Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

TomLikesPhysics

  • 2 years ago

I have a parabola slide and I am looking for a function of the downhill force which only depends on the x and/or y coordinate. I came up with a function but I am not sure if this is correct. You can see everything on the attached picture.

  • This Question is Closed
  1. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Here is what I did so far.

    1 Attachment
  2. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I assume that it is safe to assume that the parabola is y=x^2, with the tip at (0,0) dy/dx=2x |dw:1351340058220:dw|\[\tan^{-1}(\frac{dy}{dx})=\theta\] \[\theta=\tan^{-1}(2x)\] \[F=-mgsin(\theta)\]

  3. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So you seem in the right area

  4. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hmmm... actually I do not know that. It is not specified so it might be better if I write: y=ax^2.

  5. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then \[\theta=\arctan(a2x)\]

  6. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, it just looks kind of ugly if we plug that into the equation for the force. F=-mgsin(arctan(2ax)

  7. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is this really the finaly answer? Can´t we do something to make it simpler or look better? Is there perhaps a different way to determine the force in terms of x and/or y?

  8. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351340440158:dw|No, its not

  9. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351340462854:dw|

  10. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    F=-mgsqrt(1+(2ax)^2)

  11. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah... Pythagoras... I see...Now it looks better. So this is the best we can do?

  12. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Simplify sqrt(1+(2ax)^2) maybe You could try to x/y decompose the force, but that's probably uglier

  13. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Although I think it's unsimplifiable

  14. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. A big thank you to you, henpen. I really appreciate the help. Thx a lot.

  15. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiItc3FydCgxKyh4KV4yKSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi04IiwiNSIsIi02LjQyIiwiMS41OCJdfV0- It's probably correct- the force graph looks about right

  16. TomLikesPhysics
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The Force stands always normal on the slide, right? If so, it does not point at some special point all the time?

  17. henpen
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351349861448:dw| The normal (restrictive) force is always at a normal to the curve

  18. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.