Question

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?

Answer 1

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:

$x_{\operatorname{cm}}=\frac{m_1x_1+m_2x_2}{m_1+m_2}$

Where:

m1 = 5.30 g

m2 = 2.40 g

x1 = 0

x2 = 25.0 cm

Thus, we have:

$\begin{gathered} x_{\operatorname{cm}}=\frac{(5.30\times0)+(2.40\times25.0)}{5.30+2.40} \\ \\ x_{\operatorname{cm}}=\frac{0+60}{7.70} \\ \\ x_{\operatorname{cm}}=7.8\operatorname{cm} \end{gathered}$

The x-component is 7.8 cm.

• (B). What is the y-component of the CM?

To find the y-component, apply the formula:

$y_{\operatorname{cm}}=\frac{m_1y_1+m_2y_2}{m_1+m_2}$

Where:

y1 = 0

y2 = 1.90 cm

Thus, we have:

$\begin{gathered} y_{\operatorname{cm}}=\frac{(5.30\times0)+(2.40\times1.90)}{5.30+2.40} \\ \\ y_{\operatorname{cm}}=\frac{0+4.56}{7.70} \\ \\ y_{\operatorname{cm}}=0.60\text{ cm} \end{gathered}$

The y-component is 0.60 cm

ANSWER:

• (A). 7.80 cm

,

• (B). 0.60 cm