2025 TJC H2 Phy Prelim P2 Solution

2025 H2 Physics P2 Solution 1 (a) The distribution is not uniform with more mass loaded nearer to the left. B1 (b) Resultant force on the boat is zero Resultant moment about any pivot is zero B1 B1 (c) T1 +T2 = 15000 15000(0.75) =T2 (2) T1 = 9400 N T2 = 5600 N C1 A1 A2 (d) Wd = 15000 (30) P = 15000 (30)/12 = 37500 W B1 2 (a) The cube undergoes resonance when the driving frequency of the water wave equals the natural frequency of the oscillating system/cube. There is maximum transfer of energy from the water wave to the cube/ The energy of the system/cube becomes a maximum and the system/cube oscillates with maximum amplitude. B1 B1 (b) v = fλ f = 2.0 Hz Substitute f = 2.0 Hz into l gf 2 1= l = 0.0621 m M1 A1 (c) (i) Increase in wavelength results in decrease in driving frequency, thus driving frequency is not equal to natural frequency, Amplitude decreases. M1 A1 (ii) Increase in mass results in an increase in l, and an decrease in natural frequency. Thus, driving frequency is not equal to natural frequency, Amplitude decreases. M1 A1 (d) Drag force due to water on the cube causes damping. Thus, maximum amplitude of oscillation occurs at a driving frequency 2 Hz, which is smaller than the natural frequency. Since l gf 2 1= , a smaller value of f used in calculation results in a larger value of l calculated. As such, the value determined in (b) is larger than actual measurement. B1 B1

3(a) Using v = fλ v = 3 1 1.4 4.0 10 −   = 350 m s-1 M1 A1 (b)(i) Particle R (As the particle is undergoing SHM, at the amplitude, the instantaneous velocity of the particle is zero). A1 (b)(ii) Particle Q . A1 (b)(iii) Displacement of article Q will be positive next instant. A1 Vertical lines represent equilibrium position of particle along the wave. Particle P is at the centre of compression and particle Q is at the centre of rarefaction | | | | 0.7 1.4 2.1 2.8 position / m displacement / nm 5.00 −5.00 P Q R

(c)(i) Distance travelled by wave in 1 ms = vt = (350)(1 x 10-3) = 0.35 m The graph should have shifted to the left by 0.35 m. Award mark as long as one full wavelength is drawn with displacement at 5.00 nm at initial position. C1 A1 (c)(ii) Phase difference between particle R and S 0.7360 3601.4 x   =  =   180= OR Phase difference between particle Q and S is 90o. C1 A1 displacement / nm t / ms 5.00 −5.00 | | | | | | 2.0 4.0 6.0 8.0 10.0 12.0 Z | | | | 0.7 1.4 2.1 2.8 position / m displacement / nm 5.00 −5.00 P Q R Y

4 (a) 1. Waves must meet  rad out of phase. 2. Waves must have equal amplitude. A1 A1 (b) (i) Wavetrains from S1 and S2 are coherent and superpose at points along YZ. When path difference is an integral