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A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Treat the sphere as a point mass. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision

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onyebuchinnaji

The minimum initial speed of the dart so that the combination makes a complete circular loop after the collision is 58.5 m/s.

Minimum speed for the object not fall out of the circle

The minimum speed if given by tension in the wire;

T + mg = ma

T + mg = m(v²)/R

tension must be zero for the object not fall

0 + mg = mv²/R

v = √(Rg)

Final speed of the two mass after collision

Use the principle of conservation of energy

K.Ef  = K.Ei + P.E

¹/₂mvf² = ¹/₂mv² + mg(2R)

¹/₂vf² = ¹/₂v² + g(2R)

¹/₂vf² = ¹/₂(Rg) + g(2R)

vf² = Rg + 4Rg

vf² = 5Rg

vf = √(5Rg)

vf = √(5 x 2.8 x 9.8)

vf = 11.7 m/s

Initial speed of the dart

Apply principle of conservation of linear momentum for inelastic collision;

5v = vf(20 + 5)

5v = 11.7(25)

5v = 292.5

v = 58.5 m/s

Learn  more about linear momentum here: https://brainly.com/question/7538238

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