Welcome to Physics B Trina Merrick MCHS *Slides/material

1
Welcome to

• Physics B

Trina Merrick MCHS Slides/material thanks to
Dr. Peggy Bertrand of Oak Ridge High School, Oak
Ridge,TN
2
Kinematics

• Kinematics is the branch of mechanics that
  describes the motion of objects without
  necessarily discussing what causes the motion.
• We will learn to describe motion in two ways.
• Using graphs
• Using equations

3
Particle

• A particle is an object that has mass but no
  volume and occupies a position described by one
  point in space.
• Physicists love to turn all objects into
  particles, because it makes the math a lot
  easier.

4
Position

• How do we represent a point in space?
• a) One dimension
• b) Two dimensions
• c) Three dimensions

(x) (x,y) (x,y,z)
5
Distance (d)

• The total length of the path traveled by a
  particle.
• How far have you walked? is a typical distance
  question.
• SI unit
• meter (m)

6
Displacement (Dx)

• The change in position of a particle.
• How far are you from home? is a typical
  displacement question.
• Calculated by
• ?x xfinal xinitial
• SI unit
• meter (m)

7
Delta ( ? )

• ? is a Greek letter used to represent the words
  change in. ?x therefore means change in x. It
  is always calculated by final value minus initial
  value.

8
Practice Problem

• Question If ?x is the displacement of a
  particle, and d is the distance the particle
  traveled during that displacement, which of the
  following is always a true statement?
• d Dx
• d lt Dx
• d gt Dx
• d gt Dx
• d lt Dx

9
Practice Problem

• A particle moves from x 1.0 meter to x -1.0
  meter.
• What is the distance d traveled by the particle?
• What is the displacement of the particle?

2.0 m -2.0 m
10
Distance vs Displacement

• A picture can help you distinquish between
  distance and displacement.

11
Practice Problem

• You get on a ferris wheel of radius 20 meters at
  the bottom. When you reach the top on the first
  rotation
• what distance have you traveled?
• what is your displacement from the bottom?
• When you are on your way back down, does the
  distance increase, decrease, or stay the same?
  What about the displacement?
• What is the distance traveled after you have
  completed the full ride of 10 rotations? What
  about the displacement?

12
Practice Problem answers

• You get on a ferris wheel of radius 20 meters at
  the bottom. When you reach the top on the first
  rotation
• d ½ (2 ? r) ? r 20 ? m
• ? x 20 20 40 m
• distance increases, displacement decreases
• d 10 (2 ? r) 400 ? m

13
Average Speed

• How fast a particle is moving.
• save d
• ?t
• where
• save rate (speed)
• d distance
• ? t elapsed time
• SI unit
• m/s

Average speed is always a positive number.
14
Average Velocity

• How fast the displacement of a particle is
  changing.
• vave ?x
• ?t
• where
• vave average velocity
• ?x displacement
• ?t change in time
• SI unit
• m/s

Average velocity is or depending on direction.
15
Demonstration

• You are a particle located at the origin.
• Demonstrate how you can move from x 0 to x
  10.0 with an average speed of 0.5 m/s. You may
  not leave the x-axis!
• What was your average velocity in this case?

16
Demonstration

• You are a particle located at the point x 10.0
  m.
• Demonstrate how you can move from x 10.0 to x
  0 with an average speed of 0.5 m/s. You may not
  leave the x-axis!
• What is your average velocity in this case?

17
Demonstration

• You are a particle located at the origin.
• Demonstrate how you can move from x 0 to x
  10.0 and back with an average speed of 0.5 m/s.
  You may not leave the x-axis!
• What was your average velocity in this case?

18
Practice Problem

• A car makes a trip of 1½ laps around a circular
  track of diameter 100 meters in ½ minute. For
  this trip
• a) what is the average speed of the car?
• b) what is its average velocity?

19
Practice Problem

• How long will it take the sound of the starting
  gun to reach the ears of the sprinters if the
  starter is stationed at the finish line for a 100
  m race? Assume that sound has a speed of about
  340 m/s.
• Answer 0.29 s

20
Practice Problem

• Describe the motion of this particle.
• It is stationary.

21
Practice Problem

• Describe the motion of this particle.
• It is moving at constant velocity in the x
  direction.

