1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ball rotated on a string vector diagram

  1. May 23, 2016 #1
    1. The problem statement, all variables and given/known data

    is 1222.5i 1 20.2j2 m/s . For that instant, (a) sketch a vector diagram showing the components of its acceler- ation, (b) determine the magnitude of its radial accel- eration, and (c) determine the speed and velocity of the ball.
    42. A ball swings counterclockwise in a vertical circle at
    the end of a rope 1.50 m long. When the ball is 36.9°
    past the lowest point on its way up, its total acceleration is is -22.5i +20.2j m/s2 . For that instant, (a) sketch a vector diagram showing the components of its acceler- ation, (b) determine the magnitude of its radial accel- eration, and (c) determine the speed and velocity of the ball.


    2. Relevant equations
    a= acì + atj

    3. The attempt at a solution
    If the total acceleration is given by -22
    5ì + 20.2j m/s2 then isnt 22.5 is the radial acceleration and 20.2m/s2 is the tangential acceleration. Im confused can you please show me the vector diagram too
     
  2. jcsd
  3. May 23, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi Ab,

    Where did you find that relevant equation ?

    Why don't you start drawing a picture of the situation. And work it around to a free body diagram of the ball.
     
  4. May 23, 2016 #3
    The equation is in vector form
     
  5. May 23, 2016 #4
    There is tension and gravity
     
  6. May 23, 2016 #5

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the sense that it gives an x component and a y component.
    Yes. Please make the sketch.
     
  7. May 23, 2016 #6
    • FBD
     

    Attached Files:

  8. May 23, 2016 #7

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That's a start. There is a bit more information: 36.9##^\circ##, 1.5 m and ##\vec a = -22.5 \,\hat\imath + 20.2\, \hat\jmath ## m/s2. (In fact I find these values a bit strange: I would expect a negative vertical component. Brings me to the question: what are ##\hat\imath## and ## \hat\jmath## ? I don't see them in the drawing).

    Now you need a relevant equation to link the forces and the acceleration. Any idea ?
     
    Last edited: May 26, 2016
  9. May 23, 2016 #8
    F= ma
    The tension is causing the centripetal acc
     
  10. May 23, 2016 #9
    So the centripetal acc will be in direction of tension and towards the center
     
  11. May 23, 2016 #10
    I and j are unit vectors
     
  12. May 23, 2016 #11

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, that's why they have a hat. But so far you didn't reveal which way they point :smile:.
    Correct. It is a given that the ball describes a circular trajectory. Not with a constant speed (why not?).
    Now it's time for another equation. And perhaps you can already draw the figure that part (a) asks for ?

    [edit]
    This was a bit premature. Please ignore.
     
  13. May 24, 2016 #12
    Is this ok
     

    Attached Files:

  14. May 24, 2016 #13

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I'm not good at approval stamping. But I am good at asking nasty questions, so:
    • What makes you think the ##\hat \imath## and ##\hat \jmath## are radial and tangential and not simply horizontal and vertical ?
    • Where is that 36.9° angle sitting ?
     
  15. May 24, 2016 #14
    Because If a is the total acceleration then its components have to be I and J
     
  16. May 24, 2016 #15
    36.9 is below the x axis
     
  17. May 24, 2016 #16

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Agree. But this goes for horizontal and vertical just as well.
    It cleary says something else altogether.
     
  18. May 24, 2016 #17
    It tells us the location of the ball isnt
     
  19. May 24, 2016 #18

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    to me means the angle between the negative vertical axis (the ##\ -\bf \hat\jmath\ ## direction) is 36.9° .
    So the complement of the angle you draw.
     
  20. May 25, 2016 #19
    So i should break centripetal acc into components or somthn like that
     
  21. May 26, 2016 #20

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Sort of. You know the ball describes a circular trajectory. There is an equation needed to link acceleration and speed. At the moment we don't have any relevant equations at all. I hope by now ee do agree that only two forces work on the ball. And we know the resultant acceleration. To link ##\vec T + m\vec g## to the given resultant acceleration we also need a relevant equation.
    Set up a plan of approach and carry it out !
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Ball rotated on a string vector diagram
  1. String and ball (Replies: 5)

  2. A ball on a string (Replies: 29)

Loading...