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Stem notes topics 1 and 2

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motion and forces

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Stem notes topics 1 and 2

  1. 1. Mr. Motuk (Room 124) QQ To me there has never been a higher source of earthly honor or distinction than that connected with advances in science. Isaac Newton 11
  2. 2. Frames of Reference  You don't always need to see something move to know that motion has taken place  A reference point is needed to determine the position of an object  Ever felt like you were slowly moving backwards when a semi truck passed you on the highway? 22
  3. 3. Frames of Reference  You have mistakenly made the truck your frame of reference, measuring your motion relative to the truck  Both vehicles move forward relative to the stationary tree (the ground is the proper frame of reference) Proper Frame of Reference 33
  4. 4. Describing One-Dimensional  Motion- a change in position, measured by distance and time  The SI unit of length or distance is the meter (m)  Shorter distances are measured in centimeters (cm)  Longer distances are measured in kilometers (km)  The following quantities are used to describe motion:  Speed  Velocity  Acceleration Motion The fastest “thing” travels at ~670,000,000 mph… What is it? Light 44
  5. 5. Change in Position  Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark  Distance- quantity that tells you how far something has moved  The runner travels 50 m in the original direction (east) plus 30 m in the opposite direction (west), so the total distance she ran is 80 m 55
  6. 6. Change in Position  Sometimes you may want to know not only your distance but also your direction from a reference point, such as from the starting point  Displacement- the distance AND direction of an object’s position relative to a starting point  Adding displacement: 50 m east, turn around and run 30 m west = 20 m east total displacement 66
  7. 7. Speed  Speed- the distance traveled by a moving object over a period of time  Kilometers/sec, miles/hour, meters/min 77
  8. 8. Speed Formula D = S X T T = D/S S = D/T Example: A rifle bullet travels 1200 meters in 4 seconds. What is the speed of the bullet? S = 1200m/4 sec. S = 300 m/sec. S = D / T Step # 1 Step # 2 Step # 3 88
  9. 9. Constant Speed  A moving object that doesn’t change its speed travels at constant speed  Constant speed- equal distances are covered in an equal amount of time (i.e. 25 miles/hour)  This results in a linear position vs. time graph 99
  10. 10. Changing Speed  Usually speed is not constant  Usually the speed will change for any number of reasons (wind, stop lights, etc.) 1100
  11. 11. Instantaneous speed Instantaneous speed-speed at any instant which the word “speed” alone is representing “My speed is 60 miles/h” is referring to your speed at that particular moment, but likely to change 1111
  12. 12. Average Speed AA ccaarr ttrraavveellss aatt 5500 kkmm//hh,, sslloowwss ddoowwnn ttoo 00 kkmm//hh,, and speeds uupp aaggaaiinn ttoo 6600 kkmm//hh Its average speed over the whole journey: overall distance travelled total time of travel = Instantaneous speeds 1122
  13. 13. Graphing Motion  On a distance (or position)- time graph, the distance, or position, is plotted on the vertical axis and the time on the horizontal axis  Each axis must have a scale that covers the range of number to be plotted  The slope on a distance-time graph is equal to speed 1133
  14. 14. Check for Understanding  What is the difference between distance and displacement? 1144
  15. 15. Check for Understanding  __________ is the distance an object travels per unit of time. A. acceleration B. displacement C. speed D. velocity 1155
  16. 16. Check for Understanding Name two observations you can make about the cars speed from looking at the graph. Calculate the speeds of both cars from the graph by choosing two points on each line. 1166
  17. 17. Check for Understanding Calculate the average speed of the car below: 1177
  18. 18. Velocity  Velocity- a speed in a given direction  It’s possible for two objects to have the same speed, but different velocities velocity Has directio direction n! magnitude (speed) 1188
  19. 19. Earth’s speed at the equator: 1670 km/h Earth’s velocity at the equator: 1670 km/h to the East 1199
