YIJC 2023 H2Phy Prelim P3 Solution

2023 YIJC JC2 H2 Preliminary Examination Paper 3 Suggested Solutions 1 (a) The principle of conservation of momentum states that total momentum of the system remains constant provided that there is no net/resultant force exerted on the system B1 B1 (b) (i) Since no net external force, total momentum along AB remains constant. Total initial momentum along AB = Total final momentum along AB 4.0 (4.2 cos θ) + 2.8 (6.0 cos θ) = (4.0 + 2.8)(3.7) 33.6 cos θ = 25.16 θ = 41.5 C1 A1 (ii) Impulse = change in momentum Considering direction perpendicular to line AB Impulse = final momentum – initial momentum = 0 – 4.0 (4.2 sin 41.5°) = − 11.1 N s (accept positive value) C1 A1 (iii) Since, the total final momentum along the direction perpendicular to AB (vertical) is zero, the total initial momentum along the direction perpendicular to AB (vertical) must equal to zero. Since both balls have the same initial momentum (16.8 kg m s−1), the angles have to be the same, so that the total initial momentum along the direction perpendicular to AB equals to zero. B1 B1 (iv) Total KE before collision = ½ (4.0)(4.2)2 + ½ (2.8)(6)2 = 85.7 J Total KE after collision = ½ (4.0 + 2.8)(3.7)2 = 46.5 J Since the KE is not conserved, the collision is inelastic. M1 A1 2 (a) (i) 1. A gas consists of a very large number of molecules. 2. The molecules are in constant, random motion and obey Newton's laws of motion. 3. Collisions between gas molecules are elastic or the collision between gas molecules and the walls of the container are elastic. 4. Intermolecular forces act only during collisions between molecules. The duration of a collision is negligible compared with the time interval between collisions. 5. The volume of the gas molecules themselves is negligible compared with the volume occupied by the gas (this implies that almost all of the gas is empty space). Any 2 of the above B1 B1

2 (ii) As volume compresses, the time between successive collisions of a molecule against the wall decreases or the frequency of the collisions of molecules against the wall increases. For same change in linear momentum, the net force acting on the wall increases, hence increasing pressure B1 B1 (b) (i) pV = nRT For A, 1.5 × 105 × 2.0 × 10–3 = n × 8.31 × 200 n = 0.18 mol A1 (ii) 213 22 rmsE mc kT== .. 27 2 2313 40 1 66 10 1 38 10 20022 rmsc−−    =    crms = 353 ≈ 350 m s–1 M1 A1 (iii) For C to D ΔU = Q + W 3 2 (0.181)(8.31)(400 - 720) = - 50 + W W = - 670 J Work is done by the gas M1 A1 A1 3 (a) The periodic motion of an object about the equilibrium point in which its acceleration is proportional to the displacement of the object from the equilibrium poin