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

Chibi_Robo3 Group Title

An air track glider of mass 0.200 kg, moving at 1.0 m/s collides elastically with another glider of mass 0.050 kg equipped with a perfectly elastic spring, which is initially at rest. How much potential energy is stored in the bumper between the two gliders \(during\) the collision? (i.e. Ek loss during the collision at minimum separation of the two gliders). I just need an explanation on how to do this Answer is 0.02J

  • 4 months ago
  • 4 months ago

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

    I really don't know, sorry! I know that momentum is always conserved. The total energy is also conserved in an elastic collision. I think, in this problem, we assume that the first care is moving until it slows down to its post-collision velocity. And the other cart does not move all this time, until the all the energy the first cart lost becomes potential that will then cause the other cart to move. So we want to know what KE the first cart loses as it gives it all to the potential in the spring.

    • 4 months ago
  2. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I can get it using an equation from Wikipedia.

    • 4 months ago
  3. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large v_{1} = \dfrac{u_{1}(m_{1}-m_{2})+2m_{2}u_{2}}{m_{1}+m_{2}}\) Have you seen this before?

    • 4 months ago
  4. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Chibi_Robo3 ?

    • 4 months ago
  5. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry , i was afk i've seen a formula like: \(V_{f1}=(\frac{m_1-m_2}{m_1+m_2})V_{i1}\) and \( V_{f2}=(\frac{2m_1v_1}{m_1+m_2})\) but not like that..

    • 4 months ago
  6. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Is it right if I say \(E_{ki\ of\ mass\ 1} + E_{ki\ of\ mass\ 2} = E_{kf\ of\ mass\ 1} + E_{kf\ of\ mass\ 2} + E_{potential}\) \(\frac{1}{2}m_1v_{i1}^2+0=\frac{1}{2}m_1v_{f1}^2+\frac{1}{2}m_2v_{f2}^2 + E_{potential} \) \( E_{potential}=\frac{1}{2}m_1v_{i1}^2-\frac{1}{2}m_1v_{f1}^2+\frac{1}{2}m_2v_{f2}^2\) \(E_{potential}=\frac{1}{2}(0.200)(1.0)^2-\frac{1}{2}(0.200)(0.6)^2+\frac{1}{2}(0.05)(1.6)^2\) oh i forgot to tell you that I already calculated the Final velocities of the gliders I got \(v_{f1}=0.6 m/s, v_{f2}=1.6m/s\)

    • 4 months ago
  7. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The \(u\)'s are for before the collision, and the \(v\) is for after. But this formula didn't work for me. So if we say the moving cart is cart 1, then we want \(v_1\). When we have the velocity before and after, we can find the change in kinetic energy of cart 1. \(u_2=0\), which is nice. Then\[v_{1} = \frac{u_{1}(m_{1}-m_{2})}{m_{1}+m_{2}}\\= \frac{1.0~~(0.200-0.050)}{0.200+0.050}\\= \frac{1.0~~(0.150)}{0.250}\\= \frac{0.150}{0.250}\\= \frac{15}{25}\\=\frac35=v_i\] \(\Delta(KE)=\frac12m_1v_1^2-\frac12m_1u_1^2\\=\dfrac{m_1}2(v_1^2-u_1^2)\\=\dfrac{0.200}{2}\left((\frac35)^2-1^2\right)\\ =\dfrac{2}{20}\left(\dfrac9{25}-1\right)\\ =\dfrac{1}{10}\left(\dfrac9{25}-\dfrac{25}{25}\right)\\ =\dfrac{1}{10}\left(\dfrac{-16}{25}\right)\\ =\dfrac{-16}{250}\\ =\dfrac{-8}{125}\\=-0.064\neq-0.02\)

    • 4 months ago
  8. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    for the las line it should be: \(E_{potential}=\frac{1}{2}(0.200)(1.0)^2-\frac{1}{2}(0.200)(0.6)^2-\frac{1}{2}(0.05)(1.6)^2\) but still, i got the wrong answer :/

    • 4 months ago
  9. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    When the other cart's velocity is 0, your first equation is the same as Wikipedia's.

    • 4 months ago
  10. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh i solved the same way as yours before and got same results, so i tried a different one.. and really? hmm.. lemme check wikipedia then

    • 4 months ago
  11. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    That's weird! Maybe we're perceiving the problem incorrectly? It might be something to ask your teacher about?

    • 4 months ago
  12. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    alright , i'll try to ask him tomorrow :)

    • 4 months ago
  13. Chibi_Robo3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I got it! I asked my teacher and he said that DURING the collision the velocity of the two objects will be the same and I should only consider the total kinetic energy of the object BEFORE and DURING the collision.. so yeah, that makes sense to me .. I tried solving it and I already got 0.02 J for potential energy ^_^

    • 4 months ago
  14. theEric Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh, cool! Thanks :)

    • 4 months 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.