Which of the following scenarios describes an object being acted on by a conservative force?

a woman hikes up a mountain to a point 20 feet above ground.
a dishwasher was pulled up to a window by a rope, using a pulley system.
a feather falls from one end of a tube to the other inside a vacuum.
a puck glides across and slowly comes to a stop on an ice rink.

Option: A feather falls from one end of a tube to the other inside a vacuum.

Explanation:

To answer the question we need to first understand what is meant by Conservative Force.

In principle, Conservative forces are basically forces that are not affected by outside parameters (such as friction, air resistance etc). If the present force is strictly based on the initial and the final location of the object, with the inbetween path being irrelevant, the force will be conservative. A conservative force will be zero if we are looking at a closed path-system. We can also say that the system's energy loss will not be a function of the distance covered but is a function of displacement.

Looking at the available options, we can see that:

Option A: A woman hikes up a mountain to a point 20 feet above ground.

This is a Non Conservative force as this case does not depend just on displacement but also in  the path in between, i.e. hiking up the mountain there will be other forces that will affect the woman such as air resistance.

Option B: A dishwasher was pulled up to a window by a rope, using a pulley system.

This is a Non Conservative force as this case does not depend just on displacement but also in the inbetween path along with the forces present in a pulley system such as friction.

Option C: A feather falls from one end of a tube to the other inside a vacuum.

This is a Conservative force as here we are looking at a vacuum and its a closed system of no other forces present due to vacuum. However, we CAN'T say that ALL forces in a Vacuum Are Conservative because there are cases of dynamic steady state fields where the system is prone to other forces (i.e. open system).

Option D: A puck glides across and slowly comes to a stop on an ice rink.

This is a Non Conservative force as this case does not depend just on displacement but also the motion until it comes to a stop, which is possibly due to the friction between the ice rink and the puck.