  20. 20. Velocity  Velocity depends on direction as well as speed, so the velocity of an object can change even if the speed of the object remains constant  The speed of this car might be constant, but its velocity is not because the direction of motion is always changing 2200
  21. 21. Velocity and Momentum  A moving object has a property called momentum that is related to how much force is needed to change its motion  Momentum (p) takes into consideration not only an object’s velocity AND mass  Mass- the amount of matter (atoms) in an object (kg) 2211
  22. 22. Velocity and Momentum  Momentum is given the symbol p and can be calculated with the following equation p = mass (kg) X velocity (m/s)  The unit for momentum is kg · m/s. Notice that momentum has a direction because velocity has a direction. 2222
  23. 23. Velocity and Momentum  When two objects have the same velocity, the one with the larger mass has the larger momentum  The 1,000-kg car traveling at 20 m/s east has a momentum of 20,000 kg•m/s east.  p = m X v = 1000kg X 20 m/s  What about the truck?  Law of conservation of momentum- the total momentum of a system stays the same before and after an interaction 2233
  24. 24. Check for Understanding  Speed or Velocity?  A race car traveling 155 miles per hour turning left on a circular racetrack  A sprinter running 3 meters/sec  A tornado heading west at 15 km/hour 2244
  25. 25. Check for Understanding  Speed or Velocity?  A race car traveling 155 miles per hour V turning left on a circular racetrack  A sprinter running 3 meters/sec S  A tornado heading west at 15 km/hour V 2255
  26. 26. Check for Understanding  A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum? A. 1,500 kg•m/s B. 150,000 kg•m/s C. 1,400 kg•m/s D. 1,600 kg•m/s 2266
  27. 27. Check for Understanding  A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum? B. 150,000 kg•m/s 2277
  28. 28. Change in Velocity  Velocity rarely stays constant  Acceleration is the rate of change of velocity  When the velocity of an object changes, the object is accelerating  A change in velocity can be either a change in how fast something is moving, or a change in the direction it is moving  Acceleration occurs when an object changes its speed, its direction, or both 2288
  29. 29. Change in Velocity  In a car we can change our velocity 3 ways:  Speed up  Slow down  Change direction  All of these would be considered acceleration 2299
  30. 30. Change in Velocity We say that this car is accelerating because its velocity is increasing We say that this car is accelerating because its direction is changing as it turns, which means its velocity is changingeven though its speed stays constant We say that this car is accelerating because its velocity is decreasing. Decreasing velocity is still acceleration, although it is a negative acceleration 30 km/h 60 km/h 60 km/h 60 km/h 60 km/h 30 km/h 0 km/h 3300
  31. 31. Change in Velocity  Changing speed changes velocity and is therefore considered acceleration  Positive acceleration speeding up  Negative acceleration slowing down 3311
  32. 32. Velocity vs. Time Graphs The slope of the line on a speed-time graph equals the object’s acceleration NNeeggaattiivvee aacccceelleerraattiioonn PPoossiittiivvee aacccceelleerraattiioonn 3322
  33. 33. Change in Velocity  Is the velocity for each car constant or changing?  Which car has the highest velocity? 3333
  34. 34. Acceleration Formula A = Vfinal–Vinitial T OR Example: A cars velocity chang e s from 0.0m/s south to 50.0m/s south in 10.0 seconds. Calculate the cars acceleration. A = 5.0 m/s/s or m/s2 A = Vfinal – Vinitial T A = 50.0m/s – 0.0m/s 10.0s Step # 1 Step # 2 Step # 3 3344
  35. 35. Check for Understanding A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? 3355
  36. 36. Check for Understanding A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? Acceleration = Velocity(final) - Velocity(initial) time = 90 mph - 60 mph 3 seconds = 30 mph 3 seconds = 10 mph/second 3366
  37. 37. PPoossiittiivvee aacccceelleerraattiioonn Acceleration Velocity vs. Time Graph 3377
  38. 38. Check for Understanding A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? 3388
  39. 39. Check for Understanding A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? Acceleration = Velocity(final) - Velocity(initial) time = 0 mph - 60 mph 6 seconds = -60 mph 6 seconds = -10 mph/second 3399
