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Vertical velocity component

  1. Oct 21, 2011 #1
    1. A 0.20kg ball with an initial velocity of (26i-1.6j)m/s collides with a vertical wall. The wall exerts a constant force of -175i N on the ball and the ball's final horizontal velocity component is -15i m/s. Find the final vertical velocity component of the ball.



    2. I know how to find the total change in momentum of the ball and how long the ball was in contact with the wall, but i don't know how to find the vertical velocity component.



    3.
     
    Last edited: Oct 21, 2011
  2. jcsd
  3. Oct 22, 2011 #2

    ehild

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    What vertical force acts on the ball?


    ehild
     
  4. Oct 24, 2011 #3
    I am guessing gravity maybe???
     
  5. Oct 24, 2011 #4

    ehild

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    Yes, it is gravity. Gravity causes a vertical acceleration. You know the time of interaction with the wall. How much does the vertical velocity component change during that time?


    ehild
     
  6. Oct 25, 2011 #5
    I thought I had to know the final velocity in order to find the interaction time with the wall and would find it using the formula: FΔt=m(v2-v1)....is that right?
     
  7. Oct 26, 2011 #6

    ehild

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    It is true for each components separately. The wall exerts horizontal force so it changes the horizontal velocity component. You know both the initial and final horizontal velocity components and you know that the wall exerts a horizontal force of -175i N. How long does this force act on the ball?
    Gravity exerts vertical force: it changes the vertical velocity component. You need the time Δt to calculate the vertical change of velocity during the interaction with the wall.

    ehild
     
  8. Oct 26, 2011 #7
    so would the time be:
    -175Δt=.2(-15i-26i)
    -175Δt=.2(-41)
    -175Δt=-8.2
    t=.047?
     
  9. Oct 26, 2011 #8

    ehild

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    It is OK, but use one more digits as you will use this number for further calculation. So Δt=0.0469 s.

    (And either omit the i-s everywhere or use them everywhere, and do not change Δt to t.)

    Now calculate the change of the vertical velocity component because of gravity.

    ehild
     
  10. Oct 26, 2011 #9
    9.81(.0469)=.2(v2+1.6)
    .460089=.2v2+.32
    .140089=.2v2
    v2=.7004m/s
    is that right?
     
  11. Oct 26, 2011 #10

    ehild

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    No, it is wrong.

    The change of velocity is aΔt.

    ehild
     
  12. Oct 26, 2011 #11
    I'm confused.....what formula do I need to find the final vertical velocity component?
     
  13. Oct 27, 2011 #12

    ehild

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    How do you get the velocity of a falling body?

    ehild
     
  14. Oct 27, 2011 #13
    The motion equation: v(t)=v0+at?
     
  15. Oct 27, 2011 #14

    ehild

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    Yes.

    ehild
     
  16. Oct 27, 2011 #15
    -1.6+(9.81)(.0460)=-1.14
    Is that right?
     
  17. Oct 27, 2011 #16

    ehild

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    Gravity points downward. Your result is correct if the vertical axis of the coordinate system also points downward. I guess the problem meant upward y axis. Then g=-9.81 m/s^2.

    ehild
     
  18. Oct 30, 2011 #17
    In my answer key, it says that the final vertical velocity component is -1.6j, which is the same as the initial vertical velocity component. what am I doing wrong?
     
  19. Oct 30, 2011 #18

    ehild

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    I think you are correct. If that wall were in the free space, the answer key would be correct: The force of the wall in the x direction changes only the x component of the velocity. But we are on the Earth and everything is exposed to gravity, and it changes the vertical velocity during the time while the wall and ball are in contact.

    ehild
     
  20. Nov 1, 2011 #19
    In my answer key for this problem it says that the final vertical velocity component is the same as the initial vertical velocity component...is that right?
     
  21. Nov 1, 2011 #20

    ehild

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    It depends on the problem, if gravity is supposed to exist or not. Ask your teacher about it. In my opinion, talking about horizontal and vertical, and ignoring gravity at the same time is not correct.

    ehild
     
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