Projectile motion with friction?

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SUMMARY

The discussion centers on determining the optimal launch angle for projectile motion considering air resistance. Participants agree that the angle for maximum range is less than 45 degrees due to drag forces, which can be either linear or quadratic in relation to velocity. The equations of motion are derived using calculus, specifically second-order linear ordinary differential equations (ODEs). The complexity of the problem necessitates numerical methods for solutions, as no simple closed-form expressions exist for the range under these conditions.

PREREQUISITES
  • Understanding of basic physics principles related to projectile motion
  • Familiarity with calculus, specifically ordinary differential equations (ODEs)
  • Knowledge of drag forces, including linear and quadratic models
  • Ability to apply numerical methods for solving complex equations
NEXT STEPS
  • Study the derivation of second-order linear ordinary differential equations (ODEs)
  • Learn about the effects of air resistance on projectile motion
  • Explore numerical methods for solving differential equations
  • Investigate the differences between linear and quadratic drag forces
USEFUL FOR

Students studying physics, particularly those interested in mechanics and calculus, as well as educators looking to enhance their understanding of projectile motion with air resistance.

  • #31
Loup.

Here is a fairly good animation you can run.

"[URL
http://www.compadre.org/PSRC/items/detail.cfm?ID=7196

Click on Modular Approach to Physics: Projectile Motion: One Ball.

It will give you a good intuitive understanding of the problem.

I recommend making the grid, trace, and velocity visible with the buttons. Drag the end of the velocity arrow around keeping it at 100 m/s. Change the drag coefficient to 0.01[corrected] or the air drag will not be significant. In this applet the drag is proportional to v squared, as it should be, and if their language used in the applet is correct.
 
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  • #32
!
I cannot open any of the animation!
:(
 
  • #33
Phrak, good find! But I think you meant 0.01 for the drag coef.

You can also enter numbers for the velocity and angle, but you must hit the "Enter" key for them to register.
 
  • #34
loup said:
!
I cannot open any of the animation!
:(

You may need to install java, if your computer does not already have it.
http://www.java.com/en/download/manual.jsp
 
Last edited by a moderator:
  • #35
Redbelly98 said:
Phrak, good find! But I think you meant 0.01 for the drag coef.

You can also enter numbers for the velocity and angle, but you must hit the "Enter" key for them to register.

Thanks on all points, Redbelly. I was much to critical of the software--it's excellent. The use of the energy key makes all the difference.
 

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