22
Practice Problem
vave Dx/Dt

• What physical feature of the graph gives the
  constant velocity?
• The slope, because Dx/Dt is rise over run!

23
Practice Problem

• Determine the average velocity from the graph.
• Ans 1/3 m/s

24
Force Concept Inventory

• No scratch paper or calculator is necessary.
• Use pencil on BLUE side of scantron sheet.
• Name Write your NAME followed by your TEST
  NUMBER.
• Subject FCI
• Date 8/17/05
• Period ???
• When you are done, bring your scantron sheet to
  the front of the room and quietly begin working
  on tonights homework.

25
Practice
Q 7 Is it possible for a car to circle a race
track with constant velocity? Can it do so with
constant speed? Q 8 Friends tell you that on a
recent trip their average velocity was 20 m/s.
Is it possible that their instantaneous velocity
was negative at any time during the trip? P 13
The human nervous system can propagate nerve
impulses at about 102 m/s. Estimate the time it
takes for a nerve impulse generated when your
finger touches a hot object to travel the length
of your arm. (HINT How long is your arm,
approximately?)
26
Average Velocity Lab

• Purpose Figure out a way to make your cart move
  with an average velocity of as close to 0.200 m/s
  as possible. Use only the equipment provided.
  Photogate must be in PULSE mode.
• Tonight Type your BRIEF and PARTIAL lab report.
  The sections I want you to do are
• Procedure
• Data (include a table of data for 5 trials, a
  sample calculations, and a diagram of your
  setup). Clearly indicate what you predicted your
  average velocity to be, and what it actually was
  during the demo.
• Analysis (where did your errors come from?)

27
Practice Problem

• Does this graph represent motion at constant
  velocity?
• No, since there is not one constant slope for
  this graph.

28
Practice Problem
vave Dx/Dt

• Can you determine average velocity from the time
  at point A to the time at point B from this
  graph?
• Yes. Draw a line connecting A and B and determine
  the slope of this line.

29
Practice Problem

• Determine the average velocity between 1 and 4
  seconds.
• Ans 0.17 m/s

30
Practice Problem

• You drive in a straight line at 10 m/s for 1.0
  hour, and then you drive in a straight line at 20
  m/s for 1.0 hour. What is your average velocity?
• Answer 15 m/s (this is probably what you
  expected!)

31
Practice Problem

• You drive in a straight line at 10 m/s for 1.0
  km, and then you drive in a straight line at 20
  m/s for another 1.0 km. What is your average
  velocity?
• Answer 13.3 m/s (this is probably NOT what you
  expected!)
• Always use the formula for average velocity
  dont just take an average of the velocities!

32
Instantaneous Velocity

• The velocity at a single instant in time.
• Determined by the slope of a tangent line to
  the curve at a single point on a position-time
  graph.

33
Instantaneous Velocity
vins Dx/Dt
B

• Draw a tangent line to the curve at B. The slope
  of this line gives the instantaneous velocity at
  that specific time.

34
Practice Problem

• Determine the instantaneous velocity at 1.0
  second.
• Ans 0.85 m/s

35
Practice Problem

• The position of a particle as a function of time
  is given by the equation
• x (2.0 m/s) t (-3.0 m/s2)t2.
• Plot the x vs t graph for t 0 until t 1.0 s.
• Find the average velocity of the particle from t
  0 until t 0.50 s.
• Find the instantaneous velocity of the particle
  at t 0.50 s.

36
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37
Practice
Q 10 If the position of an object is zero, does
its speed need to be zero? Q 11 For what kind of
motion are the instantaneous and average
velocities equal? P 27 The position of a
particle as a function of time is given by x
(-2.0 m/s) t (3.0 m/s2) t2. a) Plot x-vs-t for
time from t 0 to t 1.0 s. b) Find the average
velocity of the particle form t 0.15 s to t
0.25 s. c) Find the average velocity from t
0.19 s to t 0.21 s.
38
Acceleration (a)

• Any change in velocity is called acceleration.
• The sign ( or -) of acceleration indicates its
  direction.
• Acceleration can be
• speeding up
• slowing down
• turning

39
Uniform (Constant) Acceleration

• In Physics B, we will generally assume that
  acceleration is constant.
• With this assumption we are free to use this
  equation
• a ?v
• ?t
• SI Unit
• m/s2

40
Acceleration has a sign!

• If the sign of the velocity and the sign of the
  acceleration is the same, the object speeds up.
• If the sign of the velocity and the sign of the
  acceleration are different, the object slows down.

