Question

The mobile in the figure(Figure 1) is in equilibrium. Object B has mass of 0.585 kg .

Determine the masses of objects A, C, and D. (Neglect the weights of the crossbars.)

Answer 1

For equilibrium of the crossbar to which C and D are attached,

mD * L5 = mC * L6

mD * 17.50 = mC * 5

mC = 3.50 * mD ----------(1)

For equilibrium of the crossbar to which B is attached,

(mC + mD) * L3 = mB * L4

(mC + mD) * 15 = 0.585 * 5

mC + mD = 0.195 -----------------(2)

From equations (1) and (2),

3.50 mD + mD = 0.195

4.50 mD = 0.195

mD = 0.195/4.50 = 0.0433 kg

From equations (1), mC = 3.50 * 0.0433 = 0.152 kg

For the equilibrium of the crossbar to which A is attached,

mA * L1 = (mB + mC + mD) * L2

mA * 30 = (0.585 + 0.152 + 0.0433) * 7.50

mA = 0.195 kg