Fluid Friction Question: Calculating Projectile Velocities with Air Resistance

In summary, the conversation discusses comparing velocities of three projectiles subject to air resistance, with specific initial velocities, mass, cross sectional area, and drag coefficient. The drag equation, Newton's second law, and differentiation are suggested as potential methods to find the velocity after 5 meters for one of the projectiles. Additionally, using the equation v = d/dt, a differential equation for x can be found to determine the time at which the projectile reaches 5 meters.
  • #1
Dragon M.
3
0

Homework Statement



I'm trying to compare the velocities at 5 meters of three projectiles subject to air resistance: the first with an initial velocity of 121.632 m/s, the second with an initial velocity of 136.8m/s, and the third at 182.442 m/s.

All three projectiles have a mass of 2.0x10^-4 kg (m), a cross sectional area of 2.81x10^-5 m^2 (A), and drag coefficient of .47 (Cd). Density of air is assumed to be 1.204 kg/m^3.

Homework Equations



The equation I have been primarily been using is the drag equation Fa = 0.5Dv^2CdA

My initial plan was to use F = ma and Vf^2 = Vi^2 + 2a[itex]\Delta[/itex]x. However, I realized after doing these calculations that Fa changes with respect to velocity.

The Attempt at a Solution


This is my attempt to the solution of finding the velocity after 5 meters for 121.632 m/s.

Fa = -(0.5)(1.204)(121.632 m/s)^2(.47)(2.81E-5) = -1.2E-1

Which I then realized that only applied initially at launch.

So I tried taking the derivative with respect to time.

dFa = (.47)(2.81E-5)(dv/dt)

I am fairly stuck at the moment. Where do I go from now? If there is not enough information, what information do I need and what hints would you give to experimentally gain this information?
 
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  • #2
Here is my suggestion.

Using the drag equation, Newton's second law and the fact that [itex]a = \frac{d v}{d t}[/itex] (where [itex]a[/itex] is the acceleration) you can find a differential equation for [itex]v[/itex]. Solving that, you can find [itex]v[/itex] at any time [itex]t[/itex]. Then, using the fact that [itex]v = \frac{d x}{d t}[/itex], you can find another differential equation for [itex]x[/itex]. Solving this, you can find the time at [itex]x = 5m[/itex]. Then you can plug in that time to the equation for [itex]v[/itex].

Let me know if it works.
 

Related to Fluid Friction Question: Calculating Projectile Velocities with Air Resistance

1. What is fluid friction?

Fluid friction, also known as drag, is the resistance force that opposes the motion of an object through a fluid (such as air or water).

2. What factors affect fluid friction?

The main factors that affect fluid friction are the speed of the object, the density of the fluid, and the shape and surface area of the object.

3. How is fluid friction calculated?

Fluid friction can be calculated using the formula Fd = ½ρAv², where Fd is the drag force, ρ is the density of the fluid, A is the cross-sectional area of the object, and v is the velocity of the object.

4. How does fluid friction impact the motion of an object?

Fluid friction can slow down the motion of an object, as it requires energy to overcome the resistance force. This can also lead to changes in the direction of the object's motion.

5. How can fluid friction be reduced?

Fluid friction can be reduced by decreasing the speed of the object, using a more streamlined shape, and reducing the surface roughness of the object. Additionally, using lubricants or adding a coating to the surface of the object can also help reduce fluid friction.

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