how does the upthrust during the free fall become 0 on account of the valve of (g) during free fall becoming -g for upthrust

To understand how upthrust, or buoyant force, behaves during free fall, we need to delve into the concepts of gravity and buoyancy. When an object is in free fall, it experiences a unique set of conditions that affect the forces acting on it.

The Basics of Free Fall

Free fall occurs when an object is falling under the influence of gravity alone, without any air resistance or other forces acting on it. In this state, the only force acting on the object is its weight, which is the product of its mass and the acceleration due to gravity (g). On Earth, this acceleration is approximately 9.81 m/s², directed downwards.

Understanding Upthrust

Upthrust, also known as buoyant force, is the upward force exerted by a fluid on an object submerged in it. This force arises due to pressure differences in the fluid; the pressure at the bottom of the object is greater than at the top, resulting in an upward force. The magnitude of this force can be calculated using Archimedes' principle, which states that the upthrust is equal to the weight of the fluid displaced by the object.

What Happens During Free Fall?

When an object is in free fall, it accelerates downwards at the rate of g. If this object is submerged in a fluid, it experiences both its weight and the buoyant force. However, during free fall, the entire system (the object and the fluid) accelerates downwards at the same rate. This leads to a critical observation:

• The object feels weightless because it is falling at the same rate as the fluid around it.
• The buoyant force, which depends on the pressure difference in the fluid, effectively becomes zero because there is no pressure difference acting on the object.

Why Does Upthrust Become Zero?

In a free-falling scenario, both the object and the fluid are accelerating downwards at -g. Since the object is not experiencing any relative motion with respect to the fluid, the pressure difference that creates the upthrust is nullified. Essentially, the downward acceleration of the object cancels out the upward pressure exerted by the fluid, resulting in:

Upthrust = Weight of the fluid displaced - Weight of the object

Since both the weight of the object and the weight of the fluid displaced are effectively experiencing the same acceleration, the net force acting on the object becomes zero. Thus, the upthrust can be considered as zero during free fall.

Illustrative Example

Imagine a small balloon filled with air, submerged in water. When you let go of the balloon, it starts to rise due to the upthrust. However, if you were to drop the entire system (the balloon and the water) from a height, both would fall together. In this case, the balloon would not rise because the buoyant force acting on it is countered by the downward acceleration of the entire system. Hence, the balloon feels no upthrust, and it remains in a state of free fall.

Final Thoughts

In summary, during free fall, the upthrust becomes zero because both the object and the fluid are accelerating downwards at the same rate, eliminating any pressure difference that would normally create buoyancy. This fascinating interplay of forces highlights the unique conditions present in free fall and helps us understand the principles of physics in a more profound way.