PHYSICS Mr Rishi Gopie Scalar and Vector Quantities Mr R Gopie PHYSICS SCALAR AND VECTOR QUANTITIES A scalar quantity is one that has magnitude A vector quantity is one that has both magnitude and direction Consider examples of both: Scalar Quantity Time Mass Distance Speed Area Volume Density Energy Work Pressure power Temperature Current voltage Vector Quantity Displacement Velocity Acceleration Force Momentum Any vector quantity can be represented by a straight line – the length of the line, drawn to some suitable scale, will represent the magnitude of the vector quantity and the direction of the line, as indicated by an arrow head drawn on the line will represent the direction of the vector quantity. In fact, such a line itself is called a vector. When vectors are added a resultant vector is produced. A resultant vector is that single vector which can replace a system (two or more) vectors all have the same overall or net or resultant effect as the system itself. Consider the resultant vector when two vectors are added is a) Parallel (i.e. act in the same direction) V1 + V2 Resultant Vector VR = (V1 + V2) Note that the greatest (i.e. maximum) resultant vector of any two vectors is obtained when the two vectors are parallel and its magnitude is given by the sum of the magnitudes of the two vectors Page 2 of 12 Mr R Gopie PHYSICS b) Anti-­‐parallel (i.e. acts in opposite directions) V1 + V2 Resultant V1 – V2 = Vr Note that the least (i.e. minimum) resultant vector of any two vectors is obtained when the two vectors are anti-­‐parallel and its magnitude is given by the difference between the magnitudes of the two vectors. c) Perpendicular (i.e. act in directions which are 90 degrees to one another The parallelogram rule is used i)
State a scale ii)
Draw a parallelogram of the vectors (V1 and V2) accurately to the scale iii)
Draw and measure the length of the appropriate diagonal that represent the resultant vector iv)
Convert the length of the diagonal, using the scale, to determine the magnitude of the resultant vector. The direction of this diagonal represents the direction of the resultant vector and can be stated either in terms of the angle ѳ it makes with V1 or in terms of the angle α it makes with V2. Diag. 2
Page 3 of 12 Mr R Gopie PHYSICS Examples: State the magnitude and direction of the resultant force in each of the following systems Show all your working. Page 4 of 12 Mr R Gopie PHYSICS Diag. 3 Page 5 of 12 Mr R Gopie PHYSICS TUTORIAL June 1995 paper 3 #1 Page 6 of 12 Mr R Gopie PHYSICS Page 7 of 12 Mr R Gopie PHYSICS June 1997 paper 2 #2 Page 8 of 12 Mr R Gopie PHYSICS Page 9 of 12 Mr R Gopie PHYSICS Page 10 of 12 Mr R Gopie PHYSICS January 1999 paper 2 # 2 Page 11 of 12 Mr R Gopie PHYSICS Page 12 of 12