more complicated because it has units in the numerator and the denominator. We want to convert 55 miles per hour into
meters per second. I’m going to start by converting the miles
into meters, and then I’ll come back and convert the hours into seconds. Just as in previous dimensional analysis problems,
I will multiply by a unit factor to convert my miles into another unit. I haven’t been given the conversion from
miles directly into meters, so I’m going to use the unit factor that contains miles. So I’ll multiply by 5,280 feet and 1 mile
– that will cancel my units of miles – and notice that if I stopped my calculations here,
I would end up with feet per hour. I don’t have meters yet, so I need to keep
going. I’m going to multiply by another unit factor;
this times something that will cancel out my feet. So 12 inches and 1 foot – the feet cancel
out – and again, if I stopped here, I would be left with inches per hour. I will convert to centimeters using 2.54 centimeters
and 1 inch – that cancels out my inches. Notice that I have centimeters per hour at
this point. But to get to meters, I will use the unit
factor that in 1 meter there are 100 centimeters. The centimeters cancel, and at this point
I have meters per hour. I have the desired unit in the numerator. But I have to address the unit in the denominator. I have hours and I need seconds. So I’m going to multiply by a unit factor
that will convert my hours first into minutes. Notice at this time I have to put the hours
on the top so that they cancel out, and we know that there are 60 minutes in an hour. So hours and hours cancel, and I would have
meters per minute if I stopped here. So let me do one more unit factor to convert
my minutes into seconds. Minutes and minutes cancel, and I have the
desired unit in the denominator. Once I have the proper units, I can do the
math – multiply my unit factors. So when I plug this into my calculator I end
up with 24.5872 meters per second. Since my measurement has three significant
figures and I don’t take into account significant figures for my unit factors because they are
exact, my answer should have three significant figures. So rounding, I get 24.6 meters per second.

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