A 25.00kg lead sphere is hanging from a hook by a thin wire 4.00m long, and is f

Question

A 25.00kg lead sphere is hanging from a hook by a thin wire 4.00m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 7.50kg steel dart that embeds itself in the lead sphere. A. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision? A 25.00kg lead sphere is hanging from a hook by a thin wire 4.00m long, and is free to swing in a complete circle. Suddenly it is struck horizontally by a 7.50kg steel dart that embeds itself in the lead sphere. 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

total mass is 30kg, centripital force must be equal to gravitational force

mv^2/r=mg
30v^2/3.5=30(9.8)

solve for v, which is the minimum speed the weight can have

now, as for the inelastic collision, final momentum after the collision, is 30v. the initial momentum of the sphere was zero, thus all that 30v momentum needs to come from the initial momentum of the 6 kg dart

thus,

30v=6x

x is the speed of the dart.

sub everything in and calculate it.

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