Questions — CAIE Further Paper 3 (127 questions)

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CAIE Further Paper 3 2022 November Q3
  1. Show that \(\mathrm { N } = \frac { 8 } { 15 } \mathrm {~W} ( 1 + 2 \mathrm { k } )\).
  2. Find the value of \(k\).
CAIE Further Paper 3 2023 November Q3
  1. Find the value of \(\tan \theta\).
  2. Find the percentage loss in the total kinetic energy of the spheres as a result of this collision.
    \includegraphics[max width=\textwidth, alt={}, center]{0270d51a-e252-46d3-8c97-7f71ba91fa65-08_560_575_258_744} A bead of mass \(m\) moves on a smooth circular wire, with centre \(O\) and radius \(a\), in a vertical plane. The bead has speed \(\mathrm { v } _ { \mathrm { A } }\) when it is at the point \(A\) where \(O A\) makes an angle \(\alpha\) with the downward vertical through \(O\), and \(\cos \alpha = \frac { 3 } { 5 }\). Subsequently the bead has speed \(\mathrm { v } _ { \mathrm { B } }\) at the point \(B\), where \(O B\) makes an angle \(\theta\) with the upward vertical through \(O\). Angle \(A O B\) is a right angle (see diagram). The reaction of the wire on the bead at \(B\) is in the direction \(O B\) and has magnitude equal to \(\frac { 1 } { 6 }\) of the magnitude of the reaction when the bead is at \(A\).
  3. Find, in terms of \(m\) and \(g\), the magnitude of the reaction at \(B\).
  4. Given that \(\mathrm { V } _ { \mathrm { A } } = \sqrt { \mathrm { kag } }\), find the value of \(k\).