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

saljudieh07

A particle of mass m moving in 3 dimensions under the potential energy function....

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    Rest of Question: A particle of mass m moving in 3 dimensions under the potential energy function \[V(x,y,z)=\alpha x+\beta y^2+ \gamma z^3\] has speed Vnaught when it passes through the origin. a) what will its speed be if and when it passes through the point (1,1,1)?

    • 2 years ago
  2. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    This is what I have done so far: F=-gradient (dot) potential energy function \[= - (\alpha i +2y \beta j + 3z^2\gamma k )\] and I make the expression above equal to= mdv/dt but now i am study, when i break down the dv/dt into 3 dimensions how do I integrate both sides with respect to x, y, and z?

    • 2 years ago
  3. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    Junkiejim to the rescue!!!!!!!!!!!!

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

    okay, having F you should be able to do this: \[\textbf{F}=m \frac{\delta \textbf{v}}{\delta t} \]\[\textbf{F} \delta t = m \delta \textbf{v}\]\[\int\textbf{F}\delta t = \int m \delta \textbf{v}\] and you integrate each component of F with respect to t, the right side just becomes mv.

    • 2 years ago
  5. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    yeh but that is force with respect to time, i need force with respect to position that is the problem! coz if you read a, it gives me a value of (1,1,1)

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

    oh, i see your issue, you want to not use force then, I think you should be using conservation of energy.

    • 2 years ago
  7. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    yeh, i have the force equation, i can make it equal to m (dv/dx dx/dt) if i break dv/dt, then i get mv dv/dx, and i can find the equation of velocity wrt to position, but the problem is, this question is three dimensional not only wrt x... so would it be F= mv (dv/dx +dv/dy + dv/dz)?

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

    OR Considering the system to be closed and forces to be conservative, you can deduce that sum of KE and PE would be constant. We know, KE+PE at origin = KE + PE at (1,1,1) 1/2*m*Vo^2 + 0 = 1/2*m*V(1,1,1) ^2 + alpha+beta+gamma Hence, you can calculate V(1,1,1)

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

    V(1,1,1)=\[\sqrt{2(m*Vo^2 /2 - \alpha-\beta-\gamma)/m}\]

    • 2 years ago
  10. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    when you say 1/2*m*Vo^2 + 0 = 1/2*m*V(1,1,1) ^2 + alpha+beta+gamma 1/2*m*V(1,1,1) ^2 << that V is the velocity with respect to position, and position is in terms of x, y, and z, so how do i find that equation, this is what i am struggling with....

    • 2 years ago
  11. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    does what i am saying makes sense? coz kenetic = 0.5m(velocity)^2

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

    you can split up your dv/dt derivative to look like this: \[\frac{dv}{dx}\frac{dx}{dt}\hat i+\frac{dv}{dy}\frac{dy}{dt}\hat j+\frac{dv}{dz}\frac{dz}{dt}\hat k\]

    • 2 years ago
  13. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    so then i will have: let us say this is the expression you wrote (dvdxdxdtiˆ+dvdydydtjˆ+dvdzdzdtkˆ ) would be equal to = -1/m (Force) where the force is: =−(αi+2yβj+3z2γk) but i still don't know how to solve that integral lol..

    • 2 years ago
  14. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    however, is the idea right?

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

    I think so, when you integrate you should have a line integral, looks something like this \[\int\textbf {F} ~\textbf{dl} = \int mv dv\] \[\text{where}~~ \textbf{dl}= dx\hat i +dy \hat j +dz\hat k\]

    • 2 years ago
  16. saljudieh07
    Best Response
    You've already chosen the best response.
    Medals 1

    hmmm, i see... iight thanks a lot man, if i only could give u more than one star i would of haha.. but yeh.. anyways, amma go sleep on this, when i wake up 2morrow am sure something good will come up with me, if not i will come back 2morrow. thanks guys!

    • 2 years 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.