Mr Rishi Gopie Scalar and Vector Quantities
PHYSICS
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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 Vector Quantity Time Displacement Mass Velocity Distance Acceleration Speed Force Area Momentum Volume Density Energy Work Pressure power Temperature Current voltage
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
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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
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Examples:
State the magnitude and direction of the resultant force in each of the following systems Show all your working.
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Diag. 3
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TUTORIAL June 1995 paper 3 #1
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June 1997 paper 2 #2
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January 1999 paper 2 # 2
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