To determine if the structure is in balance, we need to calculate the center of mass (XCM) of the system and compare it to the position of the fulcrum (xf).
The center of mass can be calculated by using the formula:
XCM = (mA * xA + mB * xB + mC * xC) / (mA + mB + mC)
Substituting the given values:
XCM = (65g * 3cm + 12g * 22cm + 22g * 30cm) / (65g + 12g + 22g)
XCM = (195g + 264g + 660g) / 99g
XCM = 1119g / 99g
XCM ≈ 11.3 cm
Since the structure is not in balance, we need to determine how far the fulcrum needs to be moved for balance. We can do this by finding the difference between XCM and xf, taking into account the sign.
Difference = XCM - xf
Difference = 11.3cm - 18.0cm
Difference ≈ -6.7 cm
Therefore, the fulcrum needs to be moved approximately 6.7 cm to the left (as indicated by the negative sign) in order for the structure to become in balance.