2022 RI Prelims H2 Phy Paper 2 Soln

Raffles Institution Year 5-6 Physics Department 1 2022 H2 Physics Preliminary Examination Solution Paper 2 1 (a) (i) particle A particle B 9mu 0 3T 2T –3mu T t p 4.2mu 1.8mu

Raffles Institution Year 5-6 Physics Department 2 (ii) As there are no resultant external forces acting in the horizontal direction on the system of particles A and B, total momentum of the system is conserved in the horizontal direction by the principle of conservation of momentum. Since the momentum of particle A decreases by 7.2mu (36 small squares) after the collision, the momentum of particle B should increase by 7.2mu (36 small squares) so that the total momentum remains constant at all times. OR Since the momentum before the collision is 6.0 mu, the total momentum of the system remains constant at 6.0mu at all times. (b) Solution 1 relative speed of approach  34ABuuu u u   relative speed of separation 4.2 0.2 4BAvv u uu   Since the relative speed of approach and the relative speed of separation are equal, the collision is elastic. Solution 2 kinetic energy,  2 2 211 22 2 k mv pEm v mm  before collision:    2222 ,, 2 , 93 922 2 92 A before B before k before AB mu muppEm u mm m m   after collision:    2222 ,, 2 , 1.8 4.2 9222 9 2 A after B after k after AB mu muppEm u mm m m   Since the kinetic energy of the system before and after the collision remains the same, the collision is elastic. (c) By Newton’s second law, resultant force R dpF dt , which is given by the gradient of the graph in Fig. 1.1. During collision, from tT to 2tT , the gradient of the graph for particle A is 7.2mu T . The gradient of the graph for particle B is 7.2mu T . Hence the horizontal resultant force on parti cle A, which is the force on A by B has magnitude 7.2mu T and the horizontal resultant force on particle B, which is the force on B by A also has the same magnitude of 7.2mu T . Since the gradients have opposite signs, this imply that the two forces are opposite in direction. This is consistent with Newton’s third law as the force on A by B and the force on B by A are equal in magnitude and opposite in direction.

Raffles Institution Year 5-6 Physics Department 3 Comments (a) (i) Generally well done. The most careless mistake made was to read the vertical axis values wrongly and either draw 4.2 mu at the wrong position (e.g. small squares above 4.0mu) or draw it at the right position, but quote the value of 4.1mu instead. Please note that each small square is equivalent to 0.2mu on the vertical axis. (ii) Weak responses failed to include the condition for momentum conservation, which is that there must be no resultant external forces on the system. Weak candidates tend to forget either the entire condition, or leave out the word