Velocity dependant drag

In summary: Then instant velocity is a function of time and k and m.In summary, when an object is dragged through an unknown fluid, it experiences a force opposite to its initial velocity that is equal to -k(v^1/2). Using the equations Fn=ma and Ff=-k(v^1/2), the instantaneous velocity of the object can be modeled by the equation v=(-kt/2m)^2 + 2(-kt/2m)D + D^2, where D is a constant determined by initial conditions and the object's mass and k are constants related to the fluid and the object's motion.
  • #1
S[e^x]=f(u)^n
23
0

Homework Statement


An object dragged through an unknown fluid experiences a force opposite to that of its initial velocity (Vi) that is equal to -k(v^1/2). find the equation that models its instantaneous velocity

Fn = Force Net
Ff = Frictional force
Vi = Initial Velocity
V = instantaneous velocity

Homework Equations


Fn=ma
Ff=-k(v^1/2)


The Attempt at a Solution



Fn=Ff
ma=-k(v^1/2)
dv/dt=(-k/m)(v^1/2)
S[dv/(v^1/2)]=(-k/m)S[dt]
2(v^1/2)=-kt/m
v=(-kt/2m)^2 + Vi

which can't be right because that would mean velocity increased as time moves positively...

i'm lost. help lol
v=
 
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  • #2
Does the object have mass m? Is another force being applied to the object?

If the force is subject only to drag, then it will deceleration in proportion to kv1/2 according to the problem as stated.

If the mass falls under gravity then the mass will decelerate or even accelerate to a constant velocity where the drag force = the force of gravity.

a = dv(t)/dt = F(t)/m, where F(t) = applied force - drag force,

and the initial condition is v(t=0) = vi/.
 
  • #3
there is no mass stated and the object is traveling horizontally and not subject to gravity.

i guess I'm having trouble deriving a velocity equation more than i am having trouble understanding the situation. I'm not even sure if the way i tried it first is the right way.

all i know for sure is that the only force acting on the point is -kv^(1/2)

could u perhaps help me find an equation for its instantaneous velocity with respect to time?
 
  • #4
S[e^x]=f(u)^n;1461783 said:

Homework Statement


An object dragged through an unknown fluid experiences a force opposite to that of its initial velocity (Vi) that is equal to -k(v^1/2). find the equation that models its instantaneous velocity

Fn = Force Net
Ff = Frictional force
Vi = Initial Velocity
V = instantaneous velocity

Homework Equations


Fn=ma
Ff=-k(v^1/2)


The Attempt at a Solution



Fn=Ff
ma=-k(v^1/2)
dv/dt=(-k/m)(v^1/2)
S[dv/(v^1/2)]=(-k/m)S[dt]
2(v^1/2)=-kt/m

you need to add a constant here:

2(v^1/2)=-kt/m + C

then

v^1/2=-kt/2m + D


v=(-kt/2m)^2 + 2(-kt/2m)D + D^2

So know solve for D using initial conditions.
 

What is velocity dependant drag?

Velocity dependant drag is a type of drag that occurs when an object moves through a fluid, such as air or water. It is caused by the resistance of the fluid against the object's motion.

How is velocity dependant drag different from other types of drag?

Velocity dependant drag is different from other types of drag, such as shape dependant drag and skin friction drag, because it is directly proportional to the object's velocity. This means that as the velocity of the object increases, so does the magnitude of the drag force.

What factors affect the amount of velocity dependant drag on an object?

The amount of velocity dependant drag on an object is affected by several factors, including the object's shape, the fluid's density and viscosity, and the object's velocity. Additionally, the roughness of the object's surface and the presence of turbulence in the fluid can also impact the amount of drag.

How can velocity dependant drag be minimized?

Velocity dependant drag can be minimized by reducing the object's velocity, streamlining its shape to reduce its surface area, and making the surface as smooth as possible. Additionally, using materials with lower densities and viscosities can also help reduce the amount of drag.

What are some real-world applications of understanding velocity dependant drag?

Understanding velocity dependant drag is important in various fields, such as aerodynamics, hydrodynamics, and sports. It is also crucial in designing vehicles and structures that need to move efficiently through air or water, such as airplanes, ships, and cars. Additionally, it is also relevant in understanding the behavior of particles in fluids, which is useful in fields such as environmental science and industrial processes.

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