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Mathematics for engineering technicians Unit 4

Mathematics for engineering technicians Unit 4. Handout No. 2 I Ford. Electronic Calculators'. Part of the pass criteria for this Math’s unit 2 is to be able to use a scientific calculator to solve calculations.

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Mathematics for engineering technicians Unit 4

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  1. Mathematics for engineering techniciansUnit 4 Handout No. 2 I Ford

  2. Electronic Calculators' • Part of the pass criteria for this Math’s unit 2 is to be able to use a scientific calculator to solve calculations. • This includes being able to enter & solve calculations in one single expression (this is sometimes referred to as a chained calculation). • You therefore need to know how to enter (and correct) complex expressions involving the use of brackets and fractions as well as basic arithmetic operations.

  3. Calculator examples (simple arithmetic) • 2 + 6 x 3 – 8 ÷ 4 Key in the following: [2] [+] [6] [x] [3] [-] [8] [÷] [4] [=] The answer should be 18 Do the following examples: • 27 – 9 x 2 + 12 ÷ 3 (13) • 2 + 4 ÷ 0.5 – 1.5 x 2 (7) • 15 ÷ (9 – 4) + 1.5 x 2 – 5 (1) • 2 x 0.4 – 10 ÷ (3.5 – 1.5) (-4.2)

  4. Calculator examples (indices) 2. 33 x 45÷ 48 Key in the following: [3] [X▪] [3] [►] [x] [4] [X▪] [5] [►] [÷] [48] [=] The answer should be 576 Do the following examples: • 43÷ 44 (0.25) • 103 x 102 (100,000) • (6) d) √9 x √16 (12)

  5. Calculator examples (Engineering notation) 3. 1.23 x 103 + 7.7 x 104 Key in the following: [1] [ . ] [2] [3] [x10x] [3] [+] [7] [ . ] [7] [x10x] [4] [=] [ENG] The answer should be 78.23 x 103 Do the following examples: • 0.6 x 106 + 1.9 x 105 (790 x 10-3) • 5.1 x 10-3 - 3.6 x 10-2 (30.9 x 10-3) • 27 x 105 x 0.15 x 10-3 (405) • 0.45 x 105÷ 17 x 107 (26.4705882 x 10-3)

  6. Formulae (use of) • When we need to understand the relationship between different quantities, we often express this in the form of a formula (equation). • To save time and effort, we write the equation using symbols rather than words

  7. Formulae (use of) example • The relationship between the distance travelled in relation to speed and time could be written as: ‘The distance travelled is the same as speed divided by time’ • However, it is easier to write an equation: S = v x t • Engineers frequently need to find the value of an unknown quantity

  8. Statement of a formula • The following statement is a formula for R in terms of ρ, l and a • The term on the left side is called the subject of the formula. • If the value of three of the four symbols are given then the forth may be calculated.

  9. Formulae examples • A current of 0.5 A flows in a 56  resistor. Given that V = I R, determine the voltage that appears across the resistor. Solution It is a good idea to get into the habit of writing down what you know before attempting an equation: We know that: I = 0.5 A R = 56  Formula given is: V = I R Therefore: V = 0.5 x 56 V = 28 V

  10. Evaluating Formulas • The surface area (A) of a hollow cone is given by the fomulae: A = rl Find the surface area in cm2 when r = 4.0 cm and l = 9.0 cm. Give the answer to 3 significant figures. (Answer=113 cm2) 2. In an electrical circuit the voltage (V) is given by V = IR. Find the voltage, when I = 7.240 ampres and R = 12.57 ohms. Give the answer to 4 significant figures. (Answer=91.01V) • A formula for calculating velocity (v m/s) is given by v = u + at. If u = 12.47 m/s, a = 5.46 m/s2 and t = 4.92 s, find v to 2 decimal places. (Answer=39.33 m/s) 4 . The area (A m2) of a circle is given by A = r2. Find the area correct to 2 decimal places given r = 4.156 m (Answer=54.26 m2)

  11. Evaluating Formulas continued 5. The power (P watts) in an electrical circuit may be expressed by the formula: Evaluate the power correct to 2 decimal places, given that V = 24.62 volts and R = 45.21 ohms. (Answer=13.41W) 6. The volume (V cm3) of a right circular cone is given by the formula: Given r = 5.637 cm and h = 16.41 cm, find the volume in standard form to 3 significant figures. (Answer=5.46x102 cm3)

  12. Evaluating Formulas continued • If force (F newtons) is given by: Where m1 and m2 are masses d their distance apart and G a constant Find the force (F) given: G = 6.67 x 10-11 Nm2kg-2 m1 = 8.43 kg m2 = 17.2 kg d = 24.2 m Express the answer in standard form to 3 significant figures. (Answer=1.65x10-11 N)

  13. Evaluating Formulas continued • The time (t seconds) of a swing of a simple pendulum is given by the formulas: Find the time, correct to 3 decimal places, given l = 13.0 m and g = 9.91 ms-2 (Answer=7.233 s) • A formula for resistance variation with temperature is: R = R0 ( 1 + t) Given that : R0 = 15.42 ohms = 0.002 70 t = 78.4C Evaluate R, correct to 2 decimal places (Answer=18.68)

  14. Evaluating Formulas continued 10. The area of a rectangle is given by: A = bh. Find h when: A = 43.5 cm2 b = 4.63 cm (Answer=9.98 cm)

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