Question

Suppose that units of force, length, and time are chosen such that the density of water and the acceleration of gravity are both of unit magnitude. If the pound is taken as the unit of force, what are the sizes of the units of length and time?

Answer 1

Answer: So a 1 pound = 0.453592kg

the density of the water is D= 997 kg/$m^{3}$ so we need to use replace the kg with pounds with 2.20462 pounds = 1kg.

then D = 2.20462*997 pounds/$m^{3}$

and we want to make this equal to one changing the metters for other thing.

we need to replace $x^{3}$ with 2.020462*997 meters qube.

then our new metters variable x = 12.6meters.

now g = 9.8 meters for second square.

in our new lenght variable x.

g = 12.6*9.8 x for second square.

so if y is our new time variable

$y^{2}$ = 12.6*9.8 seconds square. so y = 11.1seconds

so the units of length are x = 12.6 meters and for time y = 11.1 seconds.