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CAIE A-Level Mathematics 4.3.2 Conservation of Linear Momentum

Practise modelling direct impacts by conserving signed linear momentum, finding post-collision velocities or shared coalesced speed and then calculating kinetic-energy loss or…

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • write total Σmv before impact = total Σmv after impact using one consistent positive direction
  • use one common velocity after impact when particles coalesce and separate velocities otherwise
  • combine momentum results with kinetic-energy or no-further-collision conditions to find bounds

4.3.2—Momentum question 1

[Maximum number: 2]
Figure for Question 4.3.2—Momentum 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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