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F09W0

# F09W0 - Question 2 a — Ranking test Blocks suspended in...

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Unformatted text preview: Question 2 a — Ranking test: Blocks suspended in water (5 marks) A B C D E M= 150 g M= 100 g M: 200 g M= 50 g M= 100 g V = 50 cm3 V = 100cm3 V = 100cm3 V = 50cm3 V = 50 cm3 The six containers above each contain the same volume of water. Blocks of various solid materials are suspended in the containers by being hung from a supporting rod. The blocks vary in both size and mass as given in the diagram, note the mass given is in grams. Rank these situations from the greatest to the least on the basis of the tensions in the strings. Point out situations where the string tensions are equal. Largest Tension Smallest Tension Question 2b (10 marks) A two open—ended glass tubes inserted into a horizontal pipe are often used together to measure ﬂow velocity in a pipe. This conﬁguration is called a Venturi meter. Consider the arrangement below, where A1 = 0.500 m2 and A2 = 0.200 ml. The two vertical tubes are open to the atmosphere and the ﬂuid is water. a) If h; = 0.350 m, what is the gauge pressure P1 in the horizontal pipe on the left? b) If v2 = 0.40 rn/s, calculate the velocity V] and the height h2 Ph 101T 109w P 6 ys erm age wiﬂhyo gq «602.31% Q0 ﬁt (3:- SK 3LD=V "06 Question 3 (15 marks) The position versus time plots of two simple harmonic oscillators, A (represented by the solid curve) and B (represented by the dash curve) are shown in the ﬁgure below. (a) What are the amplitudes and time period for these oscillators? Amplitude of A = Amplitude of B = Time Period of A = Time Period of B = (b) What are the phase constants of these oscillators? Phase constant of A = Phase constant of B = (c) For each oscillator write an equation that gives position as a function of time, evaluate all constants. (d) What is the phase difference between the two oscillators at t = 1.0 s? (e) For oscillator B, at what time(s), less than t= 6 s, does it have zero velocity? (D For oscillator B, at what time(s), less than t = 6 s, is it movin with maximum 3 eed in the ne ative g g g x-direction? 5» ‘9 q \ 3 Phys 101 Terrnl 09W Page 7 = % raw. = 42 9% 29 ex 50.,” I sag 'woh'o 'wO-b‘o ""5 _ I Question 4a (8 marks) Six waves are described by the following equations, (distances in cm, time in seconds). D1 = 28in(3x — 4t) D2 = 28in(4x + 31‘) D3 = 23in(—6x — 2t) D4 = 2sin(—2x + 6t) D5 = 2003(6x - 4t) D6 = 25in(4x + 4t - at) i) Which of these waves are traveling in the negative x—direction? ii) Rank the waves according to their wavelength (Use = if appropriate) Greatest Smallest iii) Rank the waves according to their wave speed. (Use = if appropriate) Greatest Smallest iv) Write the equation of the wave which when combined with wave 2 will give a standing wave. v) Write the equation of a wave which interferes destructively with wave 2. KM*) in xﬂ)~fs~c 1(32+*h)"§\$‘g— Ln; C W3 \nn‘ 11: 96421000004430 K ‘ . 311 PhylelTerm109W Page8 SOsidgaczzOL.‘OLhO CEO/EO‘I'E‘O Q} “*1 Question 4b (7 marks) Two speakers are set up on your patio as shown in the diagram. After successfully completing Phys 101 you are concerned that at certain positions on the patio, there will positions of destructive interference for certain frequencies. For ease of calculation: ' assume that the grid size on the diagram is 1 meter each way ' the objects are on integer positions on the grid. ° take the speed of sound to be 340 m/s ' the speakers are in phase. i) If you are sitting in the middle of bench will this be a point of constructive or destructive interference, explain! ii) If you are sitting in the chair, what will be the lowest frequency at which there is destructive interference? iii) If you connect one of the speakers so that it is out of phase with the other one, can you restore the frequency lost in part ii) and does this change solve the problem of destructive interference for the person sitting in the chair? Please explain! iv) With one of the speakers out of phase with the other one, does this change the interference condition for someone sitting in the middle of the bench? Explain. “‘0 “Yo .wﬁm-KU‘S‘D we» ro\ mMjSQV‘RKSWD Q W1. 1 Phys]01Term109W Page9 74459) s j >00 as“? L ,‘3 2H 93> K 7.7. QaXQ mtqusuaj (1 «h Question 53 (7 marks) air n air A thin ﬁlm of material of thickness t and refractive index n=1.33 is suspended in air. Light of wavelength A is incident normally onto the ﬁlm. i) What is the phase change on reﬂection for beam 1? , ii) What is the phase change on reﬂection for beam 2? iii) Write down an equation for constructive interference of the two beams. t iv) Light of two wavelengths A1 = 420 nm and k2 = 700 nm are incident on the ﬁlm. What is the minimum thickness when both wavelengths are reﬂected with maximum intensity? Question 5b (8 marks) i) Coherent light of wavelength 500 nm is incident normally on two very ﬁne slits separated by 0.30 mm. Interference fringes are Viewed on a screen distant 1.5 m from the slits. What is the separation of the bright fringes close to the centre of the pattern? ii) The two slits are replaced by another pair also separated by 0.30 mm, but with a ﬁnite slit width of 0.075 mm. At what position at either side of the central point is the ﬁrst diffraction minimum? iii) For the pair of slits in b), how many bright fringes are in the central diffraction peak? Sketch a graph of the intensity for this pair of slits Phys 101 Terml 09W Page 10 Wu 95%) {n1 ...
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