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Neporo4naja [7]
3 years ago
12

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 wi

ll 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?
Physics
1 answer:
ahrayia [7]3 years ago
4 0

Answer:

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

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Answer:

a. The object with the smallest rotational inertia, the thin hoop

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Explanation:

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Since the thin has the smallest rotational inertia. This is because, since kinetic energy of a rotating object K = 1/2Iω² where I = rotational inertia and ω = angular speed.

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The kinetic energy K = potential energy lost = mgh where h = 20.0 cm = 0.20 m and g = acceleration due to gravity = 9.8 m/s²

So, mgh =  1/2Iω²  + 1/2mv² =  1/2Iω²  + 1/2mr²ω²

Let I = moment of inertia of sphere = 2mr²/5 where r = radius of sphere = 3.00 cm = 0.03 m and m = mass of sphere = 2.00 kg

So, mgh = 1/2Iω²  + 1/2mr²ω²

mgh = 1/2(2mr²/5 )ω²  + 1/2mr²ω²

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substituting the values of the variables, we have

ω = √(10 × 9.8 m/s² × 0.20 m/7) ÷ 0.03 m

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= 0.03 m × 55.8 rad/s

= 1.67 m/s

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