# Reason for motion after terminal velocity

• MD007
In summary: The work done is the force of gravity times the displacement. Since the object isn't accelerating, all of the work goes into moving the air in the path of the object.

#### MD007

Hi,

Let some object hang by a string. So no motion since weight was counter balanced no net force. Now string is cut. Object is falling under gravity and experiences air resistance. Terminal velocity is reached when weight is equal to the air resistance. So no net force and no net acceleration after terminal velocity. But why does the object continue to fall if there is no net force acting on it, why doesn't it just hang in mid air dead stopped ?

thanks
MD

MD007 said:
Terminal velocity is reached when weight is equal to the air resistance.
"Terminal" does not mean "end of path." The object no longer accelerates when there is no net force acting on it; NOR does it decelerate.

In order for the ball to slow down to a stop from terminal velocity, there would have to be an acceleration, or a deceleration as the case may be. For this acceleration or deceleration to occur, there would have to be a non-zero net force on the ball. Terminal velocity is the point at which the force of air resistance is exactly equal to the force of gravity. For it to slow down or stop, the force of air resistance would have to be much greater than the force of gravity. When the ball is at terminal velocity, there may not be a net force on it, but there is certainly still net momentum.

Doesn't the force of gravity increase as mass approaches, terminal velocity should therefore increase slightly shouldn't it? Does the pressure gradient cancel it?

And air density increases, decreasing it, and the problem is asked at a level that assumes both are constant, just to introduce the concept of "balanced" forces.

Just clarifying, I immediately thought from the title "motion after terminal velocity" would mean change as in decrease in thicker air but then I thought about like you stated HS physics starts out with the basic truth that it accelerates quickly when the string is cut steadily decreasing acceleration until terminal velocity is achieved countering constant air resistance.

MD007 said:
But why does the object continue to fall if there is no net force acting on it, why doesn't it just hang in mid air dead stopped?
This isn't Road Runner physics you're dealing with here.

davenn
the ball continues at the top speed it has reached based on the amount of air resistance its encountered. the only way to float the ball is if the air resistance was as great as the gravity force in which case the ball would never have accelerated at all and simply floated there after the string was cut. it could be said to have attained terminal velocity without ever moving.

Thanks all its been rewarding to read the responses. I got what i was looking for. Heres a follow up but its ok if your busy not that keenly pursuing this. Thanks again.

If its moving bcoz of inertia and if it falls distance x at terminal velocity then what's the work done ?

MD007 said:
If its moving bcoz of inertia and if it falls distance x at terminal velocity then what's the work done ?

The work done is the force of gravity times the displacement. Since the object isn't accelerating, all of the work goes into moving the air in the path of the object.

MD007 said:
If its moving bcoz of inertia

Just a reminder, PF rules prohibit "text speak" like "bcoz". Please use correct grammar to the best of your ability.

MD007 said:
Hi,

Let some object hang by a string. So no motion since weight was counter balanced no net force. Now string is cut. Object is falling under gravity and experiences air resistance. Terminal velocity is reached when weight is equal to the air resistance. So no net force and no net acceleration after terminal velocity. But why does the object continue to fall if there is no net force acting on it, why doesn't it just hang in mid air dead stopped ?

thanks
MD
Because equilibrium implies the acceleration is zero which must mean the velocity of the object experiencing zero net acceleration is either zero or some other constant unchanging number. However, zero is the state of rest, but that's not the only possibility. See? Ya know, if you were looking for a different answer and I don't exactly understand what you're asking, then I'm sorry about that. In that case, I'll be more careful next time.

MD007 said:
Thanks all its been rewarding to read the responses. I got what i was looking for. Heres a follow up but its ok if your busy not that keenly pursuing this. Thanks again.

If its moving bcoz of inertia and if it falls distance x at terminal velocity then whats the work done ?

The energy converted to heat / turbulence and, initially to KE will be mgh. Basic rules always apply in this sort of situation. You just have to go along with them and believe the result.

## 1. What is terminal velocity and why does it occur?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. This occurs because the force of gravity pulling the object down is counteracted by the force of air resistance pushing against the object.

## 2. Why does an object continue to move after reaching terminal velocity?

Even after reaching terminal velocity, an object will continue to move because the forces of gravity and air resistance are still acting upon it. The object will maintain a constant speed, but will not stop moving until another force acts upon it.

## 3. Is there a limit to how fast an object can move after terminal velocity?

Yes, there is a limit to how fast an object can move after reaching terminal velocity. This limit is determined by the properties of the fluid, such as its density and viscosity, as well as the shape and mass of the object.

## 4. Can an object ever exceed terminal velocity?

No, an object cannot exceed its terminal velocity. This is because at terminal velocity, the forces acting on the object are balanced and there is no net force to accelerate the object further.

## 5. How does the reason for motion differ between objects with different shapes and masses?

The reason for motion after terminal velocity can differ between objects with different shapes and masses. This is because the forces of gravity and air resistance act differently on different objects, causing them to reach different terminal velocities and experience different motions after reaching it.