  40. 40. NNeeggaattiivvee aacccceelleerraattiioonn Acceleration Velocity vs.Time Graph 4400
  41. 41. Acceleration in 2D  The speed of the horses in this carousel is constant, but they are accelerating because their direction is changing  This would be considered centripetal acceleration-acceleration of an object toward the center of a curved or circular path 4411
  42. 42. Horizontal & Vertical Motion Are Independent Gravity makes both bullets fall at the same rate The bullet from the gun keeps going forward while it falls. 4422
  43. 43. What if the Projectile is Thrown Upward? Projectiles keeps moving forward with . the same speed. Gravity slows projectiles down while going up and speeds them up while going down. 4433
  44. 44. CChheecckk ffoorr UUnnddeerrssttaannddiinngg  Which is NOT a form of acceleration? A. maintaining a constant speed and direction B. speeding up C. slowing down D. turning 4444
  45. 45. Check for Understanding  Which is NOT a form of acceleration? A. maintaining a constant speed and direction 4455
  46. 46. The question is… why? Why does everything in the universe move? 4466
  47. 47. The answer… Big, huge, massive forces! And little ones too. 4477
  48. 48. Forces A force is a pull (an attraction) Or, a push (a repulsion) 4488
  49. 49. Forces  All forces have two properties:  Direction  Size  A newton (N) is the unit that describes the size of a force and is equal to 1kg X m/s2 4499
  50. 50. Changing Motion  A force can cause the motion of an object to change  If you have played pool, you know that you can force a ball at rest to roll into a pocket by striking it with another ball  The force of the moving ball causes the ball at rest to move in the direction of the force  Force does not always change motion, though  5500
  51. 51. Net Force  When all the forces acting on an object are considered together, you determine the net force on the object  An object with a net force of anything other than 0 N on it will change its state of motion 5511
  52. 52. Forces in the Same Direction  When forces are applied in the same direction, they are added to determine the size of the net force 5522
  53. 53. 5533
  54. 54. Forces in Different Directions  When two forces act in opposite directions, you subtract the smaller force from the larger force to determine the net force  The net force will be in the same direction as the larger force 5544
  55. 55. Balanced Forces  Balanced forces cancel each other out! They are forces that are equal in size and opposite in direction 5555
  56. 56. Types of Forces 1. Friction 2. Gravity 3. Electromagnetic 4. Nuclear 5. Etc. 5566
  57. 57. 1. Friction  Friction- the force that opposes the sliding motion of two surfaces that are touching each other  i.e. skateboard stops rolling  It always slows a moving object down  The amount of friction between two surfaces depends on two factors¾the kinds of surfaces and the force pressing the surfaces together. 557
  58. 58. 1. Friction Force on person by box Force on floor by box Force on box by floor Force on box by person Corrugations and imperfections in the surfaces grind when things slide. How can we reduce friction? 5588
  59. 59. Cause of Friction •The larger the force pushing the two surfaces together is, the stronger these microwelds will be, because more of the surface bumps will come into contact 5599
  60. 60. Types of Friction  Static-prevents two surfaces from sliding past each other at all (move a box of books)  Sliding- opposes sliding motion (box of books that is sliding stops moving)  Rolling- acts over the area where the wheel and surface meet like traction (skateboard with box of books on it stops moving)  Fluid (Viscous)- opposes the motion of objects traveling through a fluid (air or water) 6600
  61. 61. 2. Gravity  Galileo-1600’s studied how things fell  Gravity is an attractive force between any two objects that depends on the masses of the objects and the distance between them  Isaac Newton formulated the law of universal gravitation, which he published in 1687 6611
  62. 62. Law of Universal Gravitation  This law can be written as the following equation 2  F 1 is the mmforce of gravity, G is a constant called the universal gravitational constant, and d is the distance between the two masses, and  The greater the mass of two objects, the greater the gravitational force (F) between them  The greater the distance between two objects, the less the gravitation force between them 6622
