Given:
• Mass of Particle A = 5.30 g
,
• Mass of particle B = 2.40 g
• Particle A is located at the origin.
,
• Particle B is located at (x, y) ==> (25.0 cm, 1.90 cm)
Let's solve for the following:
• A. What is the x-component of CM?
To find the x-component, apply the formula:
![x_{\operatorname{cm}}=(m_1x_1+m_2x_2)/(m_1+m_2)]()
Where:
m1 = 5.30 g
m2 = 2.40 g
x1 = 0
x2 = 25.0 cm
Thus, we have:
![\begin{gathered} x_{\operatorname{cm}}=((5.30*0)+(2.40*25.0))/(5.30+2.40) \\ \\ x_{\operatorname{cm}}=(0+60)/(7.70) \\ \\ x_{\operatorname{cm}}=7.8\operatorname{cm} \end{gathered}]()
The x-component is 7.8 cm.
• (B). What is the y-component of the CM?
To find the y-component, apply the formula:
![y_{\operatorname{cm}}=(m_1y_1+m_2y_2)/(m_1+m_2)]()
Where:
y1 = 0
y2 = 1.90 cm
Thus, we have:
![\begin{gathered} y_{\operatorname{cm}}=((5.30*0)+(2.40*1.90))/(5.30+2.40) \\ \\ y_{\operatorname{cm}}=(0+4.56)/(7.70) \\ \\ y_{\operatorname{cm}}=0.60\text{ cm} \end{gathered}]()
The y-component is 0.60 cm
ANSWER:
• (A). 7.80 cm
,
• (B). 0.60 cm