Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

kgns

A uniform sphere of mass m and radius r is set free from the top edge of a semicircle halfpipe with radius R. If R > r, what is the time-dependent velocity equation v(t) for the sphere in terms of t, m, r, R and g ignoring any effects of friction? Could anybody help me derive the differential equations?

  • one year ago
  • one year ago

  • This Question is Open
  1. Mashy
    Best Response
    You've already chosen the best response.
    Medals 0

    i think you can use conservation of energy principle!!

    • one year ago
  2. kgns
    Best Response
    You've already chosen the best response.
    Medals 0

    I doubt \[mgh = \frac{ 1 }{ 2 }mv^2\] will get me something in terms of t

    • one year ago
  3. MuH4hA
    Best Response
    You've already chosen the best response.
    Medals 0

    No, this won't get you somewhere, because the potential gravitational energy will _not_ be "transformed" into kinetic energy to 100%. There will be rotational energy, too.. you have to take that into account..

    • one year ago
  4. Mashy
    Best Response
    You've already chosen the best response.
    Medals 0

    yea.. total kinetic energy = rotational kinectic + translational kinetic.. thats not all that hard cause moment of inertia of the sphere would be known.. and m assuming its without slip!!

    • one year ago
  5. kgns
    Best Response
    You've already chosen the best response.
    Medals 0

    If it were an inclined plane, we could stick with \[gtsin \alpha\] with alpha being the angle of inclination. If we consider a semicircle as an infinitesimal sum of inclined planes, we could do \[\int\limits_{0}^{t}gsin \alpha(t) d \alpha\] But it's quite a challenge to derive alpha(t). Not even sure if possible

    • one year ago
  6. MuH4hA
    Best Response
    You've already chosen the best response.
    Medals 0

    Shouldn't the acceleration in terms of the angle look like this? |dw:1355060534242:dw| \[a(\alpha) = g \, \cos(\alpha)\]

    • one year ago
  7. kgns
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, but since we want velocity in terms of time, we also need to know alpha in terms of t

    • one year ago
  8. gleem
    Best Response
    You've already chosen the best response.
    Medals 0

    The problem does not specify that the sphere is rolling i.e. not slipping. Assuming it is rolling makes the problem more difficult especially considering the acceleration is not constant.

    • one year ago
  9. Vincent-Lyon.Fr
    Best Response
    You've already chosen the best response.
    Medals 0

    If you write down the equations, you will end up with a non-linear differential equation. There is not classical function that will yield v(t). Besides, if you ignore the effects of friction, then the sphere will not rotate and its kinetic energy will purely be given by the motion of its centre of mass.

    • one year ago
  10. MuH4hA
    Best Response
    You've already chosen the best response.
    Medals 0

    The problem does not specifiy, but the other option doesn't make any sense for this kind of example.

    • one year ago
    • Attachments:

See more questions >>>

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.