1.4 VECTORS & SCALARS 1.4 VECTORS & SCALARS

1.4.1 Distinguish between vector & scalar quantities, and give examples of each SCALAR LengthLength SpeedSpeed TimeTime MassMass VolumeVolume EnergyEnergy TemperatureTemperature PressurePressure PowerPower chargecharge VECTOR Displacement Velocity Acceleration Force Weight Momentum Torque Electric current Electric field Magnetic field flux density

What is the difference between scalar & vector quantities? Scalar (Latin: pertaining to a ladder) Have magnitude (size) onlyHave magnitude (size) only Can be added algebraically and linearlyCan be added algebraically and linearly Cannot be resolved into different planesCannot be resolved into different planes Vector (Latin: to carry) Have both magnitude & direction Can only be added linearly if they are in the same plane…ie, in the same direction Can be resolved into components in different planes Represented by a line with an arrow on the end to represent direction (length of line can be scale)

Adding Vectors Diagrammatically A vector can be represented by a scale arrowed line. The length represents the magnitude of the vector & the arrow represents the direction.A vector can be represented by a scale arrowed line. The length represents the magnitude of the vector & the arrow represents the direction. Ex:10ms -1 East Ex:10ms -1 East Therefore, let 2 cm = 5ms -1 10ms -1 Therefore, let 2 cm = 5ms -1 10ms -1

RULES for adding vectors Vectors are always added from tail to tipVectors are always added from tail to tip Ex:5m North + 5m EastEx:5m North + 5m East 5m

Resolving Vector Diagrams The solution to a vector diagram is the length from the tail of the first vector arrow to the tip of the last vector arrow (& then use the scale to resolve).The solution to a vector diagram is the length from the tail of the first vector arrow to the tip of the last vector arrow (& then use the scale to resolve). The angle/direction must be included in your answer. This is the angle from the starting point to the tip of the last arrow.The angle/direction must be included in your answer. This is the angle from the starting point to the tip of the last arrow.

Try this problem. Michael runs at 15ms -1 South & the runs West at 20ms -1. Find his average velocity. V 2 = v = 25ms -1 15ms -1 20ms -1

The Parallelogram method Draw the two vectors tail to tail.Draw the two vectors tail to tail. Use the correct angle between the two tips and add the other vector to the tip. Use the correct angle between the two tips and add the other vector to the tip. The vector diagram should now be closed with the solution being the length from the original starting point (tails) to the finishing point (tips).The vector diagram should now be closed with the solution being the length from the original starting point (tails) to the finishing point (tips).

Try this problem. Michael runs at 15ms -1 South & the runs West at 20ms -1. Find his average velocity. 15ms -1 20ms -1 15ms -1 20ms -1

Resolving Into Components In some instances the vector must be resolved into its components before adding them back together.In some instances the vector must be resolved into its components before adding them back together. Components can be:up, down, vertical, horizontal, left, right, to the horizon, x, y, z etc…Components can be:up, down, vertical, horizontal, left, right, to the horizon, x, y, z etc… Trigonometric ratios are required (SOH, CAH, TOA)Trigonometric ratios are required (SOH, CAH, TOA)

Try this problem. Resolve 30ms -1 at 40 0 above the horizontal into its’ vertical and horizontal components ms -1

ms -1 Vertically: U y = 30sin40 0 = 19.3 ms -1 Horizontally: U x = 30 cos40 0 = 22.98ms -1

An alternate method…graphically. You can also resolve vectors into components by graphical means…You can also resolve vectors into components by graphical means… Use accurate scale diagrams and your answer should be identical (often used when reading maps)Use accurate scale diagrams and your answer should be identical (often used when reading maps)

Try this problem: Dale pushes down with a force of 50N at 50 0 to the vertical. 50N 50 0 Scale: 1cm:10N

Try this problem: Dale pushes down with a force of 50N at 50 0 to the vertical. 50N 50 0