Statics: General Principles - General Procedure for Analysis - #1

Question

Question 1

If a man weighs \(155lb\) on earth, specify (a) his mass in slugs, (b) his mass in kilograms, and (c) his weight in newtons. If the man is on the moon, where the acceleration due to gravity is \(g_{m} = 5.30ft/s^{2}\), determine (d) his weight in pounds, and (e) his mass in kilograms.

Question 2

Two particles have a mass of \(8 kg\) and \(12 kg\), respectively. If they are \(800 mm\) apart, determine the force of gravity acting between them. Compare this result with the weight of each particle.

Answer

Answer 1

(a)

\[\text{Use } m=\frac{w}{g}\] \[(g = 32.2ft/s^{2})\] \[\therefore m = \frac{155lb}{32.2ft/s^{2}} = 4.81 slug\]

(b)

\[\text{Use } 1 slug = 14.59 kg\] \[\therefore 4.81 slug \times 14.59 kg = 70.3 kg\]

(c)

\[\text{Use } 1 lb = 4.448 N\] \[\therefore 4.81 slug \times 4.448 N = 689 N\]

(d)

\[\text{Use } W = mg\] \[(m = 4.81 slug, g_{m} = 5.30 ft/s^{2})\] \[\therefore 4.81 slug \times 5.30 ft/s^{2} = 25.5 lb\]

(e)

\[\text{(e) is the same as (b).}\]

Answer 2

\[\text{Use } F = G\frac{m_{1}m_{2}}{r^{2}}\] \[F\text{: force of gravitation between the two particles}\] \[G\text{: universal constant of gravitation; according to experimental evidence, } G=66.73(10^{-12})m^{3}/({kg} \cdot {s^{2}})\] \[m_{1}, m_{2}\text{: mass of each of the two particles}\] \[r\text{: distance between the two particles}\]

\[F = 66.73(10^{-12})(m^{3}/({kg} \cdot {s^{2}}))\frac{8(kg)\times12(kg)}{(800(10^{-3})(m))^{2}} = 10.0nN\] \[W_{1}=8(kg)\times9.81(m/s^{2}) = 78.5N\] \[W_{2}=12(kg)\times9.81(m/s^{2}) = 118N\]