Introduction and Mathematical Concepts Chapter 1 Introduction and Mathematical Concepts

Physics has developed out of the efforts 1.1 The Nature of Physics Physics has developed out of the efforts of men and women to explain our physical environment. Physics encompasses a remarkable variety of phenomena: planetary orbits radio and TV waves magnetism lasers many more!

Physics experiments involve the measurement 1.2 Units Physics experiments involve the measurement of a variety of quantities. These measurements should be accurate and reproducible. The first step in ensuring accuracy and reproducibility is defining the units in which the measurements are made.

SI units meter (m): unit of length kilogram (kg): unit of mass second (s): unit of time

1.2 Units

The units for length, mass, and time (as well as a few others), are regarded as base SI units. These units are used in combination to define additional units for other important physical quantities such as force and energy.

A scalar quantity is one that can be described by a single number: 1.5 Scalars and Vectors A scalar quantity is one that can be described by a single number: temperature, speed, mass A vector quantity deals inherently with both magnitude and direction: velocity, force, displacement

1.6 Vector Addition and Subtraction Often it is necessary to add one vector to another.

1.6 Vector Addition and Subtraction

1.6 Vector Addition and Subtraction When a vector is multiplied by -1, the magnitude of the vector remains the same, but the direction of the vector is reversed.

1.7 The Components of a Vector

1.7 The Components of a Vector

1.7 The Components of a Vector It is often easier to work with the scalar components rather than the vector components.

1.8 Addition of Vectors by Means of Components

1.8 Addition of Vectors by Means of Components

Example 1.1 A vector A has a magnitude of 20cm at 200⁰, and a vector B has a magnitude of 37cm at 45⁰. What is the magnitude and direction of vector difference A – B? Solution: Vector Distance Angle X-component Y-component A 20cm 200⁰ Ax = 20cos200⁰ Ay = 20sin200⁰ B 37cm 45⁰ Bx = 37cos45⁰ By = 37sin45⁰ A – B -44.95cm -33.00cm

Magnitude: |A - B|= [(Ax – Bx)2 + (Ay – By)2] = [(-44.95)2 + (-33.00)2]2 = 55.76cm Direction: θ = tan-1 [(Ay – By)]/[(Ax – Bx)] = [-33.00/-44.95] = 36.28⁰ = 216.28⁰

Problems to be solved 1.36, 1.51, 1.52, 1.57, 1.63, 1.65 B1.1: A disoriented physics professor drives 4.92km east, then 3.95km south, then 1.80km west. Find the magnitude and direction of the resultant displacement, using the method of components.

B1.2: The three finalists in a contest are brought to the centre of a large, flat field. Each is given a meter stick, a compass, a calculator, a shovel, and (in a different order for each) the following three displacements: 72.4m, 32⁰ east of north, 57.3m, 36⁰ south of west, 17.8m straight south. The three displacements lead to the point where the keys to a new Porsche are buried. Two contestants start measuring immediately, but the winner first calculates where to go. What does he calculate?

B1. 3: After an airplane takes off, it travels 10. 4km west, 8 B1.3: After an airplane takes off, it travels 10.4km west, 8.7km north, and 2.1km up. How far is it from the take-off point?