Described by Isaac Newton

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2 Described by Isaac Newton States observed relationships between motion and forces 3 statements cover aspects of motion for single objects and for objects interacting with another object

3 An object at rest remains at rest and an object in motion remains in motion with constant velocity unless acted on by unbalanced forces Objects have natural tendency to resist changes in motion (acceleration): Inertia Depends on mass of object

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6 Larger masses, more inertia: harder to accelerate Smaller masses, less inertia: easier to accelerate Unless acted on by unbalanced forces, object s inertia governs object s motion

7 Provides quantitative relationship between object s inertia and force required to produce specific acceleration F = ma F: force (N) m: mass (kg) a: acceleration (m/s 2 )

8 2 kg F = 12 N a = 6 m/s 2 6 kg F = 12 N a = 2 m/s 2

9 Unit for force (Newton) describes mathematical relationship of the 2 nd Law of motion 1 N = 1 kg x m/s 2 1 N of force is required to accelerate a 1 kg mass at a rate of 1 m/s 2 Acceleration of an object is directly proportional to the applied force and inversely related to the object s mass

10 Gravity acts as unbalanced force for many situations All matter generates attractive force of gravity Magnitude of force is directly proportional to the masses of the objects involved and inversely proportional to the distance between them

11 The force of gravity between any two masses can be calculated: F g = G(m 1 m 2 ) d 2 F: Gravity G: Newton s gravitational constant x N x m 2 /kg 2 m 1 : mass of first object m 2 : mass of second object

12 From formula, gravity increases as the masses of the objects increases; decreases as distance increases Distance more important than mass for objects at celestial scale

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14 Free fall: when the net force that causes motion is due solely to gravity Direction of motion towards Earth s center Variable: g Average for Earth: 9.8 m/s 2 Free fall acceleration on Earth is constant regardless of mass of object in motion

15 All objects fall to Earth at the same rate, experience same acceleration due to gravity Heavier objects experience larger force of gravity, but demonstrate less acceleration due to larger inertia Inertia balances extra gravitational pull to produce equal acceleration for all masses

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17 9.8 m/s2

18 Force on an object due to gravity Formula: W = mg W: weight (Newtons) m: mass (kg) g: acceleration due to gravity (m/s 2 ) Same formula as for calculating any force

19 m = 80 kg g = 9.8 m/s 2 W = 784 N

20 Astronauts in space shuttle experience continuous free fall: apparent weightlessness Shuttle and astronauts accelerate at same rate due to Earth s gravity as they fall

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22 Mass of an object is constant Weight depends on location On less massive planet, value for g is lower, so lower weight At greater distance from center of planet, value for g is lower, so lower weight Inertia dependent on mass, not weight

23 m = 80 kg g = 3.5 m/s 2 W = 280 N

24 Velocity in free fall is constant when air resistance balances weight Air resistance directed up Weight directed down When their magnitude is equal, they sum to 0 Balanced forces produce no changes in motion Terminal velocity

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26 Falling through air is not really free fall Air resistance acts on object, as well as gravity In space, air resistance is negligible: free fall acceleration Free fall responsible for orbital motion of moons and artificial satellites

27 Projectile: object launched through the air and subject to gravity Path of motion: trajectory Shape of trajectory: parabola Projectile motion has vertical and horizontal component Components are independent, do not influence each other

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29 Initial velocity given to projectile carried through unchanged in horizontal direction No unbalanced force acting in horizontal direction, so no change in velocity Air resistance actually complicates the motion Often ignored to simplify model

30 Initial vertical component of motion is zero Vertical motion initiated by unbalanced force of gravity Gravity accelerates object in vertical direction As object travels horizontally, it is simultaneously accelerating downwards

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32 Applicable to two objects interacting with each other A force applied by one object on another is met with an equal and opposite force applied by the second object on the first object For every action, there is an equal and opposite reaction

33 Drop a ball on the floor Ball applies force to the floor, floor applies equal and opposite force on the ball Ball experiences change of motion Rowing a boat, swimming, launching a rocket

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35 Forces always occur in pairs Isolated forces don t exist in nature Forces exist as action-reaction pairs No lag time between action and reaction force generation Simultaneous production of forces Action-reaction forces act on different objects, do not result in balanced forces

36 Action-reaction pairs do not necessarily result in equal changes in motion Apple falling from tree Earth pulls on apple; apple pulls on Earth with equal and opposite force Apple: small inertia, force produces significant acceleration Earth: large inertia, force produces negligible acceleration

