A poundal is the force required to accelerate a mass of 1 lbm at a rate of 1 ft/s2 , and a slug is the mass of an object that will accelerate at a rate of 1 ft/s2 when subjected to a force of 1 lbf. (a) Calculate the mass in slugs and the weight in poundals of a 135 lbm woman (i) on earth and (ii) on the moon, where the acceleration of gravity is one-sixth of its value on earth. (b) A force of 405 poundals is exerted on a 35.0-slug object. At what rate (m/s2 ) does the object accelerate?

We are given that

The

Mass of person = 135lbm

Weight of person on earth will be

= mass x gravity constant

= 135lbm x 32.174 ft/s2

=4343.49 lbm-ft/s2 x 1 poundal-s2/lbm-ft

= 4343.49 poundal

Again we are given that

Mass of person = 135 lbm

But here remember Mass remains the same

So

Weight of person on moon will be

mass x gravity constant on moon

= 135 lbm x 32.174 ft/s2 x 1/6

= 723.9 lbm-ft/s2 x 1 poundal-s2/lbm-ft

= 723.9poundal

But we know that

1 ft slug / lbf-s2 = 32.174 ft lbm/ lbf-s2

So

1 slug = 32.174 lbm

So then the Mass of person

= 135lbm x 1slug/32.174 lbm

=4.2slugs

So finally

Weight = 405 poundals is same as

405 lbm-ft/s2

So

Mass = 35 slug x 32.174 lbm/slug = 1126.09 lbm

Acceleration rate = weight /mass

= (405 lbm-ft/s2) / (1126.09 lbm)

= 0.3597ft/s2 x 0.305m/ft

= 1.179 m/s²