Conservation of Momentum

Posted on 2006-05-28
Last Modified: 2009-07-29
A 20.00kg lead sphere is hanging from a hook by a thin wire 3.50m long and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00kg steel dart that embeds itself in the lead spehere, what must the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision.

I dont know what I'm doing wrong, this stuff isnt that hard but for some reason I'm getting the wrong answer.

p_1 = p_2

m_a * v_a1 + m_b + v_b1 = v_f(m_a + m_b)

v_b1 = v_f(m_a + m_b)/m_b

v_f must be great enough for the system to have enough energy to rise 7.0m.

1/2(m_a + m_b)v_f^2 = (m_a + m_b)gh

v_f = sqrt(2gh) -> v_f = sqrt(2 * 9.8m/s/s * 7.0m) = 11.713m/s

so then

v_b1 = v_f(m_a + m_b)/m_b = (11.713m/s)(25kg)/5kg = 58.565m/s

However, the book is saying the answer is 65.5 m/s, what am I doing wrong?
Question by:BrianGEFF719
    LVL 19

    Author Comment

    Based on the books answer the system would rise to about 8.3m, I dont quite get this, am I leaving something out?
    LVL 84

    Expert Comment

    20.00kg lead sphere is less than .65m across, so it looks to me like the book is leaving something out
    LVL 19

    Author Comment

    >>20.00kg lead sphere is less than .65m across, so it looks to me like the book is leaving something out

    So i cannot safely assume that the two objects are point masses?
    LVL 84

    Accepted Solution

    I don't see how to get the book answer without changing some assumption.
    Although you might also want to question the assumption that the book answer is correct.

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