  63. 63. Gravitational Force  No matter how far apart two objects are, the gravitational force between them never completely goes to zero  Because of this gravity is called a long-range force  The strength of the gravitational field is 9.8 N/kg near Earth’s surface and gets smaller as you move away from Earth 6633
  64. 64. Weight  Because the weight of an object on Earth is equal to the force of Earth’s gravity on the object, weight can be calculated from this equation: or (m/s2)  Where Fg is the force of gravity on an object…..in other words, its weight…and g is 9.8 N/kg near Earth’s surface (9.8N/kg = 9.8 m/s2) 6644
  65. 65. Mass  Weight and mass are not the same  Weight is a force and mass is a measure of the amount of matter an object contains  Weight and mass are related. Weight increases as mass increases or (m/s2) 6655
  66. 66. Mass vs. Weight The amount of matter (atoms) in an object A measure of gravity’s pull on an object Measure with a balance Measure with a Newton scale Never changes Changes due to gravity Both are measure-ments of matter 6666
  67. 67. Check for Understanding • What is the weight of a 10-kg block? 10 kg m 9.8 N/kg Fg Fg = mg = (10 kg)(9.8 N/kg) Fg F = 98 N g = 98 N 667
  68. 68. Newton’s Laws of Motion  Newton lived from 1642–1727  #1 An object in motion stays in motion and an object at rest stays at rest unless acted upon by an unbalanced force  #2 Force equals mass times acceleration (F = ma)  #3 For every action there is an equal and opposite reaction 6688
  69. 69. Newton’s First Law An object in motion stays in motion and an object at rest stays at rest unless acted upon by an unbalanced force 6699
  70. 70. Newton’s First Law  What does this mean?  AAn object will keep doing what it’s doing UNLESS acted on by an unbalanced force like friction  If it is moving at a constant velocity it will continue  If it is at rest, it stays at rest  In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed and direction would keep going in that same direction and same speed forever 700
  71. 71. Newton’s First Law  Called the Law of Inertia- the tendency of an object to resist changes in its state of motion  Recall that mass is the amount of matter (atoms) in an object  Newton’s First Law states that all objects have inertia  The more mass an object has, the more inertia it has (and the harder it is to change its motion) 711
  72. 72. Then why don’t moving objects keep moving forever? Things don’t keep moving forever because there’s almost always an unbalanced force acting upon it A book sliding across a table slows down and stops because of the force of friction If you throw a ball upwards it will eventually slow down and fall because of the force of gravity 722
  73. 73. Newton’s Second Law Force equals mass times acceleration F = ma 7733
  74. 74. Newton’s Second Law  What Does F = ma Mean?  The force of an object comes from its mass and its acceleration so that the acceleration of an object is in the same direction as the net force on the object  A massive glacier that’s changing speed very slowly (low acceleration) can still have great force due to its mass  Something very small (low mass) like a bullet that’s changing speed very quickly (high acceleration) can still have a great force 7744
  75. 75. Force = Mass X Acceleration  Force is directly proportional to mass and acceleration  First ball: has a certain mass, m, moving at a certain acceleration, a, and therefore a certain force, f.  Second ball: has double the mass of the first ball, 2m, and the same acceleration, a, therefore has twice the force of the first ball, 2f  Third ball: has mass m moving at twice the first ball’s acceleration, 2a, would have a force of 2f. a a a m m m 7755
  76. 76. Newton’s Third Law For every action there is an equal and opposite reaction 7766
  77. 77. Newton’s Third Law  What Does this Mean?  When one object exerts a force on a second object, the second one exerts a force on the first that is equal in strength and opposite in direction  Gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force  There are balanced forces acting on you– gravity pulling down and your seat pushing up- so you are not moving gravity your seat 7777
