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Solved: PROBLEM 29ELet v1,...,Vk be points in 3 and
Chapter 1, Problem 29E(choose chapter or problem)
Let \(\mathbf{v}_{1}, \ldots, \mathbf{v}_{k}\) be points in \(\mathbb{R}^{3}\) and suppose that for j = 1,..., k an object with mass \(m_j\) is located at point \(v_j\). Physicists call such objects point masses. The total mass of the system of point masses is
\(m=m_{1}+\cdots+m_{k}\)
The center of gravity (or center of mass) of the system is
\(\overline{\mathbf{v}}=\frac{1}{m}\left[m_{1} \mathbf{v}_{1}+\cdots+m_{k} \mathbf{v}_{k}\right]\)
Compute the center of gravity of the system consisting of the following point masses (see the figure):
Questions & Answers
QUESTION:
Let \(\mathbf{v}_{1}, \ldots, \mathbf{v}_{k}\) be points in \(\mathbb{R}^{3}\) and suppose that for j = 1,..., k an object with mass \(m_j\) is located at point \(v_j\). Physicists call such objects point masses. The total mass of the system of point masses is
\(m=m_{1}+\cdots+m_{k}\)
The center of gravity (or center of mass) of the system is
\(\overline{\mathbf{v}}=\frac{1}{m}\left[m_{1} \mathbf{v}_{1}+\cdots+m_{k} \mathbf{v}_{k}\right]\)
Compute the center of gravity of the system consisting of the following point masses (see the figure):
ANSWER:
Solution : Step 1 :Let v1,...,Vk be points in 3 and suppose that for j = 1,..., k an object with mass mj is located at point vj. Physicists call such objects point masses. The total mass of the system of point masses ism = ml + m2 +m3...... + mk