Three balls are attached to a light rigid rod, as shown in the figure. A fulcrum is located at xf = 18.0 cm measured from the left end of the rod. Ball A has mass mA = 65 g and is located at xA = 3 cm. Ball B has mass mB = 12 g located at xB = 22 cm. Ball C has mass mC = 22 g located at xC = 30 cm. Calculate the x-coordinate of the center of mass XCM. Assume that the mass of the rod is small enough to be ignored in your calculation. Your answers should be accurate to within 0.1 cm
In Part 1 above, is the structure in balance? If not, how far must the fulcrum be moved so that it becomes in balance? (Answer "0.0" if it does not need to be moved. Also, signs matter: + if to the right, – if to the left.)
The the fulcrum needs to be moved 2 cm.
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.