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Four point masses are situated along the y-axis as follows:

- A 4 kg point mass is at 13 m,
- A 5 kg point mass is at 125 m,
- A 25 kg point mass is at the origin (0 m),
- A 6 kg point mass is at 215 m.

Where is the center of mass of the system?

Answer :

Answer:

xCOM = 49.175 m

Explanation:

To find the center of mass (COM) of the system, we'll use the formula:

m1x1 + m2x2 + m3x3 + m4x4 = (m1 + m2 + m3 + m4)xCOM

Where:

mi is the mass of each point mass (in kg)

xi is the position of each point mass along the y-axis (in m)

xCOM is the position of the center of mass (in m)

Plug in the values:

(4 kg × 13 m) + (5 kg × 125 m) + (25 kg × 0 m) + (6 kg × 215 m) = (4 kg + 5 kg + 25 kg + 6 kg) × xCOM

Simplify:

52 kg·m + 625 kg·m + 0 kg·m + 1290 kg·m = 40 kg × xCOM

Combine like terms:

1967 kg·m = 40 kg × xCOM

Solve for xCOM:

xCOM = 1967 kg·m / 40 kg

xCOM = 49.175 m

The center of mass of the system is approximately 49.18 m along the y-axis.

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Rewritten by : Barada