Question

A 3.00 kg mass is located at x = 2.0 cm and y = 0.0 cm. A 3.00 kg mass is located at x = 0.0 cm and y = 2.0 cm. A 4.00 kg mass is located at x = 3.0 cm and y = −3.0 cm. Where is the location of the center of mass?

Answer 1

x = 1.8 cm and y = -0.6 cm

Explanation:

Given:

Then x-coordinate of centre of mass is:

`\begin{gathered} x_m=(m_1\cdot x_1+m_2\cdot x_2+m_3\cdot x_3)/(m_1+m_2+m_3) \\ \text{ replacing:} \\ x_m=(3\cdot2+3\cdot0+4\cdot3)/(3+3+4)=(6+0+12)/(10)=1.8\text{ cm} \\ \\ y_m=(m_1\cdot y_1+m_2\cdot y_2+m_3\cdot y_3)/(m_1+m_2+m_3) \\ y_m_{}=(3\cdot0+3\cdot2+4\cdot-3)/(3+3+4)=(0+6-12)/(10)=-0.6\text{ cm} \\ \\ \text{The center mass is (1.8 cm, -0.6 cm)} \end{gathered}`

The location of the center of mass x = 1.8 cm and y = -0.6 cm