Date: 28 Oct 2021 (Thursday) Test Time: 20:00 – 21:00 Submission Time: 20:00 – 21:15 Submission Deadline Time: 21:15 (Late submission will not be accepted) Scope: L1 – L6, and corresponding tutorials Format:
Take-home Test (Open Book Test)
Four Programming Questions, 25 marks each
Type your answers on the answer sheet provided (available in Moodle before the test). Submit the PDF format of the answer sheet to Moodle submission link.
Q3. The structure is under two concentrated forces, one distributed force, and one concentrated moment as shown, Assume the support at B is a roller, and C is a fixed connected joint. Determine (a) the reactions at supports A and B, (b) the maximum bending moment in the structure.
According to the graph, the opportunity cost incurred by the economy to increase its production of rice from 50 tons to 85 tons would be 25000-10000=15000 cars.
b)
According to the graph, only points on the production probability curve utilises its existing resources efficiently. They would be point B,C and D.
c)
Point a is above the production potential current, so using its current resources cannot achieve combination A unless more resources are borrowed.
d)
i)
Rainstorm will do harm to rice fields and increase the production cost of rice, which can also be understood as the reduction of resources for rice production. At the same time, the rainstorm may inundate the automobile factory, which will increase the production cost of automobiles, which can also be understood as the reduction of resources used to produce automobiles. Therefore, the PPC curve will move to the left and down as a whole.
ii)
If Japan relocates its car factories to higher ground, future floods will mainly affect rice fields, increasing the production cost of rice. It can also be understood as reducing the resources used to produce rice, but almost without affecting the production of cars. Therefore, the PPC curve moves to the left on the rice side, while the car side remains basically unchanged.
a) A jet of water coming out of a tap always breaks up into a series of drops. It has been observed experimentally that these drops vibrate. Use dimensional analysis to predict how the frequency of vibration of the water drops will depend on their density, radius and surface tension. f6g b) An ideal polarising filter is oriented such that incident horizontally polarised light is transmitted 100% and vertically polarised light is all absorbed. (These directions relate to the electric field). (i) When light of amplitude E0 = 200 Vm1 and linearly polarised at 45% to the vertical is incident, what polarisation and what amplitude is transmitted? f4g (ii) When circularly polarised light of the same amplitude is incident, what polarisation and what fraction of the incident amplitude is transmitted? f3g c) An outdoor sound system comprises two identical loudspeakers distance d = 5 m apart as sketched in the diagram below. As part of a test they are both fed the same pure note, of same amplitude A0 and phase, corresponding to a sound wavelength l = 0:6 m (and same frequency w). L y d P y = 0 S1 S2 (i) The speakers S1 and S2 emit waves y1 = A0 cos (kx1wt) ; y2 = A0 cos (kx2wt) ; respectively, where k is the wavenumber and x1 and x2 are distances measured from S1 and S2. Show that the total wave at P is given by y (x; t) = 2A0 cos (kX Wt)cos(kD) ; and define X;W and D. f4g (ii) Show that for y << L the sound amplitude at point, P, in the diagram is expected to be proportional to cos pdy lL f4g: (iii) An observer stands L = 20 m away, at y = 0. They move along the positive y-direction. At what value of y(> 0) will they first hear a maximum amplitude. f4g
