Final answer:
The forces acting on a small object against the side of a frictionless semicircular bowl are gravitational and normal forces. The object is in equilibrium when these forces balance each other out, with gravity being countered by the normal force. A stable equilibrium allows disturbances to return the object to its equilibrium position, unlike an unstable equilibrium where disturbances lead to the object moving away.
Step-by-step explanation:
The question involves describing the forces acting on an object against the vertical side of a frictionless semicircular bowl and discussing the conditions when the object is in equilibrium. When a small object A is held against the side of such a bowl, two main forces act upon it: the gravitational force, which pulls the object downwards, and the normal force, which is exerted by the surface of the bowl perpendicularly, counteracting gravity to some extent.
In equilibrium, the sum of the forces acting on the object must be zero. In the vertical direction, this means that the normal force must equal the component of gravitational force acting perpendicular to the bowl's surface, so the object does not move vertically. The object remains in stable equilibrium as any slight disturbance will result in a restoring force, which guides it back to the equilibrium position. An example is a marble inside a bowl that, when disturbed, will naturally roll back to the center, the lowest potential energy point, which is the stable equilibrium point.
If the bowl was upside down, object A could theoretically balance at the top. However, since any slight disturbance would cause the object to roll off, this represents an unstable equilibrium. The reason is that any force applied would be directed away from the equilibrium point. A force applied to an object on a frictionless table and attached to a pivot would cause the object to accelerate around it, which is similar to what happens when a force disturbs the object at the top of an inverted bowl.