**Removing Mass from a Descending Balloon to Make it Move Upwards**

To make a descending balloon start moving upwards with a specific acceleration, we need to remove a certain amount of mass from it. Let's understand the process and calculations involved in achieving this.

**1. Understanding the Forces Acting on the Balloon:**

When a balloon is descending, various forces act upon it. The two main forces to consider are the gravitational force (mg) pulling the balloon downwards and the buoyant force (ρVg) pushing it upwards. Here, ρ represents the density of the surrounding air, V is the volume of the balloon, and g is the acceleration due to gravity.

**2. Net Force Acting on the Descending Balloon:**

The net force acting on the descending balloon is the difference between the gravitational force and the buoyant force:

Net Force = mg - ρVg

As the balloon is descending, the net force is in the downward direction, and thus, the acceleration (a) experienced by the balloon is given by:

mg - ρVg = ma

Simplifying the equation, we have:

m(g - ρV) = ma

**3. Calculating the Mass to be Removed:**

To calculate the mass that needs to be removed from the balloon to make it move upwards with the same acceleration, we need to find the new mass (m') of the balloon.

Since the acceleration (a) remains unchanged, the net force in the upward direction (when the balloon moves upwards) will be:

Net Force = ρVg - mg

Using Newton's second law, we have:

ρVg - mg = m'a

Simplifying the equation, we find:

m' = (ρVg - mg) / a

Therefore, the mass that needs to be removed from the balloon is given by:

Mass to be Removed = m - m'

**4. Final Considerations:**

It's important to note that the buoyant force depends on the volume of the balloon, which in turn depends on the mass of the balloon. So, as mass is removed from the balloon, its volume and buoyant force will also change. Therefore, after removing the required mass, it is necessary to recalculate the buoyant force and ensure that it is greater than the gravitational force for the balloon to move upwards with the desired acceleration.

By following these steps and calculations, it is possible to determine the amount of mass that should be removed from a descending balloon to make it move upwards with a specified acceleration.