41
Practice Problem

• A 747 airliner reaches its takeoff speed of 180
  mph in 30 seconds. What is its average
  acceleration?

42
Practice Problem

• A horse is running with an initial velocity of 11
  m/s, and begins to accelerate at 1.81 m/s2. How
  long does it take the horse to stop?

43
Practice Problem

• Describe the motion of this particle.
• It is moving in the x direction at constant
  velocity. It is not accelerating.

44
Practice Problem

• Describe the motion of this particle.
• It is stationary.

45
Practice Problem

• Describe the motion of this particle.
• It starts from rest and accelerates in the x
  direction. The acceleration is constant.

46
Practice Problem
a Dv/Dt

• What physical feature of the graph gives the
  acceleration?
• The slope, because Dv/Dt is rise over run!

47
Practice Problem

• Determine the acceleration from the graph.
• Ans 10 m/s2

48
Practice Problem

• Determine the displacement of the object from 0
  to 4 seconds.
• Ans 0
• Describe the motion.

The object is initially moving in the negative
direction at 20 m/s, slows gradually and
momentarily is stopped at 2.0 seconds, and then
accelerates in the direction. At 4.0 seconds,
it is back at the origin, and continues to
accelerate in the direction.
49
Demonstration
50
Demonstration
51
Position vs Time Graphs

• Particles moving with no acceleration (constant
  velocity) have graphs of position vs time with
  one slope. The velocity is not changing since the
  slope is constant.
• Position vs time graphs for particles moving with
  constant acceleration look parabolic. The
  instantaneous slope is changing. In this graph it
  is increasing, and the particle is speeding up.

52
Uniformly Accelerating Objects

• You see the car move faster and faster. This is a
  form of acceleration.
• The position vs time graph for the accelerating
  car reflects the bigger and bigger Dx values.
• The velocity vs time graph reflects the
  increasing velocity.

53
Position vs Time Graphs

• This object is moving in the positive direction
  and accelerating in the positive direction
  (speeding up).
• This object is moving in the negative direction
  and accelerating in the negative direction
  (speeding up).
• This object is moving in the negative direction
  and accelerating in the positive direction
  (slowing down).

54
Pick the constant velocity graph(s)
(This is not in the notes.)
55
Draw Graphs forStationary Particles
56
Draw Graphs forConstant Non-zero Velocity
57
Draw Graphs for ConstantNon-zero Acceleration
58
Practice Problem

• What must a particular Olympic sprinters
  acceleration be if he is able to attain his
  maximum speed in ½ of a second?
• In some problems, estimation is an important part
  of the problem!

59
Practice Problem

• A plane is flying in a northwest direction when
  it lands, touching the end of the runway with a
  speed of 130 m/s. If the runway is 1.0 km long,
  what must the acceleration of the plane be if it
  is to stop while leaving ¼ of the runway
  remaining as a safety margin?

60
Kinematic Equations

• v vo at
• Use this one when you arent worried about x.
• x xo vot ½ at2
• Use this one when you arent worried about v.
• v2 vo2 2a(?x)
• Use this one when you arent worried about t.

61
Practice Problem

• On a ride called the Detonator at Worlds of Fun
  in Kansas City, passengers accelerate straight
  downward from 0 to 20 m/s in 1.0 second.
• What is the average acceleration of the
  passengers on this ride?
• How fast would they be going if they accelerated
  for an additional second at this rate?
• Sketch approximate x-vs-t, v-vs-t and a-vs-t
  graphs for this ride.

62
Practice Problem

• Air bags are designed to deploy in 10 ms.
  Estimate the acceleration of the front surface of
  the bag as it expands. Express your answer in
  terms of the acceleration of gravity g.

63
Practice Problem

• You are driving through town at 12.0 m/s when
  suddenly a ball rolls out in front of you. You
  apply the brakes and decelerate at 3.5 m/s2.
• How far do you travel before stopping?
• When you have traveled only half the stopping
  distance, what is your speed?
• How long does it take you to stop?
• Sketch approximate x-vs-t, v-vs-t, a-vs-t graphs
  for this situation.

