Question

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.

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a. Calculate the mass is slugs and the weight in poundals of a 175 lbm man (i) on earth and (ii) on the moon, where the acceleration of gravity is one-sixth of its value on earth.
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b. A force of 355 poundals is exerted on a 25.0-slug object. At what rate (m/s2) does the object accelerate?

Answer 1

A 175 lbm man has a mass of 5.44 slugs and a weight of 5630.5 poundals on Earth, and the same mass but a weight of 938.4 poundals on the Moon. A 25.0-slug object accelerates at a rate of approximately 0.134 m/s² when a force of 355 poundals is applied.

Step-by-step explanation:

• Mass in slugs on Earth: Given that 1 slug = 32.174 lbm (since 1 lbf causes 1 slug to accelerate at 1 ft/s² and g = 32.174 ft/s²), the mass of a 175 lbm man is 175 lbm / 32.174 lbm/slug = 5.44 slugs.
• Weight in poundals on Earth: The weight in poundals can be calculated by multiplying the mass (in lbm) by the acceleration due to gravity (in ft/s²). On Earth, gravity is 32.174 ft/s², so the weight is 175 lbm * 32.174 ft/s² = 5630.5 poundals.
• Mass in slugs on the Moon: The man's mass does not change because it is an intrinsic property, so it remains 5.44 slugs on Moon.
• Weight in poundals on the Moon: Since the moon's gravity is one-sixth of Earth's, the weight in poundals is 5630.5 poundals / 6 = 938.4 poundals.

To find the rate of acceleration for a 25.0-slug object when a force of 355 poundals is applied, use Newton's second law (F = ma). In this case, acceleration a can be found using a = F/m. So, a = 355 poundals / (25 slugs * 32.174 ft/s²/lbf) = 0.44 ft/s². To convert this to meters per second squared (m/s²), multiply by the conversion factor 0.3048 m/ft, which gives us approximately 0.134 m/s².

Answer 2

a. Calculate the mass is slugs and the weight in poundals of a 175 lbm man (i) on earth and (ii) on the moon, where the acceleration of gravity is one-sixth of its value on earth.

The weight is the attraction force exerted by the earth (or moon) on the body

This force is calculated by the second Law of Newton: F = m*a = m*g = weight.

i) In the Earth:

m = 175 lbm
g = 32.17 ft/s^2

=> Weight = 175 lbm * 32.17 ft/s^2 = 5,629.75 poundal

ii) g = 1/6 * 32.17 ft/s^2 = 5.36 ft/s^2

=> Weight = 175 lbm * 5.36 ft/s^2 = 938 poundal



b. A force of 355 poundals is exerted on a 25.0-slug object. At what rate (m/s2) does the object accelerate?

Second Law of Newton: F = m*a => a = F/m

a = 355 poundal / 25.0 slug = 14.2 ft/s^2

Conversion to m/s^2:

14.2 ft/s^2 * [0.3048 m/ft] = 4.33 m/s^2