A rocket has a mass of 250 (10³)slugs on earth. Specify (a) its mass in SI units and (b) its weight in SI units. If the rocket is on the moon, where the acceleration due to gravity is gm=5.30 ft/s², determine to three significant figures (c) its weight in SI units and (d) its mass in SI units.

Question

A rocket has a mass of 250 (10³)slugs on earth. Specify (a) its mass in SI units and (b) its weight in SI units. If the rocket is on the moon, where the acceleration due to gravity is [latex]g_m[/latex]=5.30 ft/s², determine to three significant figures (c) its weight in SI units and (d) its mass in SI units.

Accepted Answer

Using Table 1–2 and applying Eq. 1–3, we have [latex]\begin{aligned} a) 250\left(10^3 ight) ext { slugs }&=\left[250\left(10^3 ight) ext { slugs } ight]\left(\frac{14.59 kg }{1 ext { slugs }} ight) \&=3.6475\left(10^6 ight) kg \&=3.65 Gg\end{aligned}[/latex]

[latex]\begin{aligned}b) W_e &=m g=\left[3.6475\left(10^6 ight) kg ight]\left(9.81 m / s ^2 ight) \&=35.792\left(10^6 ight) kg \cdot m / s ^2 \&=35.8 MN\end{aligned}[/latex]

[latex]\begin{aligned}c) W_m &=m g_m=\left[250\left(10^3 ight) ext { slugs } ight]\left(5.30 ft / s ^2 ight) \&=\left[1.325\left(10^6 ight) lb ight]\left(\frac{4.448 N }{1 lb } ight) \&=5.894\left(10^6 ight) N =5.89 MN\end{aligned}[/latex]

Or

[latex]W_m=W_e\left(\frac{g_m}{g} ight)=(35.792 MN)\left(\frac{5.30 ft / s ^2}{32.2 ft / s ^2} ight)=5.89 MN[/latex]

d) Since the mass is independent of its location, then

[latex]m_m=m_e=3.65\left(10^6 ight) kg =3.65 Gg[/latex]

Question 1.9: A rocket has a mass of 250 (10³)slugs on earth. Specify (a) ...

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