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Problem in mechanics

  1. Jun 19, 2010 #1
    1. The problem statement, all variables and given/known data
    A race car starts from rest on a circular track. the car increases its speed at a constant rate at as it goes once around the track.


    2. Relevant equations

    Find the angle that the total acceleration of the car makes- with the radius connecting the centre of the track and the car- at the moment the car completes the circle.


    3. The attempt at a solution
    First I put the angle = [tex]\theta[/tex]
    I put the total acceleration = a
    and ar= a radial
    and then I found that Cos[tex]\theta[/tex]=[tex]\frac{a r }{a}[/tex]
    then I said ar=[tex]\frac{v2}{r}[/tex]
    and v2=[tex]\frac{2 by r}{T}[/tex] where T is the period. But I stopped I have no numbers
    So can any one help me?
     
  2. jcsd
  3. Jun 19, 2010 #2

    Doc Al

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    Staff: Mentor

    Do this: Call the tangential acceleration at. Use this to figure out the speed at the end of circle and thus ar. Use those components to find the angle. (Hint: Express everything in terms of the final speed and the radius.)
     
  4. Jun 19, 2010 #3
    Got it :)
    thank you bro :D
     
  5. Jun 19, 2010 #4
    hey Doc Al am just typing the answer to make sure it is okay, cause I think there is something error because the final answer unreasonable
    This what I have done
    since at=[tex]\frac{Vf2}{2\pi r}[/tex]
    and ar=[tex]\frac{vf2}{r}[/tex]
    therefore tan[tex]\theta[/tex]= [tex]\frac{at}{ar}[/tex]
    therefore tan[tex]\theta[/tex]= [tex]\frac{v2}{4\pi r}[/tex] × [tex]\frac{r}{v2}[/tex]
    So [tex]\theta[/tex] = tan-1([tex]\frac{1}{4 \pi}[/tex]
    So [tex]\theta[/tex] = 4.548 degrees
    I think the angle is too small and it is incorrect !! ?
     
  6. Jun 19, 2010 #5

    Doc Al

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    Staff: Mentor

    That answer sounds right to me.

    FYI: Your formatting is getting messed up because you are using the sup and sub tags within Latex; keep them separate. The way to use subscripts in Latex is like a_r; to use superscripts, v^2.
     
  7. Jun 19, 2010 #6
    Ok thank you bro very much :)
     
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