June 2006 QP – M3 OCR.pdf

OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MATHEMATICS 4730 Mechanics 3 Monday 22 MAY 2006 Morning 1 hour 30 minutes.

The exam consists of 6 questions, with a total of 72 marks, and candidates are allowed to use a graphical calculator. The questions cover various topics in mechanics, including impulse, momentum, energy, and motion.

Question 1 asks about the direction of an impulse and the speed of a ball after being struck. Question 2 involves a duck being brought to rest by resistive forces. Question 3 concerns two uniform rods in equilibrium, with candidates needing to find the force exerted on one rod and the tension in a string.

Question 4 is about a simple pendulum, with candidates required to show that the motion is approximately simple harmonic and calculate the angular speed and time taken for the pendulum to move a certain distance. Question 5 involves a collision between two spheres, with candidates needing to find the speed and direction of motion of each sphere after the collision.

Question 6 is about a bungee jumper, with candidates required to find the distance fallen, maximum speed, and extension of the rope. Question 7 concerns a smooth horizontal cylinder with particles attached to a string, with candidates needing to show that a certain equation holds, find the magnitude of the contact force, and determine the transverse component of the acceleration of one particle.