HCI Assignment 01 Physical quantities, units and measurements

Physical Quantities, Units & Measurements 1 Name: Index No: Date: Class: Assignment 01: Physical quantities, units and measurements (IP) 1. (a) Make the following conversions. Show your working clearly. [9] (i) Express 2 x 10-2 MHz in kHz. (ii) Express 4.8 x 102 µm in cm. 2 x 10-2 MHz = 2 x 104 Hz = 20 kHz [1] 4.8 x 102 µm = 4.8 x 10-4 m = 0.048 cm [1] (iii) Express 905 mm2 in cm2. (iv) Express 90 km h-1 in m s-1. 10 mm = 1.0 cm Square both sides. 100 mm2 = 1.0 cm2  905 mm2 = = 9.05 cm2 [1] 90 km h-1 = h km 1 90 = s m 3600 00090 [1] = 25 m s-1 [1] (v) Express 1.36 x 104 kg m-3 in g cm-3 in standard form. (vi) Express 5.24 x 103 cm min-1 in m s-1 in standard form. 1.36 x 104 kg m-3 = 3 4 1 1036.1 m kg = 3 4 0000100 )10001036.1( cm g [1] = 1.36 x 101 g cm-3 [1] 5.24 x 103 cm min-1 = min1 1024.5 3 cm = s m 60 )101024.5( 23 − [1] = 8.73 x 10-1 m s-1 [1] (b) Derive, in terms of base units, for: (i) the watt W, the unit for power, where power is the rate of work done. (ii) the coulomb C, the unit for charge, where electric current is the rate of flow of electric charge. Show your working clearly. [2] (i) power = work done / time taken 1 W = 1 kg m2 s-2 / s = 1 kg m2 s-3 [1] (ii) current = charge / time taken 1 A = 1 C / 1 s  1 C = 1 A s [1] HWA CHONG INSTITUTION Sec 3 Physics Note: For conversion, preserve the most s.f. as the quantity is usually used for subsequent calculations.

Physical Quantities, Units & Measurements 2 2. Fig. 2.1 shows the design of a window grille and Fig. 2.2 shows the magnified diagram of a metal bar segment attached to the window grille. Fig. 2.1 Fig. 2.2 (a) The length of the metal bar segment, L, is measured usi ng a pair of digital calipers and recorded as 124.6 mm. Using informatio n from Fig . 2.1 and 2.2 , state the instrument that is able to measure the following dimensions most precisely. (i) Height of metal grille, H ...............metre rule/measuring tape.................. [1] (ii) Thickness of metal bar segment, T ..................digital micrometer......................................... [1] [Note: Spelling of instruments] (b) Given that T = 1.21 cm, determine the volume of a metal bar segment, in cm3. [2] Volume of metal bar segment = 1.21 cm x 1.83 cm x 12.46 cm [1] = 27.59 = 27.6 cm3 (correct to 3 s.f.) [1] (c) Convert your answer in (c) to SI unit and leave your answer in standard form. [2] 27.6 cm3 = 27.6 / 1000 000 [1 m3 = 1000 000 cm3] = 2.76 X 10 -5 m3 [1: conversion] [1: standard form] [Note: preserve s.f. for conversion] (d) There is a discrepancy between the actual volume and the theoretical volume of the metal bar segment. According to the specifications, the theoretical volume of the bar segment is 28.5 cm 3 with an error tolerance of 5%. Determine if the actual volume of the metal bar segment in (c) is acceptable within its tolerance. [2] Minimum volume within tolerance = 0.95 x 28.5 = 27 cm3 Maximum volume within tolerance = 1.05 x 28.5 = 29.9 cm3 [1: appropriate calculations made] Since the actual volume of 27.6 cm 3 falls in the range of 27 cm3 to 29.9 cm3, it is acceptable within its tolerance. [1: explanation] H T 1.83 cm L

Physical Quantities, Units & Measurements 3 3. Fig. 3.1 shows a square metal bar. Fig. 3.1 (a) Suggest the laboratory instruments a student should use to measure the dimensions of the square bar to the required precision as stated in Fig. 3.1. [2] Instrument to measure thickness of bar: Digital micrometer (9.53 mm) Instrument to measure length of bar: Digital calipers (6.48 cm) (b) The student took a few readings to determine the thickness of the square bar at different positions and obtained the average value of the dimension. Why is this step necessary? [2] There will be greater accuracy [1] as thickness of bar may not be uniform across its length [1]. [Note: wrong to write ‘to reduce random error ’ as the non-uniformity of the thickness of the bar is a variation of the object and not due to the random nature of measurement.] (c) The mass of the bar is measured to be 5.021 x 10 -2 kg. Determine the density of the bar , in g cm -3, to the correct number of significant figures. Hence , state the material which the bar is possibly made of, with reference to the given list of metals below. [3] material density / g cm-3 aluminum 2.70 copper 8.93 iron 7.87 zinc 7.13 brass 8.60 Volume of bar = 0.953 cm x 0.953 cm x 6.48 cm = 5.8852 cm3 [leave to more s.f. for subsequent calculations] Density = mass/ volume = 5.021 x 10-2 kg / 5.8852 cm3 [1] = 50.21 g / 5.8852 cm3 = 8.53 g cm-3 (to 3 s.f.) [1] The bar is possibly made of brass. [1] 6.48 cm 9.53 mm

Physical Quantities, Units & Measurements 4 4. The following formula is related to thermal properties. By using the values shown in the table, work out the answer to the appropriate unit and presentation. physical quantity value of quantity power, P 36 J s-1 time taken, t 1.86 x 103 s mass, m 0.20 kg change in temperature,  81 K Use the formula Pt = mc() to find the specific heat capacity, c, of the liquid. [3] Pt = mc (36 J s-1)(1.86 x 103 s) = (0.20 kg)(c)(81 K) [1] c = 4133 c = 4.1 x 103 J/(kg K) (2 s.f.) [1: correct s.f.][1: correct unit. Accept J kg-1 K-1.] 5. Fig. 5.1 shows an experimental set up used by a student to determine the period of the pendulum. The student observes the swinging pendulum from the position shown in Fig. 5.1. Using a stop watch, the student measures the time for 40 swings. Each swing is taken to be the planar motion of the bob from A to B or B to A. He repeats the process three times and records the reading in the table shown in Fig. 5.2. After some calculations, he concludes that the period of the pendulum is 1.0 2 s. The length of the pendulum bob is 1.000 m. Fig. 5.2 Fig. 5.1 Source: https://pngtree.com/freepng/painted-back-home-boy-character-back-view-design_4376506.html (a) A teacher approaches the student and tells him that he is observing the pendulum from the wrong position. Suggest what the student can do to correct this mistake. [1] Position himself so that his line of sight is perpendicular to plane of motion of pendulum. [1] [X: Position the eye at the same level as the pendulum bob / parallax error.] plane of motion laboratory bench retort stand A B C Reading Time for 40 swings / s Period / s 1st 40.6 1.02 2nd 41.3 1.03 3rd 40.2 1.01 Average 40.7 1.02 Some students expressed unit of c in base units which is m2 s-2 K-1 which is also correct, but not necessary as it is not specified in the question.

Physical Quantities, Units & Measurements 5 (b) The student also makes a mistake when he determined the period of the pendulum during the experiment. (i) State the correct period