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HELP physics prove question

  1. Nov 3, 2008 #1
    HELP!!!physics prove question

    1. The problem statement, all variables and given/known data
    A boy is seated on the top of a hemispherical mound of ice. He is given a very small push and starts sliding down the ice surface, assumed to be fricitionless. show that he leaves the ice at a point who height is 2R/3

    3. The attempt at a solution
    I don't really know how to do this question. However, I know that the normal force disappears as he leaves the ice.
     
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  3. Nov 3, 2008 #2

    tiny-tim

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    Hi Kudo Shinichi! :smile:

    Hint: calculate his speed at an angle θ, then caclulate the normal force.
     
  4. Nov 3, 2008 #3
    Re: HELP!!!physics prove question

    x-direction:
    v_0=v_0*cosθ
    then use V_f=V_0+at
    y-direction:
    V_0=V_0*sinθ
    then use V_f=V_0+at
    but I have some many unknown variables...
    Normal force=mg
    also, How can i relate the speed to the normal force since F_n=mg
     
  5. Nov 3, 2008 #4

    tiny-tim

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    Nooo … that equation (and the other two kinematic equations) only work if a is constant … which will only happen in free-fall, or on a slope.

    This is a sphere, not a slope.

    Hint: use conservation of energy. :smile:
     
  6. Nov 3, 2008 #5
    Re: HELP!!!physics prove question

    Do you mean conservation of momentum and conservation of kinetic energy?
    P=P'
    m1v1+m2v2=m1v1'+m2v2'

    KE=KE'
    1/2m1v1^2+1/2m2v2^2=1/2m1(v1')^2+1/2m2(v2')^2
    Since the initial velocity is equal to 0
    therefore,
    m1v1'=-m2v2'
    1/2m1(v1')^2=-1/2m2(v2')^2
    we don't know the mass of the boy, how can we find out the velocity...also you said find out the velocity by using angles, but i didn't need to use any angle on the above equations. I still don't really understand how to relate the velocity to the normal force, because normal force is equal to mg and both variables are nothing to do with velocity.
     
  7. Nov 4, 2008 #6

    tiny-tim

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    conservation of momentum (m1v1+m2v2=m1v1'+m2v2') and conservation of energy are entirely different things :frown:

    conservation of momentum will not work on a curved surface.
    conservation of kinetic energy does not exist

    it's conservation of energy … that's total energy, not just kinetic energy:

    KE + PE = constant
    this is obviously the wrong equation … whatever is m2?

    Try again. :smile:
     
  8. Nov 4, 2008 #7
    Re: HELP!!!physics prove question

    Total mechanical energy=PE+KE
    PE+KE=0
    PE=-KE
    mgh=-1/2mv^2
    m(9.8)(2R/3)=-1/2mv^2
    m cancels out
    v^2=9.8(2R/3)(-2)
    v=sqrt(9.8*(2R/3)*-2)

    I think this is the velocity that i need to find
    and we know that the normal force =0 when the both is at the h=2R/3, but how do we relate the velocity to the normal force and how do we show that the boy leaves at height=2R/3
     
  9. Nov 4, 2008 #8

    tiny-tim

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    Use Newton's second law in the radial (normal) direction. :smile:
     
  10. Nov 4, 2008 #9
    Re: HELP!!!physics prove question

    Total mechanical energy=PE+KE
    PE+KE=0
    PE=-KE
    mgh=-1/2mv^2
    m(9.8)(2R/3)=-1/2mv^2
    m cancels out
    v^2=9.8(2R/3)(-2)
    v=sqrt(9.8*(2R/3)*-2)

    f=m*dv/dt
    f=m*d(sqrt(9.8*(2R/3)*-2))/dt

    this is the force we got
    sorry, but I still don't get how can we prove that the boy starts from 2R/3 by using the force we got from above.
     
  11. Nov 4, 2008 #10

    tiny-tim

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    No!!

    fnet = ma.

    (a only = dv/dt if the motion is in a straight line … this is along a curve)

    What is fnet?
     
  12. Nov 4, 2008 #11
    Re: HELP!!!physics prove question

    F_net is the net force, which is also stands for all the forces we applied.
    F_net=F_1+F_2+F_3+....
    F_net=ma
    in this case a is equal to v because
    a=v(T2)-v(T1)
    and the initial velocity in the problem is zero
    therefore a= v-0 a=v a=v=sqrt(9.8*(2R/3)*-2)

    F_net=m*v=m*sqrt(9.8*(2R/3)*-2)
    = sqrt(-13.1R)*m
     
  13. Nov 5, 2008 #12

    tiny-tim

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    So what are F_1 F_2 and F_3?
     
  14. Nov 5, 2008 #13
    Re: HELP!!!physics prove question

    F_1=ma_1
    F_2=ma_2
    F_3=ma_3
     
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