37 Property of all objects in motion Product of the mass and velocity of object How difficult is it to stop a moving object? Different from inertia must have motion to have momentum Vector quantity due to velocity component

38 Force related to change in momentum When momentum changes due to velocity change, indicates action of unbalanced force Formula: F = Δp/t or Ft = Δp Ft: impulse Increase time of contact, decrease force, but increase change of momentum

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41 When objects collide, the total momentum of the system is conserved P before = P after Sum the momentums of each object before the crash and after the crash and the values will be equal Loss of momentum by one object is balanced by gain of momentum of another

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43 Conservation of momentum implies momentum can be transferred between objects Creates changes in velocity, accelerates objects Even systems initially at rest demonstrate conservation of momentum Canon firing canon ball

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47 Forces in fluids produced by mass and motion of atoms/molecules in fluid As particles move, they push against each other and against walls of container Size of force depends on mass and acceleration of particles Particles apply their force over specific area

48 Pressure: amount of force applied over a given area P = F A Force = N; Area = m 2 ; Pressure = N/m 2

49 Many phenomena regulated by differences in pressure between two areas of fluid Weather, breathing, drinking from a straw Fluids move from areas of high pressure to areas of low pressure Move down pressure gradient

50 Breathing: Air pressure outside nose equal to pressure in lungs Inhalation diaphragm drops to increase volume of lungs Pressure in lung decreases Air outside nose moves to area of lower pressure into lungs

51 Exhalation diaphragm rises to decrease volume in lungs Pressure in lungs increases Air moves from lungs to exterior environment

52 In absence of outside forces, fluids exert pressure equally in all directions Increasing pressure at one point of fluid causes that pressure to be exerted throughout entire sample of fluid Transmission of pressure equally throughout fluid is principle behind hydraulics

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54 Hydraulic devices use principles of pressure in fluids to magnify forces Apply a small force to lift a heavy object

55 How much force would this device lift?

56 P = F/A Applied force side: P = 3N/15cm 2 = 0.2 N/cm 2 Resistance force side: 0.2 N/cm 2 = F/200 cm 2 F = 40 N

57 Can set up problem as equivalent fractions: F 1 F 2 = A 1 A 2 Hydraulic devices found in brakes, barber chairs, industrial lifts

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59 Gravity pulls on all particles in a sample of fluid Can produce pressure differences with different depths With descent, weight of fluid increases; force increases; pressure increases With ascent, weight of fluid decreases; force decreases, pressure decreases

60 The pressure at any point in a column of fluid depends upon the depth of the measurement and the density of the fluid P = ρgh P: pressure; ρ: density; g: acceleration due to gravity; h: height

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62 Tall, fluid-retaining structures need reinforcement at bottom to withstand extra pressure of fluid Dams, grain silos Deep-sea animals adapted to tremendous pressures Must be handled carefully when brought to surface for scientific study

63 Objects submerged in a fluid appear to weigh less than they do on land Neither mass nor gravity has changed Force of object opposed by force of fluid pushing upwards on object Buoyant force

64 Objects placed in a fluid displace some of the fluid to make room for their own volume Displaced fluid has an associated weight Archimedes Principle: the size of the buoyant force on an object is equal to the weight of the fluid displaced by an object

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66 Size of buoyant force relative to the weight of the object determines whether the object will float or sink in the fluid Buoyant force > weight of object: Floats Buoyant force < weight of object: Sinks

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68 Density property of matter that determines floating and sinking D = M/V Can determine floating and sinking If displaced fluid has density greater than object, weight of displaced fluid will be greater than weight of object

69 For complex objects, density is determined by the densities and proportions of the object s components Ships float due to presence of air, which lowers the total density Air also has buoyant force, but it is very small

70 You feel lighter in water than in air since upwards force of water is greater than upwards force of air Water s buoyant force subtracts more of your force, leaving a smaller net force (weight)

71 The pressure in a moving stream of fluid is less than the pressure of the surrounding fluid Faster the fluid, lower the pressure

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73 Most famous application is principle of flight Wings: Curved on top and flat on bottom Air on top of wing and air on bottom of wing meet at rear of wing at same time

74 Air on top of wing covers longer distance in same amount of time than air on bottom of wing Air on top of wing moving faster lower pressure Fluids move from areas of high pressure to areas of low pressure Air moves upwards under wing, providing lift

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76 Other examples: Kites flying, smoke going up chimney, perfume atomizer

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