Question

A 5kg ornament is hanging by a 1.5 m wire when it is suddenly hit by a 3 kg missile travelling horizontally at 12m/s. The missile embeds itself in the ornament during the collision. What is the tension in the wire immediately after collision?

Answer 1

so an 8 kg pendulum bob has been created

momentum is conserved
... so the momentum of the bob equals the momentum of the missle
... this gives the immediate velocity of the bob

the centripetal force necessary (to keep the bob moving in a circle) is
... m v^2 / r

the tension in the wire supplies the centripetal force
... AND overcomes the force of gravity (m g)

tension = centripetal + weight