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

Solved

Posted on 2006-05-28

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?

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?

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