Dimensional Analysis

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 = 2πL

g

(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 M

r

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.