64
Practice problems

• 39. Landing with a speed of 115 m/s and traveling
  due south, a jet comes to rest in 7.00 x 102 m.
  Assuming the jet slows with constant
  acceleration, find the magnitude and direction of
  its acceleration.

65
Practice problems

• 40. When you see a traffic light turn red you
  apply the brakes until you come to a stop. If
  your initial speed was 12 m/s, and you were
  headed due west, what was your average
  acceleration during braking?
• 41. Suppose the car in the previous problem comes
  to rest in 35 m. How much time does this take?

66
Practice problems

• 42. Starting from rest, a boat increases its
  speed to 4.30 m/s with constant acceleration
• (a) What was the boats average speed?
• (b) If it takes the boat 5.00 s to reach this
  speed, how far has it traveled?

67
Practice problems

• 43. A cheetah accelerates from rest to 25 m/s in
  6.2 s. Assuming constant acceleration,
• (a) how far has the cheetah run in this time?
• (b) How far has the cheetah run in 3.1 s?

68
Lab Report Analysis

• The GOOD procedure
• The BAD procedure
• The UGLY procedure
• The POETIC procedure
• LAB REPORT FORMAT

69
Lab

• The Physics 500
• PartI Determine your speed (use multiple trials,
  etc.) while doing two activities using a
  meterstick and stopwatch.
• PartII After choosing which of your
  activities is more reliable, surrender your
  meterstick and use you and your activity speed to
  determine the unknown distance marked off by your
  teacher.

70
Labs

• Tumble Buggy Lab
• TumbleBuggy Lab AP Physics
• Constant Velocity
• Devise a method to determine the speed of your
  TumbleBuggy.
• Determine the Speed of the TumbleBuggy.
• Devise a method to determine the length of the
  hall USING THAT INFORMATION! The TumbleBuggy
  cannot, however enter the hallway. You also MAY
  NOT measure the hallway with a meterstick!!
• In the open area (hallway) devise a method to
  construct a table of data of position versus time
  for your tumblebuggy. You are restricted to
  usingt he materials on the materials table. All
  of them may not be needed. (Tape, paper, post-it
  notes, paper clips)
• Construct a Position vs. Time graph for the
  tumblebuggy.
• Using information from that graph, determine the
  speed of the tumblebuggy. Compare to the speed to
  the data from Part II.
• Use that information to graph velocity versus
  time for the tumblebuggy. Determine the
  acceleration from the graph.
• Plot acceleration versus time for the tumblebuggy.

71
Lab

• Picket Fence Lab
• Purpose To determine an approximate value for
  the gravitational acceleration constant.
• Theory The gravitational acceleration constant,
  g, is approximately 9.8 m/s2 near the surface of
  the earth. Objects in free-fall therefore
  accelerate toward the earth at a rate of 9.8
  meters per second per second. The downward
  instantaneous velocity of a freely falling object
  follows the following equation v v0 - gt. If
  the instantaneous velocity at various points
  during free-fall can be determined, the
  gravitational acceleration constant should be
  able to be estimated.
• Equipment
• Photogate Stopwatch Meterstick Picket
  Fence CBL
• Discussion How did the acceleration you observe
  compare to the actual acceleration due to
  gravity? What assumptions did we make that could
  account for the differences? What are some
  possible sources of human and equipment error?

72
Lab Free Fall Times

• Purpose To investigate the relationship between
  the distance an object falls from rest with the
  time it takes to travel that distance.
• Theory In the case of falling from rest, the
  second kinematic equation
• x xo vot ½ a t2
• can be use to derive the free fall equation
• y -1/2 g t2
• where g is the acceleration due to gravity (9.8
  m/s2), t is the time, and y is the distance
  fallen.
• Equipment Photogate timers, droppable objects,
  meter sticks.
• Procedure Come up with a method to test the
  validity of the free fall equation using the
  equipment given. Must include the dropping of
  more than one type of object from several
  different heights.
• Data and calculated results Must appear in a
  clear and neat table, and must include a
  comparison of calculated and measured results.
  You might find the following equation handy
• difference measured result theoretical
  result
• theoretical result
• Conclusion/Discussion Should include problems
  encountered in devising the procedure, a
  comparison of the free fall characteristics of
  different objects (the same or different) and a
  comparison of the calculated and measured
  results. Can you think of any errors that you
  might have encountered and explain how these
  errors might have affected your results?

