Newton's Laws: Elevator Acceleration and Cork Movement

In summary, the cork will move towards the top of the water as the elevator begins accelerating upwards with acceleration a due to an increase in the buoyant force on the cork. This is because the effective gravitational field becomes g+a, causing the spring to stretch more, thus moving the cork towards the top of the water. This can be explained by considering the forces on a small volume of water in the bucket, and how they are affected by the acceleration of the elevator. Therefore, the correct answer is option B.
  • #1
Grapz
30
0
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
 
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  • #2
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.
 
  • #3
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.)
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the relationship between the forces acting on an object and its motion. They were first formulated by Sir Isaac Newton in his book "Philosophiæ Naturalis Principia Mathematica" in 1687.

2. What is the first law of motion?

The first law of motion, also known as the law of inertia, states that an object will remain at rest or in a state of uniform motion unless acted upon by an external force. This means that an object will not change its velocity unless a force is applied to it.

3. What is the second law of motion?

The second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In other words, the greater the force applied to an object, the greater its acceleration will be. This law is often summarized by the equation F=ma, where F is force, m is mass, and a is acceleration.

4. What is the third law of motion?

The third law of motion, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object exerts an equal and opposite force back. This is why we feel a recoil when shooting a gun or experience a push back when we push against a wall.

5. How do Newton's Laws of Motion apply to everyday life?

Newton's Laws of Motion can be observed in many everyday situations. For example, the first law can explain why objects on a table remain at rest unless pushed or why a ball continues to roll until it encounters friction. The second law can explain why it takes more force to push a heavy object than a lighter one. The third law can be seen in activities like walking, where our feet push against the ground, and the ground pushes back to propel us forward.

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