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**SACE Stage 1 Conceptual Physics**

Vectors

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**Vector and Scalar Quantities**

Quantities that require both magnitude and direction are called vector quantities. Examples of vectors are Force, Velocity and Displacement.

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**Vector and Scalar Quantities**

Quantities that require just magnitude are known as Scalar quantities. Examples of scalar quantities are Mass, Volume and Time.

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**Vector Representation of Force**

Force has both magnitude and direction and therefore can be represented as a vector.

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**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.

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**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.

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**Vector Representation of Velocity**

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**Vector Representation of Velocity**

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**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.

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**Geometric Addition of Vectors**

The resultant vector (black) is the addition of the other 2 vectors (blue + green)

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**Mathematical Addition of Vectors**

When we add vectors mathematically, we use a vector diagram. This may include using Pythagoras’ Theorem.

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**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

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**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.

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**Mathematical Addition of Vectors**

Solution Use Pythagoras’ Theorem to find R Draw a vector representation of the velocities involved.

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**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.

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**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.

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Equilibrium Combining 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!

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Equilibrium Can 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.

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Equilibrium If we hang the same block by 2 scales, they each read 5N. The scales pull up with a combined force of 10N.

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Equilibrium What 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.

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Components of Vectors The force applied to the lawn mower may be resolved into two components, x for the horizontal and y for the vertical.

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Components of Vectors The 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.

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**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.

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Components of Weight Vector A represents the amount of acceleration of the ball and vector B presses it against the surface. Steeper the slope, more A.

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Projectile Motion A 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.

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Projectile Motion The horizontal component of the motion is just like looking at the horizontal motion of a ball rolling freely on a horizontal surface.

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Projectile Motion The 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.

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Projectile Motion A multi-image photograph displaying the components of projectile motion.

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Projectile Motion The horizontal component of the motion is completely independent of the vertical motion of the object and can be treated differently. Ph14e – projectile motion

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Projectile Motion In 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.

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**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.

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**Upwardly Moving Projectiles**

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**Upwardly Moving Projectiles**

The distance from the dotted line can be calculated using the formula introduced previously.

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**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.

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**Upwardly Moving Projectiles**

The horizontal component of the motion will determine the range (how far horizontally the projectile will travel).

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**Upwardly Moving Projectiles**

The following diagram displays the different angle of a projectile launched with the same initial speed.

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**Upwardly Moving Projectiles**

Angles that add up to 90 degrees and launched with the same initial speed have the same Range. Ph14e – projectile motion

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**Air Resistance on a Projectile**

Air resistance affects both the horizontal and vertical components of the motion negatively.

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**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.

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Physics in Surfing

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