June 2016 QP – M3 OCR.pdf

This is a mathematics exam paper for the A2 GCE Mathematics course, specifically the Mechanics 3 module (4730/01). The exam consists of 5 questions, with a total of 72 marks, and candidates have 1 hour 30 minutes to complete it. The questions cover various topics in mechanics, including impulse, collisions, projectiles, and equilibrium.

The first question involves a particle moving on a smooth horizontal surface, which is struck by a horizontal impulse, causing it to change direction. Candidates must find the magnitude of the impulse and the angle its line of action makes with the original direction of motion.

The second question concerns a particle projected horizontally from a fixed point, with a force acting on it in the positive x-direction. Candidates must find an expression for the velocity of the particle at time t and determine the maximum and minimum values of the velocity.

The third question involves two uniform smooth spheres colliding on a horizontal surface. Candidates must find the speed of one sphere after the collision and the component of the velocity of the other sphere along the line of centres after the collision.

The fourth question concerns a particle attached to two light elastic strings, which are fixed to two points on a smooth horizontal plane. Candidates must find the greatest kinetic energy of the particle in the subsequent motion.

The fifth question involves a particle attached to a light inextensible string, which is projected horizontally from a fixed point. Candidates must find an expression for the tension in the string and determine the height of the particle above its initial level when the string becomes slack.

The sixth question concerns two uniform rods freely jointed at a point, resting in equilibrium on two rough horizontal steps. Candidates must find an equation relating the weights and forces acting on the rods and determine the vertical component of the force acting on one of the rods.