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1 Physical Science, 6e Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 Motion Motion can be defined as the act or process of changing position relative to some reference during a period of time

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2 Overview Description Position Velocity Acceleration Applications Horizontal motion on land Falling objects Compound (2-D) motion Explanation Forces Newton’s laws Applications Momentum Circular motion Newton’s law of gravitation

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3 Measuring motion Two fundamental components: Change in position Change in time Three important combinations of length and time: 1.Speed 2.Velocity 3.Acceleration

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4 Speed Change in position with respect to time Average speed - most common measurement Instantaneous speed - time interval approaches zero

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5 Calculate average speed between trip times of 1 h and 3 h v= 150km - 50km 2h = 50km h Example: average speed

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6 Velocity Describes speed (How fast is it going?) and direction (Where is it going?) Graphical representation of vectors: length = magnitude; arrowheads = direction

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7 Acceleration Rate at which motion changes over time Speed can change Direction can change Both speed and direction can change

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8 Forces - historical background Aristotle Heavier objects fall faster Objects moving horizontally require continuously applied force Relied on thinking alone Galileo and Newton All objects fall at the same rate No force required for uniform horizontal motion Reasoning based upon measurements

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9 Force A push or pull capable of changing an object’s state of motion Overall effect determined by the (vector) sum of all forces - the “net force” on the object

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10 Horizontal motion on land “Natural motion” question: Is a continuous force needed to keep an object moving? No, in the absence of unbalanced retarding forces Inertia - measure of an object’s tendency to resist changes in its motion (including rest) YES, with unbalanced retarding forces such as air resistance and friction forces

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11 Balanced and unbalanced forces Motion continues unchanged w/o unbalanced forces Retarding force decreases speed

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12 Balanced and unbalanced forces Boost increases speed Sideways force changes direction

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13 Falling objects Free fall - falling under influence of gravity without air resistance Distance proportional to time squared

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14 Falling objects Free fall - falling under influence of gravity without air resistance Speed increases linearly with time

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15 Falling objects Free fall - falling under influence of gravity without air resistance Trajectories exhibit up/down symmetries Acceleration same for all objects

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16 Compound motion Three types of motion: 1.Vertical motion 2.Horizontal motion 3.Combination of 1. and 2. Projectile motion An object thrown into the air Basic observations: 1.Gravity acts at all times 2.Acceleration (g) is independent of the object’s motion

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17 Projectile motion Vertical projectile Slows going up Stops at top Accelerates downward Force of gravity acts downward throughout Horizontal projectiles Horizontal velocity remains the same (neglecting air resistance) Taken with vertical motion = curved path

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18 Fired horizontally versus dropped Vertical motions occur in parallel Arrow has an additional horizontal motion component They strike the ground at the same time!

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19 Example: passing a football Only force = gravity (down) Vertical velocity decreases, stops and then increases Horizontal motion is uniform Combination of two motions = parabola

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20 Three laws of motion First detailed by Newton (1564-1642 AD) Concurrently developed calculus and a law of gravitation Essential idea - forces

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21 Newton’s 1 st law of motion “The law of inertia” Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force

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22 Newton’s 1 st law of motion “The law of inertia” Inertia resists any changes in motion

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23 Newton’s 2 nd law of motion Forces cause accelerations Units = Newtons (N) Proportionality constant = mass; units = kilograms (kg) More force, more acceleration (with constant mass) More mass, less acceleration (with constant force)

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24 Examples - Newton’s 2 nd law More mass, less acceleration, (with constant force) again Focus on net force –Net force zero here –Air resistance + tire friction match applied force –Result: no acceleration; constant velocity

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25 Examples - Newton’s 2 nd law More mass, less acceleration, again Focus on net force –Net force zero here –Air resistance + tire friction match applied force –Result: no acceleration; constant velocity

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26 Weight and mass Mass = quantitative measure of inertia; the amount of matter Weight = force of gravity acting on the mass Pounds and newtons measure of force Kilogram = measure of mass

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27 Newton’s 3 rd law of motion Source of force - other objects 3rd law - relates forces between objects “Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object.”

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28 Newton’s 3 rd law of motion Source of force - other objects 3rd law - relates forces between objects “Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object.”

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29 Momentum Important property closely related to Newton’s 2nd law Includes effects of both motion (velocity) and inertia (mass)

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30 Conservation of momentum The total momentum of a group of interacting objects remains the same in the absence of external forces Applications: Collisions, analyzing action/reaction interactions

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31 Impulse A force acting on an object for some time t An impulse produces a change in momentum Applications: airbags, padding for elbows and knees, protective plastic barrels on highways

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32 Forces and circular motion Circular motion = accelerated motion (direction changing) Centripetal acceleration, a c present Centripetal force, F c must be acting Centrifugal force - apparent outward tug as direction changes Centripetal force ends: motion = straight line

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33 Newton’s law of gravitation Attractive force between all masses Proportional to product of the masses Inversely proportional to separation distance squared Explains why g = 9.8 m/s 2 Provides centripetal force for orbital motion

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34 Newton’s law of gravitation Attractive force between all masses Proportional to product of the masses Inversely proportional to separation distance squared Explains why g = 9.8 m/s 2 Provides centripetal force for orbital motion

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