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CAIE A-Level Mathematics AS 4.3.2 Momentum Questions

Practise applying conservation of momentum and kinetic energy changes to particle collisions.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • apply conservation of linear momentum in collisions
  • calculate velocities and speeds before and after impact
  • find kinetic-energy loss and collision times in mechanics models

CAIE A-Level Mathematics AS 4.3.2 Momentum Questions question 1

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Figure for Question CAIE A-Level Mathematics AS 4.3.2 Momentum Questions question 1 — CAIE A-Level Mathematics AS

A machine for driving a nail into a block of wood causes a hammerhead to drop vertically onto the top of a nail. The mass of the hammerhead is 1.2 kg and the mass of the nail is 0.004 kg (see diagram). The hammerhead hits the nail with speed v m s−1v \mathrm{~m} \mathrm{~s}^{-1} and remains in contact with the nail after the impact. The combined hammerhead and nail move immediately after the impact with speed 40 m s−140 \mathrm{~m} \mathrm{~s}^{-1}.

Calculate v, giving your answer as an exact fraction.

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