1991 (b) A smooth sphere moving with velocity 4 + 5 m/s collides with an identical sphere moving with P, Q velocity 2 + 3 m/s where is a unit vector along the line of centres at the moment of impact. If is the coefficient of restitution e find the velocity of each sphere after impact. Calculate the value of if is deflected through an angle tan-1as a result of the collision. e P 1983 (full question) State the laws governing oblique collisions between two smooth elastic spheres. Two such spheres and of mass 5 kg and 10 kg respectively, collide obliquely. A B The coefficient of restitution is 1/7. Immediately before collision the velocity of is 5 + 4 and that of is where speeds are in m/s and A B –2–2, and are unit vectors along and perpendicular to the line of centres. Find the velocity of (i) and (ii) after impact. A B Show that the loss of kinetic energy is 80 J. the tan of the angle through which is deflected after the collision. B 2016 (b) Two identical smooth spheres P and Q collide. The velocity of P after impact is 3i j and the velocity of Q after impact is 2i +j, where j is along the line of – the centres of the spheres at impact. The coefficient of restitution between the spheres is ½. Find the velocities, in terms of and j, of the two spheres before impact to the nearest degree, the angle through which the direction of motion of P is deflected by the collision. 2006 (b) A smooth sphere A moving with speed collides with an identical smooth sphere B which is moving in a u, perpendicular direction with the same speed u The line of centers at the instant of impact is perpendicular to the direction of motion of sphere B. The coefficient of restitution between the spheres is e Find, in terms of the speed of each sphere after impact and hence, or otherwise, show that it is not e, possible for the two spheres to have the same speed after impact. Prove that where is the angle through which sphere B is turned as a result of the impact. θ Deflected through an angle of 90° 1995 (b) A ball falls vertically and strikes a smooth fixed plane.
1991 (b) A smooth sphere P, moving with velocity 4 + 5 m/s collides with an identical sphere Q moving with velocity 2 + 3 m/s where is a unit vector along the line of centres at the moment of impact. If e is the coefficient of restitution find the velocity of each sphere after impact. Calculate the value of e if P is deflected through an angle tan-1as a result of the collision. 1983 (full question) State the laws governing oblique collisions between two smooth elastic spheres. Two such spheres A and B of mass 5 kg and 10 kg respectively, collide obliquely. The coefficient of restitution is 1/7. Immediately before collision the velocity of A is 5 + 4 and that of B is –2–2, where speeds are in m/s and and are unit vectors along and perpendicular to the line of centres. Find the velocity of (i) A and (ii) B after impact. Show that the loss of kinetic energy is 80 J. the tan of the angle through which B is deflected after the collision. 2016 (b) Two identical smooth spheres P and Q collide. The velocity of P after impact is 3i – j and the velocity of Q after impact is 2i +j, where j is along the line of the centres of the spheres at impact. The coefficient of restitution between the spheres is ½. Find the velocities, in terms of and j, of the two spheres before impact to the nearest degree, the angle through which the direction of motion of P is deflected by the collision. 2006 (b) A smooth sphere A moving with speed u, collides with an identical smooth sphere B which is moving in a perpendicular direction with the same speed u The line of centers at the instant of impact is perpendicular to the direction of motion of sphere B. The coefficient of restitution between the spheres is e Find, in terms of e, the speed of each sphere after impact and hence, or otherwise, show that it is not possible for the two spheres to have the same speed after impact. Prove that where θ is the angle through which sphere B is turned as a result of the impact. Deflected through an angle of 90° 1995 (b) A ball falls vertically and strikes a smooth fixed plane.
5.%20Collisions.docx