Question 2.38: If F = mV²/r, find m, when F = 2560, V = 20 and r = 5.

By direct substitution:

2560=\frac{m \ (20)^2}{5} so (2560)(5) = m (400)

400 m = 12800

m=\frac{12800}{400} then m = 32

Alternatively, we can transpose the formula for m and then substitute for the given values:

F=\frac{m V^2}{r} \ \text { and } \ F r=m V^2 \ \text { so } \ \frac{F r}{V^2}=m \\ \text { then } \ m=\frac{F_r}{V^2} \ \text { and } \ m=\frac{(2560)(5)}{(20)^2}\\ =\frac{12800}{400}=32

As we would expect, this gives the same result as before.