73
Model problem (HW 44)

• A kid slides down a hill on a toboggan (a HAT?)
  with an acceleration of 3.0 m/s2. If he starts
  from rest, how far has he traveled in
• (a) 1.0 s?
• (b) 2.0 s?
• (c) 3.0 s?

74
Model Problem (47)

• Two car drive on a straight highway. At time t
  0, car A passes mile marker 0 traveling due north
  with a speed of 28.0 m/s. At the same time, car B
  is 2.0 km south of mile marker 0 traveling at
  30.0 m/s due south. Car A is speeding up with an
  acceleration of magnitude 1.5 m/s2, and car B is
  slowing down with an acceleration of magnitude
  2.0 m/s2. Write x-vs-t equation of motion for
  both cars.

75
Model Problem (48)

• A 1-ton baby elephant jumps onto the roof of a
  Volkswagon. Upon impact, the elephants speed is
  5.0 m/s. The elephant makes a dent in the roof of
  the Voltswagon that is 50 cm deep. What is the
  magnitude of the elephants deceleration, assuming
  it is constant.

76
Model Problem (49)

• Superman leaps into the air and moves straight
  upward with constant acceleration. After 5
  seconds, Superman has reached a height of 2,000
  m.
• A) What is Supermans acceleration?
• B) What is his speed at this time?

77
Model Problem (55)

• A yacht cruising at 2.0 m/s is shifted into
  neutral. After coasting 8.0 m, the engine is
  engaged again and the yacht resumes cruising at a
  reduced speed of 1.5 m/s. How long did it take
  the yacht to coast the 8.0 m?

78
Free Fall

• Occurs when an object falls unimpeded.
• Gravity accelerates the object toward the earth
  the entire time it rises, and the entire time it
  falls.
• a -g -9.8 m/s2
• Acceleration is always constant and toward the
  center of the earth!!!

79
Symmetry in Free Fall

• When something is thrown upward and returns to
  the thrower, this is very symmetric.
• The object spends half its time traveling up
  half traveling down.
• Velocity when it returns to the ground is the
  opposite of the velocity it was thrown upward
  with.
• Acceleration is 9.8 m/s2 everywhere!

80
Demonstration

• Object dropped from rest
• Object thrown up that falls.

81
Practice Problem

• You drop a ball from rest off a 120 m high cliff.
  Assuming air resistance is negligible,
• how long is the ball in the air?
• what is the balls speed and velocity when it
  strikes the ground at the base of the cliff?
• what is the balls speed and velocity when it
  has fallen half the distance?
• sketch approximate x-vs-t, v-vs-t, a-vs-t graphs
  for this situation.

82
Announcements 2/7/2013
83
Practice Problem

• You throw a ball straight upward into the air
  with a velocity of 20.0 m/s, and you catch the
  ball some time later.
• How long is the ball in the air?
• How high does the ball go?
• What is the balls velocity when you catch it?
• Sketch approximate x-vs-t, v-vs-t, a-vs-t graphs
  for this situation.

84
Pretest Free Response

• Case 1 Ball A is dropped from rest at the top
  of a cliff of height h as shown. Using g as the
  acceleration due to gravity, derive an expression
  for the time it will take for the ball to hit the
  ground.

A
85
Pretest Free Response

• Case 2 Ball B is projected vertically upward
  from the foot of the cliff with an initial speed
  of vo. Derive an expression for the maximum
  height ymax reached by the ball.

B
86
Pretest Free Response

• Case 3 Ball A is dropped from rest at the top of
  the cliff at exactly the same time Ball B is
  thrown vertically upward with speed vo from the
  foot of the cliff such that Ball B will collide
  with Ball A. Derive an expression for the amount
  of time that will elapse before they collide.

A
h
vo
B
87
Pretest Free Response

• Case 4 Ball A is dropped from rest at the top of
  the cliff at exactly the same time Ball B is
  projected vertically upward with speed vo from
  the foot of the cliff directly beneath ball A.
  Derive an expression for how high above the
  ground they will collide.

A
h
vo
B