Physical Science Reviewer.docx

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) MODELS OF THE UNIVERSE AND EARLY ASTRONOMY 

Predictable patterns in the sky have aided humans in modelling the universe (open, flat, closed [geometry of the universe])

Geocentric Model – Earth at the center of the solar system Heliocentric Model – assumes the sun to be the center of the solar system

GEOCENTRIC MODELS (Earth and other heavenly bodies were assumed to be spheres)     

The Pythagorean Model Plato’s “Saving the Appearances” Eudoxus’ Model Aristotle’s Model Ptolemy’s Model

1. Pythagorean Model  By Pythagoras  Earth is round  “The Music of Spheres” – motion of planets was mathematically related to musical standards and numbers o Anaxagoras – determined the relative positions of the sun, the earth and the moon during solar and lunar eclipses 2. Plato’s “Saving the Appearances”  Adaptation of Pythagorean Model  Assumed that all motions are perfectly circular  Assumed that all heavenly bodies are ethereal/perfect o Retrograde Motion – motion of heavenly bodies is from west to east (clockwise) 3. Eudoxus’ Model  Celestial spheres share one common center – Earth  First model of geocentric model  Made up of 27 concentric spheres  Five planets – Mercury, Venus, Mars, Saturn and Jupiter

4. Aristotle’s Model  Proved that the earth is spherical  Believed that the earth is fixed at the center of the solar system and that everything revolves around it  Believed that all stars are fixed points which rotate on a single celestial sphere  It has 56 spheres (2 realms) TERRESTRIAL REALM  objects in the realm moved naturally according to their material composition  ephemeras (lasting for a very short time) and undergoing decay

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CELESTIAL REALM at/above moon’s orbit 5th element called Aether/Ether Ether was unchanging and perpetual (neverending/changing)

5. Ptolemy’s Model  Apollomius Ptolemy – the great geometer  Shows the deterrent, circular paths in which planets move and epicycle (circle where planets move)  Proposed the equant (a point close to the orbit’s center)  Philoaus proposed Pyrocentric Model (bridge that connected Geocentric to Heliocentric)  Neither earth nor sun as the center

HELIOCENTRIC MODELS 1. Aristarchus Model  First to place the sun at the center of the universe  The sun and the stars are fixed  The earth is revolving around the sun in a circular orbit  Did not last because of the general acceptance of Ptolemy’s model  2. Copernicus Model  Celestial motions are uniform, infinite and circular  Planets revolved around the sun

© Reign Alejandra Esteva

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) 3. Tycho’s Model  Plotted all of his observations of the heavens using instruments of his own design  Was extremely thorough to achieve more accurate methods than any other  His model was both Heliocentric and Geocentric with planets revolving around the sun, and the sun revolving the earth  He witnessed and recorded 2 supernovae which opposed to Ptolemy’s idea that stars were unchanging 4. Kepler’s Model  planetary orbits were based on the geometric shape (ellipse)  the planets move around the sun were elliptical though  he believed that the closer planets were t the sun, the faster they orbited  this enables to predict motions of the universe fairly accurately Galileo’s Astronomical Observations (supported by Copernican Theory) 1. 2. 3. 4. 5.

Lunar Craters (Mountain Valleys Craters) Phases of Venus (Similar Phases of Venus) Moons of Jupiter (Jupiter had 4 moons) 61 moons Sunspots (Surface of the sun has blemishes) Supernova (stars appeared to be points of light in the Milky Way) 6. Apparently identical size of the stars (Stellar Parallax is extremely different to be observed) Kepler’s Law of Planetary Motion (EEH) Law of Ellipses 

Orbit of a planet is an ellipse with the sun at one focus o Perihelion – point nearest to the sun o Aphelion – point farthest to the sun

Law of Equal Areas  

Planets travel equal areas of space in equal periods of time Planets travel faster during perihelion, travel slower during aphelion

Harmonies  

The larger the planet’s orbit, the longer the revolution The square of the revolutions of the planet are directly proportional to the cubes of their average distance

KINEMATICS   

Displacement Velocity Acceleration

Magnitude – how small or how large a quantity is (10 meters, 2 hours) Scalar Quantities – quantities that have magnitude only (50 km/hr) Vector Quantities – quantities that have both magnitude and direction (50 km/hr at 20 North of East) SCALAR QUANTITY Distance (d) – 40m Speed (v) – 30ms2 Time (r) - 15s Energy (E) – 2000J

