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HussAhmad · Jun 1, 2011, 10:48 AM

A controlling variable is a motor speed that varies from 800 to 1750 rpm.If the speed is controlled by a 25- to 50- v
dc signal, calculate (a) the speed produced by an input of 38v, and (b) the speed calculated as a percent of span.

jcaron2 · Jun 1, 2011, 11:57 AM

Assuming the relationship is linear, you need to write the equation of a line f(x)=mx+b, where f(x) is the rotational speed and x is the input voltage. So basically it boils down to a simple algebra problem:

Find the equation of a line passing through the points (25,800) and (50,1750). Use that equation to calculate f(38).

Presumably if you're taking physics, you learned how to do this kind of algebra several years ago. If you're stuck, post back and we'll give you further guidance.

jcaron2 · Jun 2, 2011, 10:39 AM

First of all, the red "No" or "Not Helpful" response is reserved for answers that are factually wrong, not responses that don't spoon-feed your homework answers to you.

Second, since this is almost certainly for homework, you should read the homework rules for this website. Volunteers are here to HELP you do your homework, not do it for you. It's a shame that my reputation as an expert gets impacted by your "not helpful" response, just because you apparently never learned to write the equation of a line.

So getting back to your question, let me write it out in excruciating detail for you:

A line is described by the equation y=mx+b, where m is the slope (a.k.a. gradient), and b is the y-intercept. The line passes through the point (25,800) because an input of 25 volts results in an output of 800 rpm. The line also passes through the point (50,1750) because an input of 50 volts results in an output of 1750 rpm. We calculate the slope as

$m=\frac{\Delta y}{\Delta x}=\frac{1750-800}{50-25}=\frac{950}{25}=38 \text{ rpm/volt}$

That means for every volt increase in the control input, the output increases by 38 rpm.

Now we can find the y-intercept by simply substituting the x and y values for one of the points we know it passes through:

$y=38x+b$

$800=38 \cdot 25+b$

$b=800-950=-150$

Thus the equation for the line is

$y=38x-150$

So now, as I said, to find the output value for an input of 38 volts, just substitute 38 for the value of x.

$y=38 \cdot 38 -150=1294\text{ rpm.}$

Congratulations. You've now been shown how to do math that an average 13-year-old student could do.

Now can you calculate that as a percent of span, or are you also unable to do math for 10-year-olds?