HCI SPECIMEN PAPER D Higher Paper Answer

1 Name: __________________________________ ( ) Class: _________ HWA CHONG INSTITUTION SAMPLE D HIGHER PHYSICS Level : Secondary Three Duration : 1 hour INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your name, index number and class on the top of this page. Answer the questions in Section A and B in the spaces provided. All workings must be shown. In Section B, answer only 2 questions out of the 3 questions. INFORMATION FOR CANDIDATES In Sections A and B, the intended marks for each question or part of a question are given in brackets [ ]. Any working should be done in the space provided. When necessary, take acceleration due to gravity, g to be 10 m s-2. ______________________________________________________________________ This question paper consists of 12 printed pages, including this page.

2 Section A [20 marks] 1 This question is about liquid flow. The diagram shows a storage container for liquids. The container is filled from above. The distance between the base of the container and the ground is h0. The initially empty container is then filled at a constant rate. The height h of the liquid surface above the ground is measured as a function of tim e t. The results of the measurements are shown plotted on the following page.

3 (a) Draw a best-fit line for the data. [1]: Line going through each error bar [1] (b) It is hypothesized that h is directly proportional to t. State and explain whether this hypothesis is correct for the periods (i) 0 to 120 s.tt== [1]: line does not go through (0,0) / origin. Hence, no. [1] (ii) 120 s.t [1]: line is curved / gradient, not constant. Hence, no [1] 3.5 4.5 5.5 6.5 7.5 8.5 0 200 400 600 800 1000 Liquid surface height above ground h / m time t / s [1]: graph starts at the same point but half initial gradient by eye; [1]: line always lower than original by eye and ending about 1/4 way down y-axis

4 (c) Use data from the graph to determine the value of 0h . [1]: line is drawn to find intercept on the y-axis [1]: ..4 2 0 1 m [2] (d) The area of the base of the container is 1.8 m 2. Deduce that the volume of liquid entering the storage container each second is approximately .. 310 02 m s− large (at least half of line) triangle from a straight-line portion of the graph [1]: ( ) ( ).. 1slope 0 012 0 001 ms −= [1]: . 31volume per second 0 022 m sarea slope −=  = Alternatively, determines height difference over time range within 0 and 120 s ( ). . 311 8 difference in heightsvolume per second 0 022 m stime between heights −== [2] (e) The container is filled after 850 s. Calculate the total volume of the container. ( ) ( ).. 33850 0 022 19 m or 850 0 02 17 m =  = Volume = ………………………. m3 [1] (f) The empty container is now filled at half the rate in (d). Using the same axes on page 3, sketch a graph to show the variation of h with t in the range 0 to 900 s.tt== [2]

5 2 This question is about waves in earthquakes. P and S waves are waves associated with earthquakes. A P wave is a compressional wave. The disturbance travels longitudinally with the particle motion. A n S wave is a shear wave because the particle motion is perpendicular to the direction of wave travel. (see the picture below) Longitudinal P wave Transverse S wave In an earthquake, a P wave and an S wave travel at different speeds, and we can use this difference to help us locate the ‘epicentre’ of the earthquake (where the disturbance took place). (a) Assuming typical speeds of 8.5 km s -1 and 5.5 km s -1 for P and S waves, respectively, how far away did an earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 minutes apart? [1]: conversion of units to be consistent, e.g. 1.5 min to 90 s [1]: Let t be the time taken for the P wave and 90 t− time taken for the S wave ( ) ( )P wave 1 S wave 1 90v t v t =− [1]: ( )( ) ( )( )118500 5500 90tt =− [1]: .1 35 36 st = [1]: .. 5Distance from earthquake 8500 35 36 3 0 10 m=  =  Solution by graphical methods, i.e. using geometrical shapes to determine areas under vt− graphs, are accepted. distance from epicentre = ………………………………….. m [5]

6 (b) Is one seismic station sufficient to determine the position of the epicentre? If yes, explain your reasoning. If not, suggest the minimum number of stations need ed to determine the epicentre position and explain your reason. You may use the space below to draw diagrams for your explanation. [1]: minimum 3 stations are needed. [1]: idea of distance in (a) provide a locus of radius . 53 0 10 m [1]: idea that a minimum of three circles are needed for a specific intersection point. [3] (c) P waves tend to shake buildings vertically (up and down), while S waves tend to cause buildings to shake horizonta lly (left and right). This wave is not the same as the drawings on page 5 because the waves are deep inside the Earth and not surface waves. State and explain which type of wave is more damaging. [1]: S waves [1]: Buildings are built to withstand weight which is acting vertically and not necessarily in vertical direction. [2]

7 Section B [20 marks] Answer two out of three questions in this section. 3 This question is about optics. A small disc, 6 mm in diameter, lies centrally at the bottom of a cylindrical beaker of height 150 mm and is illuminated from below. A converging lens of focal length 100 mm rests on the rim of the beaker and forms an image of the disc. You can assume that the lens is thin. (a) Determine, by calculation or otherwise, the image distance of the disc. [1]: 1 1 1 1 1 1 100 150f u v v= +  = + [1]: 300 mmv= Image distance = …………………….. mm [2]

8 (b) The beaker is now filled with water to a height .h Derive an equation, in terms of h , for the effective object distance. Take the refractive index of water to be 4 3 . [1]: Real depth 4 3 3 Apparent depth Real depthApparent depth 3 4 4nh= =  =  = [1]: Object position is elevated by 1 4 h [1]: 1Effective object distance 150 4 h=− [3] (c) Based on the equation that you have worked out in (b), explain whether it is possible to form a virtual image for this set-up. [1]: .3minimum effective object distance 112 5 mm4 h== [1]: larger than the focal length, hence no ecf permitted for this question [2] (d) When the water level is at half the beaker’s height, the image appears at a distance of 420 mm away from the lens. Calculate the diameter of the new image. [1]: ( ). 420Magnification, M 1150 0 5 1504 v u== − [1]: ( ) ( ) . 420Image size M object size 6 mm 1150 0 5 1504 =  =  − [1]: .19 2 mm= Image diameter = …………………. mm [3]

9 4 This question is about forces and motion. (a) Two identical boxes, A and B, stand on a floor with two sides parallel and only a few cm apart , as shown. Insert a long stiff pole vertically in the space between the boxes and pull horizontally at the upper end of the pole to separate the boxes. Will both boxes move simultaneously or just one of them? If it is one of them, whic