VECTOR QUANTITY Displacement (s) – 40m east direction Velocity (v) – 30ms2 Force (F) – 100N upward direction Acceleration (a) – 98ms2 downward direction

Distance vs. Displacement   

How much ground an object has covered during its motion How far you traveled regardless of direction Total ground covered

Distance  

Length between two points Traveled length of an object © Reign Alejandra Esteva

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) Displacement  

Defined as the change in position of an object How far the object is from its starting point

Inertia 

Vectors    

Vectors are quantities represented by a line segment with an arrowhead Tail – Origin Line segment – magnitude Arrowhead – direction

Displacement (Resultant Vector) 

Description of the final position of a moving object with respect to its initial position, regardless of the path taken o Vector Addition o Pythagorean Theorem o SOH-CAH-TOA

Vector Addition – sum of 2 or more vectors is represented by a single vector called resultant

NEWTON’S LAWS OF MOTION

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SECOND LAW: LAW OF ACCELERATION 

An unbalanced force produces an acceleration with the direction of the force.  Force ( 𝐹⃗ )is directly proportional to acceleration ( 𝑎⃗ ) (or vice versa) o More Force, more Acceleration o Less Force, less Acceleration o Acceleration is inversely proportional to the mass. o Less acceleration, the object is more massive o More acceleration, the object is less massive Net Force o o o

Sir Isaac Newton (1642 – 1727)  

Only 25 when he formulated most of his discoveries in math and physics His book Mathematical Principles of Natural Philosophy is considered to be the most important publication in the history of Physics

FIRST LAW: LAW OF INERTIA 

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In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity. o Newton’s First Law describes what happens in the absence of a force. The First Law also allows the definition of force as that which causes a change in the motion of an object.

the natural tendency of ALL objects to remain at rest or in uniform motion along a straight line; “resists changes in motion” o MASS – quantitative measure of inertia of a body o FORCE – action exerted upon by/to a body that changes its state of motion The larger the mass of a body, the more force is needed to overcome its inertia/change its state of motion

Vector sum of all the forces acting on an object Can change an object’s state of motion The SI unit of force is NEWTON (N) or kg⋅ m/sec2

Force, Mass, Acceleration A. a = F/m B. If we double the force, we double the acceleration. C. If we double the mass, we half the acceleration. THIRD LAW: LAW OF INTERACTION  

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For every action, there is an equal and opposite reaction. Whenever one body exerts a force on a second body, the second body exerts a force back on the first that is equal in magnitude but opposite in direction. Action Force Reaction Force Fa = - Fb or m1a1 = -m2a2 © Reign Alejandra Esteva

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) LOCOMOTION – constantly affect our everyday activities

Two Types of a Projectile Motion Projectile motion 1 (PM 1)

FREELY FALLING BODIES (Uniformly accelerated rectilinear motion)    

Freely falling motion is a motion of an object when gravity is the only significant force acting on it. The acceleration of an object due only to the effect of gravity is known as free-fall acceleration. This motion is an example of uniformly accelerated 𝑚 rectilinear motion. (constant acceleration = - 9.80 𝑠2 ) This motion is moving in a straight line (vertical line @ y-axis) wherein its speed is constantly changing.

Total Time of Flight ( ttotal )  Total time of flight is the amount of time spends in the air until it reaches to the ground.  The time of flight is just double the maximum-height time. MOTION AND FORCES IN TWO DIMENSIONS: PROJECTILE MOTION 

the motion of object in two dimensions (horizontal and vertical components) an object following a projectile motion is called a projectile Gravity is the only force acting on a projectile the path that a projectile follows is called its trajectory trajectory of a projectile results in a parabola (since it moves both along the horizontal and vertical directions) Since a projectile moves in two dimensions, therefore it has two components:

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o o

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Horizontally Launch

Projectile motion 2 (PM 2) 

Angled Launch

In presence of gravity:  

A projectile travels with a constant horizontal velocity and a downward vertical acceleration. The horizontal and vertical motions of a projectile are completely independent of each other. Horizontally Launched Projectiles

Horizontal velocity is constant. Vertical velocity is changing due to gravitational acceleration.

Vertically Launched Projectiles

The horizontal velocity component remains the same size throughout the entire motion of the cannonball.

