A system is made of four objects. The masses and the positions of their centers of mass in a rectangular frame are as follows: Particle 1 of mass 2.0 kg is placed at r₁ = 3.0i - 2.0j m; particle 2 of mass 3.0 kg is placed at r₂ = -1.0i + 1.0j m; particle 3 of mass 2.0 kg is placed at r₃ = 3.0j m; and particle 4 of mass 4.0 kg is placed at r₄ = -1.0i m. The x component of the center of mass of the system is A) -1.0 m. B) -0.090 m. C) 13 m. D) 0.090 m. E) 1.0 m.

Question

Quizplus · Accepted Answer

The x-component of the center of mass of the system can be calculated using the formula: $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$, where $m_i$ is the mass of the ith particle and $x_i$ is the x-coordinate of the ith particle. Plugging in the values given:$$x_{cm} = \frac{(2.0 \times 3.0) + (3.0 \times -1.0) + (2.0 \times 0) + (4.0 \times -1.0)}{2.0 + 3.0 + 2.0 + 4.0}$$$$x_{cm} = \frac{6.0 - 3.0 + 0 - 4.0}{11}$$$$x_{cm} = \frac{-1}{11}$$$$x_{cm} = -0.0909 \, m$$Rounded to three significant figures, the x-component of the center of mass is -0.090 m.

A System Is Made of Four Objects