Question

Please show how the solution was arrived at I'm trying to understand how to do the problem.

4.(2) The fern is defined as the unit of force required to accelerate a unit of mass, called the bung, with the gravitational acceleration on the surface of the moon, which is one-sixth the normal gravitational acceleration on earth. a) What is the conversion factor that would be used to convert a force from the natural unit to the derived unit in this system (“gc”)? b) What is the weight in ferns of a 5.6 bung object on the moon? What does the same object weigh in Seattle?

Answer 1

a) Given: Mass, m= 1 bung

Acceleration due to Gravity on Moon, a=1/6th of Gravitational Acceleration on Earth(g_c)

Force is F=ma

1 fern= 1 bung* 5.362 ft/s²1 fern=5.3623 bung. ft/s²

Conversion Factor (to convert to fern) is 1 fern/5.3623 bung ft/s²

b) Weight of the object on Moon is W=ma

Mass, m= 5.6 bung and Acceleration, a =5.362 ft/s²

W= 5.6 bung

Weight of object in Seattle (or Earth) is W=ma

Mass, m=5.6 bung and Acceleration due to gravity, a=32.174 ft/s²

W= 33.60 fern

Weight of object on Moon is 5.6 fern and Weight of object in Seattle (or Earth) is 33.6 fern

(The problem can also be solved using the following steps

Acceleration due to Gravity on Moon, g_moon(or a)=1/6th of Gravitational Acceleration on Earth(g_c)

Hence, g_c = 6g_moon

g_moon= F/m=1 fern/1 bung, then g_c = 6(1 fern/bung)= 6 fern/bung

Thus, Weight of an object on moon= 5.6 fern

Weight of an object in Seattle (or Earth)= 6*5.6 fern= 33.6 fern)