(a) When a ball bearing falls through glycerin, several forces are acting on it:
Gravitational force (Weight): The ball bearing experiences a downward force due to gravity, which pulls it towards the center of the Earth. This force is responsible for the ball bearing's initial acceleration.
Buoyant force: The ball bearing also experiences an upward buoyant force due to its displacement of the glycerin. The buoyant force opposes the gravitational force and reduces the net force acting on the ball bearing.
Viscous drag force: As the ball bearing moves through the glycerin, it experiences a resistance force called viscous drag. This force is due to the interaction between the ball bearing and the glycerin molecules. The viscous drag force opposes the motion of the ball bearing and increases as its velocity increases.
Applied force (if any): If an external force is applied to the ball bearing, such as pushing or pulling it, an additional force may act on it. However, if we consider a freely falling ball bearing without any external force, this force can be ignored.
(b) The relationship between these forces can be described as follows:
At the initial stage, when the ball bearing starts falling through the glycerin, the gravitational force is greater than the viscous drag force and buoyant force. As a result, the net force is downward, and the ball bearing accelerates.
As the ball bearing gains speed, the viscous drag force increases due to its velocity-dependent nature. Eventually, the viscous drag force becomes equal to the gravitational force, resulting in a balanced net force.
At this point, the ball bearing reaches its terminal velocity, where the viscous drag force equals the gravitational force. The ball bearing continues to fall, but its speed remains constant as the forces acting on it are balanced.
Therefore, at terminal velocity, the gravitational force, buoyant force, and viscous drag force are in equilibrium, with the viscous drag force balancing the other two forces.