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Particle A has a mass of 5.30 g and particle B has a mass of 2.40 g. Particle A is located at the origin and particle B is at the point (x, y) = (25.0 cm, 1.90 cm).A. What is the x-component of the CM?B. What is the y-component of the CM?

User ChrisTorng
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1 Answer

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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

User ChrisN
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