1. Understand Center of Gravity
* The center of gravity (CG) is the point where the entire weight of an object can be considered to act.
* For a uniform object, the CG is at its geometric center.
2. Treat the Masses as Point Masses
* Since the masses are small compared to the board, we can treat them as point masses located at their respective corners.
3. Calculate the Moments
* Moment is the product of a force (in this case, the weight of each mass) and its perpendicular distance from a reference point.
* We'll choose the bottom left corner of the board as our reference point.
4. Moment of the Board:
* The board's weight acts at its center, which is 10.0 cm from the bottom left corner (half the width).
* Moment of the board = (mass of board * g) * 10.0 cm
* Moment of the board = (0.2 kg * 9.8 m/s²) * 0.1 m = 0.196 Nm
5. Moments of the Masses:
* Mass 1 (50.0 g):
* Moment = (0.05 kg * 9.8 m/s²) * 0.1 m = 0.049 Nm
* Mass 2 (80.0 g):
* Moment = (0.08 kg * 9.8 m/s²) * 0.2 m = 0.1568 Nm
6. Total Moment:
* Total moment = Moment of board + Moment of mass 1 + Moment of mass 2
* Total moment = 0.196 Nm + 0.049 Nm + 0.1568 Nm = 0.4018 Nm
7. Find the x-coordinate of the CG:
* The total moment is also equal to the total mass of the system multiplied by the x-coordinate of the CG.
* Total moment = (Total mass * g) * x
* 0.4018 Nm = (0.2 kg + 0.05 kg + 0.08 kg) * 9.8 m/s² * x
* x = 0.4018 Nm / (0.33 kg * 9.8 m/s²) ≈ 0.124 m = 12.4 cm
8. Find the y-coordinate of the CG:
* The CG will lie on the vertical line passing through the center of the board.
* The y-coordinate of the CG is simply half the height of the board: 10.0 cm / 2 = 5.0 cm
Therefore, the center of gravity of the system is located at approximately (12.4 cm, 5.0 cm) relative to the bottom left corner of the board.
