A 20.00 kg lead sphere is hanging from a hook by a thin wire 3.00 m long, and is

Question

A 20.00 kg lead sphere is hanging from a hook by a thin wire 3.00 m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.50 kgsteel dart that embeds itself in the lead sphere.

Part A

What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

A 20.00 kg lead sphere is hanging from a hook by a thin wire 3.00 m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.50 kgsteel dart that embeds itself in the lead sphere.

Part A

What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

Explanation / Answer

By using the conservation of energy method

let Mo = 5.5 kg and m = Mo + M and M = 20kg

Initial kinetic energy = potential energy at top of circle

Potential Energy = KE
mgh = 0.5 mv^2
(20+5.5)*9.8*(2*3) = 0.5*(20 + 5.5)V^2
1499.4 = 12.75V^2
V^2 = 117.6
V= 10.84 m/s

Now using the conservation of momentum

Mo*v = (20+5.5) * V

5.5*v = 25.5*10.84

v = 50.278 m/s

Therefore minimum initial speed = 50.278m/s

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