2 Vector and Scalar Quantities Quantities that require both magnitude and direction are called vector quantities.Examples of vectors are Force, Velocity and Displacement.
3 Vector and Scalar Quantities Quantities that require just magnitude are known as Scalar quantities.Examples of scalar quantities are Mass, Volume and Time.
4 Vector Representation of Force Force has both magnitude and direction and therefore can be represented as a vector.
5 Vector Representation of Force The figure on the left shows 2 forces in the same direction therefore the forces add. The figure on the right shows the man pulling in the opposite direction as the cart and forces are subtracted.
6 Vector Representation of Velocity The figure on the left shows the addition of the wind speed and velocity of the plane.The figure on the right shows a plane flying into the wind therefore the velocities are subtracted.
9 Geometric Addition of Vectors Consider a pair of horses pulling on a boat.The resultant force is the addition of the two separate forces F1 + F2.
10 Geometric Addition of Vectors The resultant vector (black) is the addition of the other 2 vectors (blue + green)
11 Mathematical Addition of Vectors When we add vectors mathematically, we use a vector diagram. This may include using Pythagoras’ Theorem.
12 Mathematical Addition of Vectors Pythagoras’ Theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a2 + b2 = c2
13 Mathematical Addition of Vectors Example – An 80km/hr plane flying in a 60km/hr cross wind. What is the planes speed relative to the ground.
14 Mathematical Addition of Vectors SolutionUse Pythagoras’ Theorem to find RDraw a vector representation of the velocities involved.
15 Mathematical Addition of Vectors As velocity is a vector, we need to find the direction of the vector.Can do this by finding an angle (a) with in the vector diagram.Use trigonometry to find the angle.
16 Mathematical Addition of Vectors The answer should include both the size and direction of the vector.The velocity of the plane relative to the ground is 100km/hr at 36.9o to the right of the planes initial velocity.
17 EquilibriumCombining vectors using the parallelogram rule can be shown by considering the case of being able to hang from a clothes line but unable to do so when it is strung horizontally, it breaks!
18 EquilibriumCan see what happens when we use the spring scales to measure weight.Consider a block that weighs 10N (1Kg), if suspended by a single scale it reads 10N.
19 EquilibriumIf we hang the same block by 2 scales, they each read 5N. The scales pull up with a combined force of 10N.
20 EquilibriumWhat if the 2 scales weren’t vertical but were attached at an angle. We can see for the forces to balance, the scales must give a reading of a larger amount.
21 Components of VectorsThe force applied to the lawn mower may be resolved into two components, x for the horizontal and y for the vertical.
22 Components of VectorsThe rule for finding the vertical and horizontal components is simple.A vector is drawn in the proper direction and then horizontal and vertical vectors are drawn from the tail of the vector.
23 Components of Weight Why does a ball move faster on a steeper slope? We can see what happens when we resolve the vector representing weight into its components.
24 Components of WeightVector A represents the amount of acceleration of the ball and vector B presses it against the surface.Steeper the slope, more A.
25 Projectile MotionA projectile is any object that is projected by some means and continues in motion by its own inertia.An example is a cannon ball shot out of a cannon or a stone thrown in the air.
26 Projectile MotionThe horizontal component of the motion is just like looking at the horizontal motion of a ball rolling freely on a horizontal surface.
27 Projectile MotionThe vertical component of an object following a curved path is the same as the motion of a freely falling object as discussed in section 2.
28 Projectile MotionA multi-image photograph displaying the components of projectile motion.
29 Projectile MotionThe horizontal component of the motion is completely independent of the vertical motion of the object and can be treated differently.Ph14e – projectile motion
30 Projectile MotionIn summary, the a projectile will accelerate (change its speed) in the vertical direction while moving with a constant horizontal speed. This path is called a parabola.
31 Upwardly Moving Projectiles Imagine a cannon ball shot at an upward angle in a gravity free region on Earth. The cannon ball would follow a straight line.But there is gravity, the distance the cannon ball deviates from the straight line is the same distance that is calculated from a freely falling object.
33 Upwardly Moving Projectiles The distance from the dotted line can be calculated using the formula introduced previously.
34 Upwardly Moving Projectiles The following diagram shows the vectors that represent the motion of the projectile.Only the vertical component is changing, the horizontal component has remained the same.
35 Upwardly Moving Projectiles The horizontal component of the motion will determine the range (how far horizontally the projectile will travel).
36 Upwardly Moving Projectiles The following diagram displays the different angle of a projectile launched with the same initial speed.
37 Upwardly Moving Projectiles Angles that add up to 90 degrees and launched with the same initial speed have the same Range.Ph14e – projectile motion
38 Air Resistance on a Projectile Air resistance affects both the horizontal and vertical components of the motion negatively.
39 Air Resistance on a Projectile Need to consider how air resistance effects the horizontal and vertical motion separately.Continuously slows down horizontally and maximum height is reduced.