The mobile in Fig. 12–91 is in equilibrium. Object B has mass of 0.748 kg. Determine the masses of objects A, C, and D. (Neglect the weights of the crossbars.)
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Verified step by step guidance

1. Identify the points of equilibrium where the torques balance each other. Since the mobile is in equilibrium, the sum of the torques around any pivot point must be zero.
2. Choose a pivot point on one of the crossbars and write down the torque balance equation. Remember that torque is given by the product of the force and the distance from the pivot point, and the force here is due to the weight of the objects (weight = mass x gravity).
3. Set up equations for each crossbar where the torques on the left side of the pivot must equal the torques on the right side. Use the distances given in the figure and the known mass of object B to express the masses of objects A, C, and D in terms of each other.
4. Solve the system of equations obtained from the torque balance on each crossbar. You may need to use substitution or elimination methods to find expressions for the unknown masses.
5. Check your solution by substituting the values back into the original torque balance equations to ensure that they indeed sum to zero, confirming that the mobile will remain in equilibrium.

Key Concepts

Equilibrium

Equilibrium in physics refers to a state where the net force and net torque acting on an object are both zero. This means that the object is either at rest or moving with a constant velocity. In the context of the mobile, it implies that the torques produced by the weights of the objects must balance out to maintain stability.

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). In this scenario, each mass contributes to the torque about the pivot point of the mobile, and the sum of these torques must equal zero for the system to be in equilibrium.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms, while weight is the force exerted by gravity on that mass. In this problem, the weights of objects A, C, and D can be calculated using the formula weight = mass × gravitational acceleration (approximately 9.81 m/s²), which is essential for determining the torques acting on the mobile.