Dimensional Analysis

PHYS 101: Homework 1 Instructions (a) The questions in this homework assignment are based on your lectures and material in Chapter 1 of your prescribed textbook. Answer all questions and (where necessary) clearly motivate each step of your reasoning. (b) You are guaranteed to excel in tests and examinations if you fully understand how to answer the questions in this assignment. (c) Express final numerical answers in scientific notation. (d) Please write your name and student number on each page of your assignment. Staple all pages together. Work neatly. (e) The assignment must be handed in BEFORE the start of class on Monday morning, 12 December 2016. No late submissions will be accepted. Questions 1. What is Physics and why is it necessary for you to study Physics at BIUST? 2. Within the context of Dimensional Analysis, explain what is meant by the concept of a dimension. 3. Give three examples of dimensions. 4. What is meant by the method of dimensional analysis and why is it useful in Science and Engineering? 5. Use Dimensional Analysis to find a possible equation relating acceleration (a), speed (v), and radius (r) for an object moving at constant speed in a circle. 6. Given that energy (E) carries the dimensions of mass times length squared divided by time squared, use Dimensional Analysis to find a possible equation which related energy (E) to mass and speed. 7. The period (T) of a pendulum is measured in time units and is related to acceleration (g) and length (L) via the following equation (that you will be able to derive at a later stage this course): T=2πLg (a) Is this equation dimensionally consistent? Motivate your answer using Dimensional Analysis. (b) Is this equation unit consistent? Motivate your answer. 8. True or false. An equation that is dimensionally correct is always physically correct, up to a constant of proportionality? Give an example (from high school Physics) to motive your answer. 9. Newton’s Law of Universal Gravitation is represented by the following equation: F=G m Mr where F is the gravitational force expressed in SI base units of kg m/s2, and represents a distance between two objects with masses m and M. Determine the SI base units of the proportionality constant G? 10. The period T of a pendulum is measured in time units is given by the following formula: =2 + where g is the gravitational acceleration, m denotes mass, and A is a constant. (a) Express in terms of SI base units. (b) What are the SI base units of ? 11. The consumption of natural gas by a company satisfies the following empirical equation: V=1.50 t+0.0800t where V is the volume in cubic meters and t is the time in seconds. (a) Explain why the above equation is NOT dimensionally consistent. (b) Rewrite this equation in a form that is dimensionally consistent? 12. Convert 6.30 g/cm to units of kg/m. 13. A solid object has a mass of 6.30 μg and a volume of 4.2 dm3. What is the density of the object in SI base units? 14. Explain what is meant by the concept of a significant figure within the context of a measurement. 15. A person measures a length to be 25.0 cm. (a) How many significant figures does this measurement have? (b) What is the uncertainty (or error) in this measurement? (c) Between which minimum and maximum values does the measurement lie? 16. A person measures a mass to be 26 kg. (a) How many significant figures does this measurement have? (b) What is the uncertainty (or error) in this measurement? (c) Between which minimum and maximum values does the measurement lie? 17. How many significant figures do the following measurements contain: (a) 0.03 cm (b) 0.0037840 kg (c) 1.0045 m (d) 1.020 m (e) 0.0405 s (f) 200 kg (g) 1.00 × 10 kg 18. State the addition/subtraction rule for working with significant figures. 19. State the multiplication/division rule for working with significant figures. 20. Perform the following calculations to the correct number of significant figures (all numbers with units are the results of measurements, whereas all other numbers are exact.): (a) 0.0036 m ×81.520 m (b) 0.0036 m+ 81.520 m (c) . . (d) 2.0 m+ 3 kg (e) . ( )(. )(. ) (. )[NOTE: only round-off in the final answer] (f) sin(3° × 10) (g) sin(3 0.0°) (h) √3.16 m (i) (2 m)cos(54.78°) 21. Estimate the order of magnitude of the number of ping pong (table tennis) balls that would fit into your tutorial venue without being crushed. Clearly explain your assumptions and explain each step of your reasoning. 22. Suppose that someone offers to give you 1 billion dollars if you can finish counting it out using only one-dollar bills. Estimate the order of magnitude in years that it will take you to finish counting? Assume that you can count one bill every second, and be sure to note that you need about 8 hours a day for sleeping and eating. Clearly explain your assumptions and explain each step of your reasoning.