Just a question on terminal velocity

In summary, the terminal velocity is the same as constant velocity where the net force is 0 and therefore the acceleration is also 0.
  • #1
flyingpig
2,579
1

Homework Statement



It is a definition that the terminal velocity is the same as constant velocity where the net force is 0 and therefore the acceleration is also 0

Here is what I don't get, why must the terminal velocity must such that it is constant? I know that to be "terminal" it means it can no longer change it's velocity, but how come gravity will able to counteract it such that the sum of forces is 0? I mean what if air resistance is so strong that gravity can't counteract it? Wouldn't it mean the sum of forces is no longer 0 and the terminal velocity can never be reached or at that point, that is the terminal velocity?
 
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  • #2
hi flyingpig! :wink:
flyingpig said:
… what if air resistance is so strong that gravity can't counteract it? Wouldn't it mean the sum of forces is no longer 0 and the terminal velocity can never be reached or at that point, that is the terminal velocity?

air resistance depends on speed

if air resistance is very strong, that means that it is very much stronger than usual for each particular speed

so air resistance will balance gravity at a lower speed …

ie terminal velocity is lower :smile:

(oh, and terminal velocity is never quite reached anyway … the speed gets exponentially close to terminal velocity :wink:)
 
  • #3
tiny-tim said:
hi flyingpig! :wink:


air resistance depends on speed

if air resistance is very strong, that means that it is very much stronger than usual for each particular speed

so air resistance will balance gravity at a lower speed …

ie terminal velocity is lower :smile:

(oh, and terminal velocity is never quite reached anyway … the speed gets exponentially close to terminal velocity :wink:)

That is even more confusing now...

I just don't understand why or how gravity can balance out the terminal speed.
 
  • #4
when v = 0, air resistance (let's call it R(v)) is 0,

so using a = F/m, we have a = mg/m = g

when R(v) is larger, a = (g - R(v))/m < g;

eventually R(v) = g, and then a = 0, ie the speed is constant :smile:
 
  • #5




Terminal velocity is a concept that applies to objects falling through a fluid medium, such as air or water. It is the maximum velocity that an object can reach while falling, when the forces acting on it are balanced and the acceleration is zero. This occurs when the drag force of the fluid is equal to the gravitational force pulling the object downwards.

To answer your question, the terminal velocity must be constant because at this point, the forces acting on the object are in balance and there is no net force causing a change in velocity. This means that the object will continue to fall at a constant speed until it reaches the ground or encounters a change in the fluid medium.

In the scenario you mentioned, if the air resistance is so strong that it overcomes the gravitational force, then the object will not reach a terminal velocity. Instead, it will continue to accelerate downwards until it reaches the ground or encounters a change in the fluid medium. In this case, the sum of forces is no longer zero and the object is not at a state of terminal velocity.

It is important to note that the strength of air resistance depends on various factors such as the shape and size of the object, the density of the fluid, and the speed of the object. Therefore, the terminal velocity can vary for different objects falling through the same fluid medium.

In summary, terminal velocity is a state of constant velocity that an object reaches when the forces acting on it are balanced. It is not a predetermined value, but rather a result of the balance between the object's weight and the drag force of the fluid.
 

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when it is falling through a fluid, such as air or water. It occurs when the force of gravity is equal to the force of air resistance acting on the object.

2. How is terminal velocity calculated?

The formula for calculating terminal velocity is: vt = √(2mg/pAC), where vt is terminal velocity, m is the mass of the object, g is the acceleration due to gravity, p is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient.

3. What factors affect terminal velocity?

The factors that affect terminal velocity include the mass, size, and shape of the object, as well as the density and viscosity of the fluid it is falling through. The force of gravity and the air resistance also play a role in determining terminal velocity.

4. Can terminal velocity be exceeded?

In most cases, terminal velocity cannot be exceeded. However, in some extreme situations, such as when an object is falling through a very thin or non-existent fluid, it is possible for the object to continue accelerating past its terminal velocity.

5. How is terminal velocity important in real-world applications?

Terminal velocity is important in fields such as aeronautics, skydiving, and meteorology. It helps engineers design aircraft and parachutes that can safely reach the ground without exceeding their maximum speed. In meteorology, terminal velocity of raindrops and hailstones can help determine the strength of a storm. It is also important in understanding how objects fall and interact with different fluids.

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