Mechanics Problem using Polar Coordinates

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Homework Help Overview

The discussion revolves around a mechanics problem involving polar coordinates, specifically focusing on the forces acting on a bead on a surface and the equations of motion. Participants are attempting to analyze the problem using concepts such as centripetal force and acceleration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are sharing their attempts to apply equations like mv^2/r = mg and mr'' = mg, while expressing confusion about the next steps. Some are questioning the correctness of their second derivatives and the forces to consider for the second part of the problem.

Discussion Status

There is a mix of urgent requests for help and guidance on how to approach the problem. Some participants are encouraged to clarify their work and identify forces, while others express frustration over their lack of progress. The discussion reflects a collaborative effort to explore the problem without reaching a consensus on a solution.

Contextual Notes

Participants mention time constraints, with some indicating that the assignment is due imminently. There are references to forum rules against providing direct answers, which shapes the nature of the assistance being offered.

MathDestructor
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Homework Statement
I don't know how to take polar derivatives.
Relevant Equations
r = Rcos(theta) + Rsin(theta)
1580492747754.png


1580493310652.png

This is what I have so far, please need urgent help. I don't understand and know what to do.

For the first part, I got a really long answer, for the second part I am trying in terms of mv^2/r = mg, or mg = m*(answer to first), but I am getting nowhere. PLease help
 
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Please show your work. We don't give answers away but point out mistakes.
 
1580493253059.png
This is all I have, I don't know what to do after, I've been stuck for 2 days, and its due in half an hour.
 
MathDestructor said:
This is all I have, I don't know what to do after, I've been stuck for 2 days, and its due in half an hour.
As long as the bead stays on the surface ##\dot R## = 0. That should simplify things for you.
 
Is my second derivative right?
 
What forces should I use to try and solve the second part.
 
MathDestructor said:
What forces should I use to try and solve the second part.
Please show the revised velocity and acceleration in view of my comments in post #4. You cannot proceed to the second part unless you get the first part right. If you have to post pictures (a practice we discourage) at least make sure they are right side up.
 
1580493893133.png
 
I tried mv^2/r = mg and mr''= mg. None of them are working
 
  • #10
MathDestructor said:
I tried mv^2/r = mg and mr''= mg. None of them are working
You need to write a vector equation. How many different forces act on the bead when it is on the surface at angle φ? Write their vector sum in unit vector notation and set it equal to ##m\vec a## in unit vector notation. Your expressions for the velocity and acceleration are correct.
 
  • #11
kuruman said:
You need to write a vector equation. How many different forces act on the bead when it is on the surface at angle φ? Write their vector sum in unit vector notation and set it equal to ##m\vec a## in unit vector notation. Your expressions for the velocity and acceleration are correct.
I don't know what that means, or how to do that.
 
  • #12
I have 10 mins left, I would really appreciate it if you would help me in a hurry just this once. Please.
 
  • #13
MathDestructor said:
I have 10 mins left, I would really appreciate it if you would help me in a hurry just this once. Please.
Sorry, it is against forum rules. Do your best. Identify the forces that act on the bead, draw a free body diagram and use it to write each force in unit vector notation.
 
  • #14
I know this doesn't give you an answer, but, you can just google for Polar Coordinate Vector System Derivation.
I did that and it all finally made sense.
Some YouTube videos also helped.
It wasn't a part of my curriculum so far, but, learning it helped me understand so many things that, as a result, I have become near-invicible when it comes to inclined plane problems.
 

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