Will a sprinter's speed keep increasing all the time?

[yasar1967]

when a sprinter starts running he applies force to overcome fraction and air drag. is his speed keeps going up as F=ma governs to? if he's stamina was enough to fuel him for hours will his speed will keep going up and up even though he applies a constant force until the air drag force becomes so big that his muscles' force merely counteracts the fraction plus drag and drops to zero thus reaching constant speed?
What if hypothetically he runs in space on a surface which an artificial fraction made?
I'm aware of the limit due to reaching speed of light and mass increase. I'm not going that far.

 

[Nabeshin]

Air friction roughly scales with the square of the moving object's speed, so a doubling of the runner's speed quadruples the amount of work he needs to put into maintain this speed. I'm not sure if this is the limit, though, as I don't know much about running. However I am more inclined to believe that actual sprinters are more limited by how fast they can move their legs, since the legs have quite a bit of inertia on their own.

 

[hotvette]

I'm of the opinion that there is an asymptotic limit, but the tail could be very long. In addition to more specialized physical training and medical advances, environmental factors will increamentally help (i.e. advances in footgear, running surfaces, and clothing).

 

[russ_watters]

Air friction roughly scales with the square of the moving object's speed, so a doubling of the runner's speed quadruples the amount of work he needs to put into maintain this speed.

But in addition, work (power, actually), is a linear function of speed even if force is held constant, so actually, the power the runner has to expend is a cube function of speed. Doubling the speed means 8x the power. Four times the force times twice the speed.

I'm not sure if this is the limit, though, as I don't know much about running. However I am more inclined to believe that actual sprinters are more limited by how fast they can move their legs, since the legs have quite a bit of inertia on their own.

Agreed.

 

[PJC01]

I can say that a sprinter's speed will not continue to increase all the time. While the formula F=ma does govern their acceleration, there are other factors at play that will eventually limit their speed.

Firstly, as the sprinter continues to run, their muscles will fatigue and their force production will decrease. This means that even if their stamina is enough to fuel them for hours, their speed will eventually plateau and not continue to increase.

Additionally, air drag and friction will also play a role in limiting the sprinter's speed. As they run faster and faster, the air drag force will become stronger and eventually balance out the force applied by the sprinter, resulting in a constant speed. The same applies for friction on the ground - as the sprinter runs faster, the friction force will also increase, eventually balancing out the applied force and resulting in a constant speed.

In a hypothetical scenario where the sprinter is running in space on a surface with artificial friction, the same principles would apply. The only difference would be that there would be no air drag force, so the limiting factor would be the friction force on the surface.

It's also important to note that the limit of reaching the speed of light and the increase in mass are not just hypothetical concepts. These are fundamental principles of physics and cannot be ignored.

In conclusion, while a sprinter's speed may continue to increase for a short period of time, it will eventually reach a plateau due to factors such as muscle fatigue, air drag, and friction.