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Particle A has a mass of 5.60 g and particle B has a mass of 1.40 g. Particle A is located at the origin and particle B is at the point (x, y) = (25.0 cm, 4.50 cm).A. What is the x-component of the CM? B. What is the y-component of the CM?

Sagot :

Given data

*The particle A has a mass is m_1 = 5.60 g

*The particle B has a mass is m_2 = 1.40 g

*The particle A is located at the origin is (x_1, y_1) = (0, 0)

*The particle B is located at the point is (x_2, y_2) = (25.0, 4.50)

(A)

The formula for the x-component of the center of mass (C.M) is given as

[tex]X=\frac{m_1x_1+m_2x_2}{m_1+m_2}[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} X=\frac{(5.60)(0)+(1.40)(25.0)}{(5.60)+(1.40)} \\ =5\text{ cm} \end{gathered}[/tex]

(B)

The formula for the y-component of the center of mass (C.M) is given as

[tex]Y=\frac{m_1y_1+m_2y_2}{m_1+m_2}[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} Y=\frac{(5.60)(0)+(1.40)(4.50)}{(5.60)+(1.40)} \\ =0.9\text{ cm} \end{gathered}[/tex]

Hence, the y-component of the CM is Y = 0.9 cm

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