Chapter 1ENGINEERING PHYSICS I.pdf

ENGINEERING PHYSICS I ELECTRICITY AND MAGNETISM DR.MOHAMED MOSTAFA ELFAHAM Associate Prof. of Physics Basic Science Department Faculty of Engineering Banha University E-Mail : [email protected] Vector vs. Scalar A library...

ENGINEERING PHYSICS I ELECTRICITY AND MAGNETISM DR.MOHAMED MOSTAFA ELFAHAM Associate Prof. of Physics Basic Science Department Faculty of Engineering Banha University E-Mail : [email protected] Vector vs. Scalar A library is located 0.5 m from you. Can you point where exactly it is? You also need to know the direction in which you should walk to the library! All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (value + unit) and direction A scalar quantity is completely specified by only a magnitude (value + unit) Vector and Scalar Quantities  Vectors  Scalars: Displacement Distance Velocity (magnitude and direction!) Speed (magnitude of Acceleration velocity) Force Temperature Momentum Mass Energy Time To describe a vector we need more information than to describe a scalar! Therefore vectors are more complex! Important Notation  To describe vectors we will use: The bold font: Vector A is A  Or an arrow above the vector: A In the pictures, we will always show vectors as arrows Arrows point the direction To describe the magnitude of a vector we will use  absolute value sign: A or just A, Magnitude is always positive, the magnitude of a vector is equal to the length of a vector. Properties of Vectors Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction Movement of vectors in a diagram Any vector can be moved parallel to itself without being affected  Negative Vectors Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)    A  B; A  A  0 A  B Adding Vectors When adding vectors, their directions must be taken into account Units must be the same Geometric Methods Use scale drawings Algebraic Methods More convenient Adding Vectors Geometrically (Triangle Method)  Draw the first vector A with the appropriate length and in the direction specified, with respect to a coordinate system    A B  Draw the next vector B with the appropriate length B and in the direction specified, with respect to a coordinate system whose origin is the end of vector and parallel to the coordinate system used for : “tip-  to-tail”. A  The resultant is drawn  from the origin of A to the end of the last vector B Adding Vectors Graphically When you have many vectors, just keep repeating the process until   A B all are included The resultant is still drawn from    A B C the origin of the first vector to the end of the last vector   A B http://www.physicsclassroom.com/mmedia/vectors/ao.cfm  Adding Vectors Geometrically (Polygon Method)    A B Draw the first vector A with the appropriate length and in the direction specified, with respect to a coordinate system  B  Draw the next vectorB with the appropriate length and in the direction specified, with respect to the  same coordinate system A Draw a parallelogram The resultant is drawn as a diagonal from the origin     A B  B  A Vector Subtraction Special case of vector addition Add the negative of the  subtracted vector B A  B  A  B   Continue with standard vector A  addition procedure   B A B Describing Vectors Algebraically Vectors: Described by the number, units and direction! Vectors: Can be described by their magnitude and direction. For example: Your displacement is 1.5 m at an angle of 250. Can be described by components? For example: your displacement is 1.36 m in the positive x direction and 0.634 m in the positive y direction. Components of a Vector The x-component of a vector is the projection along the x-axis A cos q  x Ax  A cos q A The y-component of a vector is the projection along the y-axis Ay sin q  Ay  A sin q A q Then,    A  Ax  Ay A  Ax  Ay  Components of a Vector The previous equations are valid only if θ is measured with respect to the x-axis The components can be positive or negative and will have the same units as the original vector θ=0, Ax=A>0, Ay=0 θ=45°, Ax=Acos45°>0, Ay=Asin45°>0 ax < 0 ax > 0 θ=90°, Ax=0, Ay=A>0 ay > 0 ay > 0 θ θ=135°, Ax=Acos135°0 ax < 0 ax > 0 θ=180°, Ax=-A