A solid sphere falls with a terminal velocity of 20m/s in air. If it allowed fall in vaccum

When a solid sphere falls through air, it eventually reaches a point where the force of gravity pulling it down is balanced by the drag force acting against it. This is known as terminal velocity, which in your case is 20 m/s. However, if the same sphere were to fall in a vacuum, the situation changes significantly.

The Concept of Terminal Velocity

Terminal velocity occurs when the net force acting on an object is zero. In air, the forces at play are:

• Gravitational Force: This is the weight of the sphere, calculated as the mass of the sphere multiplied by the acceleration due to gravity (approximately 9.81 m/s²).
• Drag Force: This force opposes the motion of the sphere and depends on factors like the sphere's speed, cross-sectional area, and the density of the fluid (in this case, air).

What Happens in a Vacuum?

In a vacuum, there is no air or any other fluid to create drag. Therefore, the only force acting on the sphere is gravity. As a result, the sphere will not experience terminal velocity in a vacuum. Instead, it will continue to accelerate downwards at a constant rate of 9.81 m/s² until it hits the ground.

Comparative Analysis

To illustrate this further, let’s consider two scenarios:

• Falling in Air: The sphere accelerates until it reaches 20 m/s, where the drag force equals the gravitational force, resulting in no further acceleration.
• Falling in Vacuum: The sphere starts from rest and continues to accelerate at 9.81 m/s², meaning it will fall faster than 20 m/s throughout its descent.

Real-World Implications

This difference has practical implications. For example, in space missions, objects in free fall experience weightlessness because they are in a vacuum, and they do not reach a terminal velocity like they would on Earth. This is why astronauts can float inside the International Space Station.

Final Thoughts

In summary, while a solid sphere falling through air reaches a terminal velocity of 20 m/s due to the balance of forces, in a vacuum, it will continue to accelerate under the influence of gravity alone, falling faster than it would in air. This fundamental difference highlights the significant role that air resistance plays in motion through fluids.