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Chapter 2: Motion

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

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

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Speed Change in position with respect to time Three common “speeds” –Constant Speed –Average Speed –Instantaneous Speed Change in position with respect to time Three common “speeds” –Constant Speed –Average Speed –Instantaneous Speed

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Calculate average speed between trip times of 1 h and 3 h Example: average speed Fig 2.2

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Example: average speed How else could we determine v ? Fig 2.3

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Example 2.1

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Example 2.2

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Velocity Describes speed (How fast is it going?) AND direction (Where is it going?) Graphical representation of vectors: length = magnitude; arrowheads = direction Describes speed (How fast is it going?) AND direction (Where is it going?) Graphical representation of vectors: length = magnitude; arrowheads = direction Fig 2.4

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Acceleration Rate at which motion changes over time Three ways (think of when you’re in the driver’s seat) 1.Speed can change 2.Direction can change 3.Both speed and direction can change Rate at which motion changes over time Three ways (think of when you’re in the driver’s seat) 1.Speed can change 2.Direction can change 3.Both speed and direction can change Fig 2.6

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Acceleration Fig 2.5 Correct “5 s” to “4 s” in Caption Constant speed: no accelerationChange in speed: acceleration

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This example shows that you sometimes need to tie a couple of relationships together Approach it the same way: “How to Solve Problems” This example shows that you sometimes need to tie a couple of relationships together Approach it the same way: “How to Solve Problems”

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Forces – historical background (FYI) Aristotle Heavier objects fall faster Objects moving horizontally require continuously applied force Relied on thinking alone 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 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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Force A “push” or a “pull”… …capable of changing an object’s state of motion Sum of all forces acting on an object –Net Force “Final Force“: after the forces are “added” A “push” or a “pull”… …capable of changing an object’s state of motion Sum of all forces acting on an object –Net Force “Final Force“: after the forces are “added” Fig 2.8

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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 –Related to its Mass “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 –Related to its Mass

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Balanced and unbalanced forces Motion continues unchanged w/o unbalanced forces Retarding force decreases speed Boost increases speed Sideways force changes direction Motion continues unchanged w/o unbalanced forces Retarding force decreases speed Boost increases speed Sideways force changes direction

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Galileo’s Breakthrough

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Falling objects Free fall: falling under influence of gravity w/o air resistance Distance proportional to time squared Speed increases linearly with time “Acceleration” same for all objects Free fall: falling under influence of gravity w/o air resistance Distance proportional to time squared Speed increases linearly with time “Acceleration” same for all objects

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Three laws of motion First detailed by Newton (1642-1727 AD) Concurrently developed calculus and a law of gravitation Essential idea: –Relationship of forces and changes of motion First detailed by Newton (1642-1727 AD) Concurrently developed calculus and a law of gravitation Essential idea: –Relationship of forces and changes of motion

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Newton’s 1st law of motion “The law of inertia” Inertia resists any changes in motion Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force (bolded print) “The law of inertia” Inertia resists any changes in motion Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force (bolded print)

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Newton’s 2nd law of motion (see bolded print) Relationship between: Net Force, Mass, & Acceleration Forces can cause accelerations Units = Newtons (N) More force, more acceleration More mass, less acceleration Relationship between: Net Force, Mass, & Acceleration Forces can cause accelerations Units = Newtons (N) More force, more acceleration More mass, less acceleration

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Where a Newton (N) is defined as [ kg · m / s 2 ] Rearrange

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Mass vs. Weight Mass = quantitative measure of inertia; the amount of matter Weight = force of gravity acting on the mass Pounds and Newtons are measures of force Kilogram is a measure of mass Mass = quantitative measure of inertia; the amount of matter Weight = force of gravity acting on the mass Pounds and Newtons are measures of force Kilogram is a measure of mass

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Newton’s 3rd law of motion 3rd law - relates forces between objects –See bolded print “For every action, there is an equal and opposite reaction” –But neither force is the cause of the other 3rd law - relates forces between objects –See bolded print “For every action, there is an equal and opposite reaction” –But neither force is the cause of the other Rutger’s Homepage

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Momentum Important property closely related to Newton’s 2nd law Includes effects of both motion (velocity) and inertia (mass) Important property closely related to Newton’s 2nd law Includes effects of both motion (velocity) and inertia (mass) Fig 2.24 Rutger’s Homepage

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Conservation of momentum 2 Movies

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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 The total momentum of a group of interacting objects remains the same in the absence of external forces Applications: Collisions, analyzing action/reaction interactions Fig 2.25

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Impulse A force (F) acting on an object for some time, t An impulse produces a change in momentum (Δp) Applications: airbags, hitting a baseball, padding for elbows and knees, orange plastic barrels on highways A force (F) acting on an object for some time, t An impulse produces a change in momentum (Δp) Applications: airbags, hitting a baseball, padding for elbows and knees, orange plastic barrels on highways

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Forces and circular motion Circular motion = accelerated motion (direction changing) Centripetal acceleration present thus F c present Centripetal force must be acting (inward) Centripetal force ends: motion = straight line Circular motion = accelerated motion (direction changing) Centripetal acceleration present thus F c present Centripetal force must be acting (inward) Centripetal force ends: motion = straight line http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon

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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 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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Compound motion Three types of motion: 1.Vertical motion 2.Horizontal motion 3.Combination of 1. & 2. Three types of motion: 1.Vertical motion 2.Horizontal motion 3.Combination of 1. & 2. 3. 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 3. 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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Projectile motion Vertical projectile Slows going up Stops at top Accelerates downward –Force of gravity acts downward throughout Vertical projectile Slows going up Stops at top Accelerates downward –Force of gravity acts downward throughout Horizontal projectile Horizontal velocity remains the same (neglecting air resistance) Taken with vertical motion = curved path –Force of gravity acts downward throughout Horizontal projectile Horizontal velocity remains the same (neglecting air resistance) Taken with vertical motion = curved path –Force of gravity acts downward throughout

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Shot horizontally versus dropped (neglecting air resistance) Vertical motions occur in parallel Arrow has an additional horizontal motion component They strike the ground at the same time! Vertical motions occur in parallel Arrow has an additional horizontal motion component They strike the ground at the same time!

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

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