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Pendulum-Work Question

  1. Jan 29, 2017 #1
    1. The problem statement, all variables and given/known data
    A pendulum of lenght ##L=1.25m##.Its bob (which effectively has all the mass) has speed ##v_0## when the cord makes an angle ##θ_0=40.0^°## with the vertical.##(a)## What is the speed of the bob when it is in its low (est position If ##v_0=8.00m/s## ? What is the least value that ##v_0## can have If the pendulum is to swing down and then up ##(b)## to a horizontal position,and ##(c)## to a vertical position with the chord remaining straight ? ##(d)## Do the answers to parts ##(b)## and ##(c)## increase,decrease,or remain the same if ##θ_0## is increased by a few degrees ?

    2. Relevant equations
    ##-ΔU=W##
    ##W=Δ(KE)##
    3. The attempt at a solution

    I found the answer of (a) using -
    ##-ΔU=W##
    ##W=Δ(KE)##
    it came ##v=8.35\frac m s##

    I didnt understand (b) and part (c).so I stucked there...

    Thanks
     

    Attached Files:

  2. jcsd
  3. Jan 29, 2017 #2

    haruspex

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    Do the same calculation as you did for part a) to get an expression for the speed v at any given angle, θ, in terms of v0, θ0, L, g and θ.
     
  4. Jan 30, 2017 #3
    ##\sqrt {(v_0)^2+2gL(cosθ-cosθ_0)}=v##
     
  5. Jan 30, 2017 #4

    haruspex

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    Ok. So what is θ in b)?
     
  6. Jan 30, 2017 #5
    90 degree
     
  7. Jan 30, 2017 #6

    haruspex

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    So plug that in. What is the smallest value v0 can have?
     
  8. Jan 30, 2017 #7
    Ok I found but for c what would be the angle ?
     
  9. Jan 30, 2017 #8

    haruspex

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    θ0? Same as before.
     
  10. Jan 30, 2017 #9
    θ ?
     
  11. Jan 30, 2017 #10

    haruspex

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    You told me in post #5.
    I have the feeling that there is something you are not understanding about the question, and I can't figure out what it is.
     
  12. Jan 30, 2017 #11
    I found the answer of (b),plotting θ=90
    For (c) what is θ=?
     
  13. Jan 30, 2017 #12

    haruspex

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    I'm very sorry, my eyes kept jumping to the wrong line, so I was reading b instead of c.
    For c there is a complication. For b, the speed at the horizontal position could be 0. Could the speed be zero at the top of the loop?
     
  14. Jan 30, 2017 #13
    It cant
     
  15. Jan 30, 2017 #14

    haruspex

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    Right. So what is the minimum speed at the top.
     
  16. Jan 30, 2017 #15
    ##v=2\sqrt {gL}##
     
  17. Jan 30, 2017 #16

    haruspex

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    No. Consider this condition
    What forces act on the bob at the top? What must the net force be?
     
  18. Jan 30, 2017 #17
    Yeah I made a mistake I know I noticed now
     
  19. Jan 30, 2017 #18
    v=6.72
     
  20. Jan 30, 2017 #19

    haruspex

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    That's not right for the speed atthe top. How did you get that? Or is that your answer for v0?
     
  21. Jan 30, 2017 #20
    At the bottom total energy is 1/2mv^2 which here v is as we found ot 8.35 and at the top energy is 1/2mv^2+mg2L so I thought the should be equal
     
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