TJC 2022 Prelim P2 Guide

H2 Physics Prelim 2022 Solutions 1 (a) Thrust = resistive force since velocity is constant. Power = Fv = Dv D x 15 = 90000 D = 90000/15 = 6.0 kN C1 A1 (b) F = Thrust Power = Fv F – D = ma P/v – D = ma 120000/15 – 6000 = 800a a = 2.5 m s-2 M1 A1 (c) As the velocity increases with time, the resistive force also increases . The driving force decreases as the speed of the boat increases since driving power stay constant, the net force on the boat decreases and hence acceleration decreases with time. Acceleration drops to zero when the resistive force is equal to the driving force on the boat. B1 B1 B1 B1 2 (a) (i) Gravitational force provides centripetal force. Same gravitational force acting on star and planet. ( ) ( ) 2 27 28 27 2 98 8 2 2.0 10 6.0 10 2. m1 5.2 10 1.68 1031 1 0 10 1 306.0 0 G p p s s ps s p s F m r m r rr r r r  =   =  = =  =  == C1 A1 (a) (ii) ( ) ( ) ( ) 2 2 2 2 11 27 2 8 29 6 2 6.67 10 2.0 10 21.68 10 5.2 10 1.16 10 s GC sp ss sp ss FF Gm m mrd Gm m mr Td T T − = = =   =  = C1 A1

(a) (iii) Planet moves in front of star periodically. A1 (b) (i) Between starting height 6.40 x 106 m & ending height 7.225 x 106 m 6 6 -1 () area under g-r graph 6.74 10 to 7.61 10 J kg dg dr g dr =− = = =    2300 Um = =  = 1.55 x 1010 to 1.75 x 1010 J OR 2 MgG r= and MG r =−  gr =− ( ) 2300( )f i i i f fU m m g r g r   =  = − = − 662300( 9.75 6.4 10 7.625 7.225 10 )= −   +    1.60 x 1010 J C1 M1 M1 C1 M1 M1 (b) (ii) ( ) 10 11 66 24 111.6 10 6.67 10 2300 6.40 10 7.225 10 5.85 10 kg E s E f f s E E i i GM m GM m x U rr M U M U −  =  − = − =− − −   =      C1 A1 (b) (iii) Advantages to low polar orbit: • High(er) resolution imaging/clearer images • Image more of the planet as the Earth spins underneath the satellite Geostationary: • Remain at the same position in the sky so satellite dishes can keep locked on to signal/no steerable dishes needed/ send & receive signals all the times/continuous/uninterrupted/stable signals • Higher orbit means greater coverage of the signals A1 A1 3 (a) angular speed of grating, ω = 2 π / T = 2 π / 3.0 = 2.1 rad s -1 A1 (b) The peaks represent the positions of constructive interference/maxima. B1 B1

The effect of diffraction through the slits of diffraction grating causes interference fringes of higher order to have lower intensity than the zeroth order maxima. (Peak C corresponds to the zeroth order of the diffraction pattern whereas peaks B and D the first order and Peaks A and E the second order.) (c) (i) Time interval = 3.7 x 0.1 = 0.37 s θ = ωt = 2.1 x 0.37 = 0.78 rad (ecf) C1 A1 (c)(ii) Using the grating equation n λ = d sin θ, d = 1 x 10-3 / 55