A $6.00 \mathrm{~kg}$ mass is located at $(1.0 \mathrm{~m},-2.00 \mathrm{~m}, 3.00 \mathrm{~m})$, a $5.00 \mathrm{~kg}$ mass is located at $(1.0 \mathrm{~m}, 3.00 \mathrm{~m},-2.00$ $\mathrm{m})$, and a $4.00 \mathrm{~kg}$ mass is located at $(-1.0 \mathrm{~m},-2.00 \mathrm{~m}, 2.00 \mathrm{~m})$. The center of gravity of the system of masses is
A) $(5 / 15 \mathrm{~m},-17 / 15 \mathrm{~m}, 5 / 15 \mathrm{~m})$.
B) $(12 / 15 \mathrm{~m},-5 / 15 \mathrm{~m}, 16 / 15 \mathrm{~m})$.
C) $(7 / 15 \mathrm{~m},-5 / 15 \mathrm{~m}, 16 / 15 \mathrm{~m})$.
D) $(16 / 15 \mathrm{~m},-1 / 15 \mathrm{~m}, 17 / 15 \mathrm{~m})$.
E) $(5 / 15 \mathrm{~m},-1 / 15 \mathrm{~m}, 17 / 15 \mathrm{~m})$.

Question

Quizplus · Accepted Answer

The center of gravity (CG) of a system of masses is calculated using the formula $\vec{r}_{CG} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$, where $m_i$ and $\vec{r}_i$ are the mass and position vector of the $i^{th}$ mass, respectively. For the given system:- The total mass is $6 + 5 + 4 = 15 \, \mathrm{kg}$.- The x-coordinate of the CG is $\frac{(6 \cdot 1) + (5 \cdot 1) + (4 \cdot -1)}{15} = \frac{6 + 5 - 4}{15} = \frac{7}{15} \, \mathrm{m}$.- The y-coordinate of the CG is $\frac{(6 \cdot -2) + (5 \cdot 3) + (4 \cdot -2)}{15} = \frac{-12 + 15 - 8}{15} = \frac{-5}{15} \, \mathrm{m}$.- The z-coordinate of the CG is $\frac{(6 \cdot 3) + (5 \cdot -2) + (4 \cdot 2)}{15} = \frac{18 - 10 + 8}{15} = \frac{16}{15} \, \mathrm{m}$.Thus, the center of gravity is at $(7 / 15 \, \mathrm{m}, -5 / 15 \, \mathrm{m}, 16 / 15 \, \mathrm{m})$.

A 6.00 kg6.00 \mathrm{~kg}6.00 kg Mass Is Located At (1.0 m,−2.00 m,3.00 m)(1.0 \mathrm{~m},-2.00 \mathrm{~m}, 3.00 \mathrm{~m})(1.0 m,−2.00 m,3.00 m)

A $6.00 \mathrm{~kg}$ Mass Is Located At $(1.0 \mathrm{~m},-2.00 \mathrm{~m}, 3.00 \mathrm{~m})$