Horizontal velocity (Vx) Vertical velocity (Vy)

Two independent motions happening at the same time:  

Rectilinear Motion @ X- axis Freely Falling Bodies @ Y-axis

Two velocities happening at the same time:  

Vx (velocity at x) Vy (velocity at y) © Reign Alejandra Esteva

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) FORMULAS:

Projectile Motion

Kinematics

PROJECTILE MOTION 1

1. √c2 = √a2+b2 𝑏

2. tan = 𝑎 3. Velocity =

𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 𝑉𝑓−𝑉𝑖

4. Acceleration =

𝑡

5. Vf = Vi + at 6. Vi = Vf – at 7. T =

NOTE: Vix = initial horizontal velocity, Viy = 0

𝑉𝑓−𝑉𝑖 𝑎

8. F = ma

PROJECTILE MOTION 2 9.

Freely Falling Bodies 1. g =

Vf −Vi

if a is unknown

t

2. Vf = Vi + gt 3. Vi = Vf – gt 4. t =

Vf −Vi

1 5. 𝑑⃗ = Vit + 2 gt2

upward 1 6. 𝑑⃗ = 2 gt2

(acceleration = 0, no acceleration) Velocity at x-axis is constant

dy =

𝑉𝑓𝑦^2−𝑉𝑖𝑦^2 2𝑔

Tmax =

𝑉𝑓𝑦−𝑉𝑖𝑦 𝑔

Ttotal = (Tmax)(2) Vix = Vicos Viy = Visin

if object is falling down/going if Vi = 0, release in mid-air

2𝑑

7. t = √ 𝑔 2

@ y-axis Viy = Visin 1 dy = Viyt + 2 gt2

if t is unknown

g

Vf - Vi 8. 𝑑⃗ = 2g

if Vf is unknown if Vi is unknown

@ x-axis Vix = Vicos Range = (Vix)(Ttotal)

if Vi = 0, release in mid-air 2

if t is unknown, falling down/going upward

9. tmax =

𝑉𝑓 −𝑉𝑖 𝑔

(time at max height)

10. ttotal = tmax × 2

© Reign Alejandra Esteva

PHYSICAL SCIENCE REVIEWER (3RD QUARTER) PRACTICE PROBLEMS: Kinematics 1. A student walks 4 meters East, 2 meters South, 4 meters West and 2 meters North. A. What is the total distance? B. What is the final displacement? 2. Zari walks 16 km to the North, 12 km back to the East and 15 km to the West. A. Determine the distance which Zari moved. B. Determine Zari’s displacement 3. Luna leaves the base camp and hikes 11 km North and then hikes 11 km East. Determine Luna’s resulting displacement. 4. In order for Tanya to reach her workplace, she drove 10 km West and 5 km South. Determine Tanya’s displacement.

Freely Falling Bodies 1. A construction worker accidentally drops a brick from a high scaffold. A. What is the velocity of the brick after 10.00 s? B. How far does the brick fall during this time? C. Use 9.80 m/s2 for the acceleration due to gravity in solving for both problems 2. A student drops a ball from a window 5.50 meters above the sidewalk. A. How long will it hit the ground? B. How fast is it moving when it hits the ground? 3. A bullet is fired vertically upward with a muzzle velocity of 600.00 m/s. How long will it remain in midair until it returns the ground?

5. A student was fed up with doing her kinematic formula homework, so she threw her pencil straight upward at 18.30 m/s. The height it took the pencil was 12.20 meters. What was the velocity at this height? How long did the pencil take to reach at 12.20 meters?

Projectile Motion 1. A stone is thrown horizontally from the top of a building 65.0 meters high with an initial horizontal velocity of 24.0 m/s. A. The time required for the stone to reach the ground B. The maximum range 2. A bullet is fired from a gun mounted at an angle of 54.000. The muzzle velocity is 350.00 m/s. A. B. C. D.

The initial velocities Maximum height Total time of flight Range

3. A stream of water emerges horizontally from a fire hose at a velocity of 180.00 m/s. If the nozzle is 85.00 m above the ground, find the following: A. Time required for the water to reach the ground B. The horizontal distance the water travels 4. A cannon ball on the ground is fired at 35.00o with an initial velocity of 250.00 m/s. A. How long will it take to hit the ground, B. How far from the cannon ball will it hit the ground, and C. Compute for the maximum height to be reached by the cannon ball.

4. A ball was thrown vertically upward with an initial velocity of 29.0 m/s . Find the ball's maximum altitude.

© Reign Alejandra Esteva