Answer:
a. f = 17.5/c
b. 8.75 N
Step-by-step explanation:
<h3>(a)</h3>
Inverse variation means one variable is proportional to the inverse of the other. The equation for that is ...
f = k(1/c) . . . . . . force (f) is proportional to the inverse of distance (c)
We find the value of k using data given for a specific instance.
3.5 N = k(1/(5 cm)) . . . . use the given values
17.5 N·cm = k . . . . . . multiply by the denominator
Then the equation of interest is ...
f = 17.5/c . . . . . . . where c is in cm, and f is in newtons
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<h3>(b)</h3>
Using the above equation, we find the force to be ...
f = 17.5/2 = 8.75 . . . . newtons
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<em>Additional comment</em>
We often look at several different kinds of proportionality:
- y = kx . . . . direct
- y = k(1/x) . . . . inverse
- y = kx² . . . . proportional as the square
- y = kx·z . . . . jointly proportional to x and z
and there are combinations of these, such as ...
- y = kr²h . . . . jointly proportional to h and the square of r
You may have noticed that when x and y are inversely proportional, their product is a constant. y = k/x ⇒ xy = k
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We have left off the units of k in the problem above. Sometimes it is a good idea to retain them, or to pay close attention to what they are. This can avoid using the wrong measures for the variables.
f = (17.5 N·cm)/(2 cm) = 8.75 N . . . . . units of cm cancel