  78. 78. Newton’s Third Law  For every action force, there must be an equal and opposite reaction force  Forces occur in pairs The action force is exerted by the _____ hhaannddss on the _____. bbaarr The reaction force is exerted by the _____ bbaarr on the _____. hhaannddss Action Reaction Newton’s Laws on teachersdomain 7788
  79. 79. Check for Understanding One newton is a force which imparts an acceleration of 1 m/s2 to a mass of 1 kg. FF ((NN)) == mm ((kkgg)) aa ((mm//ss22)) What resultant force will give a 3 kg mass an acceleration of 4 m/s2? F = m a 3 kg F = 3 kg X 4 m/s2 FF == 1122 NN F = ? a = 4 m/s2 7799
  80. 80. Check for Understanding  Inertia is__________.  A. the tendency of an object to resist any change in its motion  B. the tendency of an object to have a positive acceleration  C. The tendency of an object to have a net force of zero.  D. The tendency of an object to change in speed or direction. 8800
  81. 81. Check for Understanding  Inertia is__________.  A. the tendency of an object to resist any change in its motion 8811
  82. 82. Check for Understanding  Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object.  A. acceleration  B. momentum  C. speed  D. velocity 8822
  83. 83. Check for Understanding  Newton’s second law of motion states that _________ of an object is in the same direction as the net force on the object.  A. acceleration 8833
  84. 84. Newton’s Law Applied to Life  Newton’s 3 laws can be used to explain everyday events, such as falling, and collision  These laws have been applied to aid in technology, safety, and countless other ways  Newton’s Laws on Science360 8844
  85. 85. Newton’s First Law with Seat Belts  Don’t let this be you  Due to inertia, objects (including you) resist changes in their motion. When you and the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 km/hour 8855
  86. 86. Newton’s First Law with Air Bags  Air bags also reduce injuries in car crashes by providing a cushion that reduces the force on the car's occupants  When impact occurs, a chemical reaction occurs in the air bag that produces nitrogen gas  The air bag expands rapidly and then deflates just as quickly as the nitrogen gas escapes out of tiny holes in the bag 8866
  87. 87. Newton’s First Law and Centripetal Force  According to Newton, as a car tries to make a turn, the car would continue in a straight line unless there was a force acting on the car to turn it  This force of friction acting upon the turned wheels provides centripetal force required for circular motion 8877
  88. 88. Newton’s First Law and Centripetal Force Inertia Without a centripetal force, an object in motion continues along a straight-line path With a centripetal force, an object in motion will be accelerated and change its direction Centripetal Force 8888
  89. 89. Newton’s First Law and Centripetal Force  As a bucket of water is spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion  The force of gravity acting upon the moon provides the centripetal force required for orbit  Nascar and Centripetal Force 8899
  90. 90. Newton’s Second Law and Gravitational Acceleration  If gravity is the only force being exerted on an object’s mass then the net force is Fg   ****Combining the above gravitational law with Newton’s second law, F=ma, the force due to gravity only would cause an object to accelerate at 9.8 m/s/s (m/s2)  Papers falling demo 9900
  91. 91. Acceleration Due to Gravity  Gravity causes objects to accelerate at the SAME rate, 9.8 m/s/s (~10 m/s/s)  WITHOUT air resistance, a friction-like force, all objects would fall at the same speed  Galileo on the moon  Doesn’t depend on mass  After 1 second falling at ~10 m/s  After 2 seconds ~20 m/s  3 seconds ~30 m/s 9911
  92. 92. Terminal Velocity  Air resistance (fluid friction) will increase as object falls faster causing an upward force on the object  Eventually gravity will balance with air resistance  Reaches terminal velocity - highest speed reached by a falling object  Terminal velocity No air resistance Air resistance which is greater on the feather 9922
  93. 93. 9933
  94. 94. Summary of Formulas  Speed = distance traveled (m) time (s)  Velocity = displacement (distance with direction) (m) time (s)  Momentum (p) = velocity (m/s) X mass (kg)  Acceleration = change in velocity (m/s) or m/s2 time (s)  Force of gravity (weight in N) = mass (kg) X gravitational strength 9.8 (N/kg)  Force = mass X acceleration (9.8 m/s2 if due to gravity) 9944
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