Newton's Laws: Elevator Acceleration and Cork Movement

[Grapz]

You have a bucket filled with water. A spring has been soldered to the bottom of the bucket, and a cork is attached to the other end of the spring. The cork is suspended motionless under the surface of the water. You are standing on a stationary elevator holding the bucket. The elevator then begins accelerating upwards with acceleration a. What does the cork do?


(A) Stays where it is relative to the bucket.
(B) Moves towards the top of the water
(C) Moves towards the bottom of the bucket.
(D) There is not enough information given to solve this problem

Answer is B however i do not know why can someone explain

 

[Doc Al]

What forces act on the cork and how are they are affected by the acceleration? Hint: It may help to consider the forces on a small volume of water in the bucket.

 

[Shooting Star]

If an elevator is accelerating in a direction with acceleration ‘a’, then in that frame an effective gravitational field of ‘-a’ can be considered to be there, on top of any real g-field.

Suppose the elevator is in free fall. Then there is zero gravity in that frame and so no buoyancy of the cork is there, and the spring remains un-stretched.

When the elevator is at rest, there is g acting downward, and the spring is stretched upward due to buoyancy of the cork.

By a continuity argument, there should be more buoyant force when the effective g is increased. So, when the g-field is increased to g+a due to upward acceleration ‘a’ of the elevator, the spring should be more stretched due to more buoyant force acting on the cork.

The mathematics is not too difficult.

(Note that the net force on a body heavier than water, which is immersed in water, actually increases.)