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Math Help - mechanics problem

  1. #1
    Member billym's Avatar
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    mechanics problem

    A ball is projected upward with initial velocity = 20 m/s.

    I have to show that the acceleration at time t is a(t)i, in which

    a(t) = -g/b^2 * (v(t)^2 + b^2),

    where v(t)i is the velocity of the ball at time t, and b^2 = mg/0.2D^2.

    I'm taking a course that is kind of just quickly breezing through simple mechanics, but it's insufficiently explained and i find my tutor unhelpful.

    Can somebody explain what exactly is being asked here and... nudge me in the right direction.
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  2. #2
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    Billym have you posted the whole question ?, generally speaking a ball projected vertically has constant acceleration. Can you give us some background on what you do know ?

    Bobak
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  3. #3
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    Billy,

    I believe the situation you have described by the equation you posted is taking into account the air resistance (or drag) that the ball experiences. Generally the derivation of such equations rely on Newton's Second Law, F = ma. Do you have the equation for the drag force F_{D}? The acceleration should be a = g + F_{D}/m.

    Best,

    m_s_d
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  4. #4
    Member billym's Avatar
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    I don't really know what I know at this point. Sorry, I should have mentioned that air resistance is involved and that the quadratic model applies, -0.2*D^2*v^2.

    I'm in one of those situations where my homework involves questions that I haven't seen before. I know the idea is that I'm supposed to "use what I have learned" to solve the problem, but I obviously haven't learned enough.

    I'm not asking anyone to do the problem for me, really, it would just be helpful if someone could post a link to basic problem where a ball is being projected upwards and I have to find the max height, etc. taking air resistance into account. Essentially the use of newton's second law and air resistance.

    I just need to see one sample problem worked through so I can see how its done... i guess...
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by billym View Post
    I don't really know what I know at this point. Sorry, I should have mentioned that air resistance is involved and that the quadratic model applies, -0.2*D^2*v^2.

    I'm in one of those situations where my homework involves questions that I haven't seen before. I know the idea is that I'm supposed to "use what I have learned" to solve the problem, but I obviously haven't learned enough.

    I'm not asking anyone to do the problem for me, really, it would just be helpful if someone could post a link to basic problem where a ball is being projected upwards and I have to find the max height, etc. taking air resistance into account. Essentially the use of newton's second law and air resistance.

    I just need to see one sample problem worked through so I can see how its done... i guess...
    There is a downward force mg on the object and a downward force (your drag force) of 0.2D^2v^2.

    So Newton's 2nd in the upward direction (with upward positive) says
    F = -mg - 0.2D^2v^2 = ma

    So
    a = -\frac{mg}{m} - 0.2\frac{D^2}{m}v^2

    a = -\frac{0.2D^2g}{m} \left ( v^2 + \frac{m}{0.2D^2} \right )

    Setting
    b^2 = \frac{m}{0.2D^2}
    gives the required form:
    a = -\frac{g}{b^2}(v^2 + b^2)

    -Dan
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