Package sliding down a round surface

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SUMMARY

The discussion focuses on calculating the maximum angle (φ_max) at which a 1 kg package begins to veer off a smooth circular track with a radius (R) of 0.5 m, given an initial speed of 1 m/s. The participants derive the necessary equations using centripetal force and gravitational components, ultimately determining that φ_max is 42.7 degrees. Key formulas discussed include centripetal acceleration (F_centripetal = m * v^2 / R) and the relationship between gravitational force components and centripetal force.

PREREQUISITES
  • Understanding of centripetal force and acceleration
  • Knowledge of gravitational force components
  • Familiarity with trigonometric functions and their applications in physics
  • Ability to apply conservation of energy principles
NEXT STEPS
  • Study the derivation of centripetal force equations in circular motion
  • Learn about energy conservation in mechanical systems
  • Explore the application of trigonometry in physics problems
  • Investigate the effects of varying mass and speed on circular motion dynamics
USEFUL FOR

Students in physics, mechanical engineers, and anyone interested in understanding the dynamics of objects in circular motion.

  • #31
Thanks. Check if 1/2+0.5*9.81=5.905:devil:

ehild
 
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  • #32
Done! :smile:
(And edited my full solution to eliminate the calculation errors.)
 
  • #33
You guys are incredible!

Test's over and I did very well. We're not going to study mechanics next semester. :smile: So, I just want to say big thanks^^ Next year I might be the tutor for the 1st year mechanics students, so my adventures in the realms of basic mechanics might (or very probably) not be over yet. I still have a few holes to fill, but I think I'll worry about closing them later^^

This problem is definitely too big and too complex! Reminds me of the crashing airplanes, even though I eventually solved it. There have been a few questions throughout the year in our basic mechanics course considered controversially too difficult. This might as well be one of them!
 
  • #34
Whaaaaaaat! But, but, but, ... you can't!
You can't stop doing mechanical problems! Sniff! :cry:
And btw, the planes didn't crash (WHOAA!), so there's still more stuff to see, to learn...
 
  • #35
They did crash, because the distance is so small! And, frankly, I'm already having a mechanical itch, so I'll never really stop doing mechanics, it's just that I'll be doing it from now on at a much slower pace! :smile:

So now I can be relaxed and go over this problem for instance and there was a 3D statics problem at the test that I'm still looking at how to solve it. So, this is for the best, since I can now invest more time and effort in a single problem, rather than shooting all over the place to get as much as I can. I think you'll like me better that way :smile:
 
  • #36
I have no complaints about how much time and effort you invest in all of your problems!
And I like you any which way I can, as long as we're interacting. :shy:
Of course it helps if you make a drawing every now and then!
(And if you don't secretly remove a cord from a problem! :wink:)
 

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