How does air resistance affect terminal velocity for a diver?

[Janiceleong26]

Homework Statement

Homework Equations

F=ma

The Attempt at a Solution

As the diver's velocity increases, then force F due to air resistance would increase, so D is out. And C is out too, as air resistance would be equal to its weight at terminal velocity. The answer is B, but how do we know if the air resistance increases non linearly or linearly?

 

[haruspex]

You are right that it is not easy to show that the resistance does not increase linearly, at least to start with. But is it reasonable that it should suddenly stop increasing at terminal velocity? Indeed, would you expect terminal velocity ever to be actually reached?

Edit: it would be easy to see that it does not start linear if you were told to assume drag is proportional to square of speed, but you are not given that.

 

[dean barry]

not as straightforward as I first thought, try googling "equations for a falling body"
choose an arbitrary Cd value for a free faller (say 0.24)
Set up an excel sheet to create a data table of
time (s) : velocity (m/s) : resistance force (N)
(use elapsed time as the base, say every 1 second)
(resistance force in N = velocity^2 * Cd)
use the time : resistance force results to create a graph
Have fun

 

[Janiceleong26]

You are right that it is not easy to show that the resistance does not increase linearly, at least to start with. But is it reasonable that it should suddenly stop increasing at terminal velocity? Indeed, would you expect terminal velocity ever to be actually reached?

Edit: it would be easy to see that it does not start linear if you were told to assume drag is proportional to square of speed, but you are not given that.

Erm I guess in reality, at terminal velocity, air resistance still increases but in a very very small amount?
I found this explanation in a website:

Thanks for your time

 

[Janiceleong26]

not as straightforward as I first thought, try googling "equations for a falling body"
choose an arbitrary Cd value for a free faller (say 0.24)
Set up an excel sheet to create a data table of
time (s) : velocity (m/s) : resistance force (N)
(use elapsed time as the base, say every 1 second)
(resistance force in N = velocity^2 * Cd)
use the time : resistance force results to create a graph
Have fun

Ok thx

 

[haruspex]

Erm I guess in reality, at terminal velocity, air resistance still increases but in a very very small amount?
I found this explanation in a website:
View attachment 91153
Thanks for your time

Well, no. The point is that the theoretical terminal velocity is a limit, so in theory is never actually reached. Consider a time at which the speed is just 0.01 m/s less than terminal velocity. The air resistance almost equals the weight, so the acceleration is very low, so resistance increases very slowly. On this basis I would reject A because it shows the force increasing linear,y with time, then suddenly levelling out.

 

[Janiceleong26]

Well, no. The point is that the theoretical terminal velocity is a limit, so in theory is never actually reached. Consider a time at which the speed is just 0.01 m/s less than terminal velocity. The air resistance almost equals the weight, so the acceleration is very low, so resistance increases very slowly. On this basis I would reject A because it shows the force increasing linear,y with time, then suddenly levelling out.

Oh ok thanks