AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 11

I'm in the Charlottesville airport ready for my trip to see the Portland Thorns.  At school, physics fight preparation starts Monday.  

Friday was my last class with the AP Physics 1 section.  They will be mentoring conceptual students in preparation for the physics fight tournament on May 21.  

The discussion in Friday's class turned to physics teaching,  We talked about meeting their mentees where they are, not where mentors want them to be.  We talked about mentoring not being about the glory of the mentor, but about support for the students being mentored.  

As a practical example, I gave this algebra-based section a 30-second explanation of free-fall with air resistance, including the differential equation for velocity and how that results in an exponential change from acceleration of g to terminal speed.  As their mouths hung open, I asked the class: how would you have felt if I had started with this presentation on the first day of class?  It's fully correct, after all... and are you ready to explain free-fall with air resistance?  Why not?  I've explained it to you...

They got my point in a visceral way.  I saw the students nodding, I saw the figurative light bulb go on over their heads.  Not that I won't have to help out some mentors who talk at their group at way too high a level!  But at least now I'll be able to say "remember what we talked about?"

FUNDAMENTALS CHECK #11

101.  Planet A and Planet B orbit one another.  Planet A is four times the mass of planet B.  What is the ratio of the net force on planet A to the net force on planet B?

102. Under what conditions is the angular momentum of a system conserved?

103. The unbalanced force on an object is in the direction of ________.

104. A 1 kg block falls from a table to the floor 1 m below; air resistance is negligible.  Consider the block-earth system.  How much work was done by external forces on the block during its fall?

105. A person stands on a scale in an elevator.  Give all ways the elevator could be moving if the scale reading is greater than the person's weight.

106. A block slides along the floor to the right, slowing down due to friction.  What is the Newton's third law force pair to the force of friction on the block?

107. A block slides along the floor to the right, slowing down due to friction.  What is the direction of the block's acceleration?

108. A block attached to a string oscillates as a pendulum in simple harmonic motion.  Describe the direction of the unbalanced force on the block throughout its motion.

109. How do you determine speed from a position-time graph?

110. A meterstick of mass m hangs horizontally.  How much torque is provided by the earth about the meterstick's center of mass?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 10

Now's the time to be TAPERED for the AP physics exams.  See this post.  Point is, the less we require now, the more political capital we'll gain with our students - both current students and future students. 

 Most students taking AP Physics are also taking other AP exams, and the teachers of those courses are putting all sorts of last minute burdens on their classes - Saturday practice exams, multiple choice practice tomes, study shaming, etc.  

Think how much better our students will feel if we say "Meh, you're as ready as you're gonna be.  Spend the next two weeks relaxing, doing one fundamentals quiz a day, and maybe doing a practice problem here and there with your friends."  And this approach won't in any way hurt their performance on exam day.

Fundamentals Check #10:

91. An object hangs on a vertical spring.  Let the position where the object hangs in equilibrium be the zero of potential energy.  What is the formula for the potential energy of the spring-object-earth system?  Define each variable briefly.

92. Consider a wooden block on a wooden surface.  Which is larger, the coefficient of static friction between the surfaces, or the coefficient of kinetic friction?

93. An object slides up an incline which sits at an angle θ above the horizontal.  What is the formula for the component of the object's weight that acts perpendicular to the incline?

94. Under what conditions does an object experience balanced forces?

95. Sophia pushes a ball to the right.  After she lets go, the ball rolls right and slows down.  While the ball slows down, what is the direction of the force applied by Sophia to the ball?

96. What is the weight of a 90 kg person on earth?

97. Write the kinematics equation for angular displacement under constant angular acceleration.

98. A block which weighs 100 N is attached to a string, which pulls vertically upward.  The block moves upward and slows down.  Is the tension in the string greater than, less than, or equal to 100 N?

99. What are the units of the coefficient of static friction?

100. Two 1 kg carts are connected by a compressed spring, and are initially at rest.  The spring uncoils, causing the carts to move in opposite directions, each with 1 m/s of speed.  What is the total momentum of the two-cart system after the spring uncoils?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 9

These fundamentals checks are just as appropriate for AP Physics C (mechanics) as for AP Physics 1.  Those two courses cover the exact same topics!  And, if you're going to be successful on the C exam, you need to first understand everything on the 1 exam.

I've been repeatedly asked about the viability of teaching a combined section of APC and AP1.  That's totally doable... because I'd teach it as just AP Physics 1 until about March.  Then, as the AP1 students do cumulative review for the exam, the APC students can do their review in the context of practicing calculational problems, and of learning some of the calculus techniques unique to the C exam.  

My experience, and the physics education literature, all demonstrate clearly that it's straightforward for a students to use a strong conceptual foundation as a springboard for success in mathematical physics.  But it's very difficult to go the other way around, for a student to use mathematical problem solving skills as a platform for developing strong conceptual understanding.  Even though that seems counterintuitive to professional physicists.  

Fundamentals Check #9:

81. I attach a 20 g mass to a spring, set the spring in harmonic motion, and measure its period.  The mass is determined using period = 2πroot(m/k).  Did I determine gravitational mass or inertial mass?

82. Define torque.

83. How do you determine an object's speed from a velocity-time graph?

84. A car moves east at 30 m/s.  Ten seconds later, the car moves east at 10 m/s.  What is the magnitude and direction of the car's acceleration?

85. Cart A, of mass 1 kg, moves left with speed 1 m/s.  Cart B, of mass 1 kg, moves right with speed 1 m/s.  What is the total kinetic energy of the two-cart system?

86. Cart A, of mass 1 kg, moves left with speed 1 m/s.  What is the magnitude and direction of cart A's momentum?

87. A ball has 100 J of gravitational potential energy relative to the ground when it is dropped from rest from a high cliff.  The ball has 60 J of kinetic energy right before hitting the ground.  How much work was done by air resistance during the ball's fall?

88. A ball is launched vertically off of a table, 70 cm above the floor.  The ball reaches a maximum height of 160 cm above the floor, then falls to the floor.  What is the magnitude of the ball's displacement between the table and the floor?

89. What is the formula for rotational inertia of a point object?

90. About how much of a circle is a radian?  (Your answer may not reference π). 

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 8

Just in case any readers from Portland, Oregon are out there: for my sabbatical, I get funding to attend a bunch of National Women's Soccer League games all over the country.  On Saturday April 29 I don't have class... so I am flying across the country to Portland to attend the Thorns vs. Angel FC game at Providence Park.  

I've been to Providence Park before... but for the first time, I'll be sitting with the Rose City Riveters - the crazy fans who chant and cheer the whole game.  They tend to paint their hair red, which I won't be doing.  But I'll definitely be wearing one of my several Thorns jerseys, I'll learn the songs, and I'll cheer hard for the Thorns players I've grown to love watching.  We'll see how it goes - 'twill be, um, an interesting experience for me.  I'm both excited and apprehensive.

Point is, if you're in Portland, I plan to hang out at Powell's Books in the late afternoon between my flight arriving and the game.  I'd be happy to talk physics teaching with anyone over coffee or dinner.  Just email me (via Woodberry Forest School) if you'd like to say hi.  Yes, I'm primarily talking to physics teachers... but if you have a group of several physics students who'd like to say hello, I'd love to meet youall, too!

Fundamentals Check #8

71. What are the units of mass?

72. An object moves in a circular path and speeds up.  Describe the direction of the object's acceleration.

73. I throw a ball upward with initial speed 10 m/s.  Is the highest position reached greater than, less than, or equal to 10 m above where I threw it? [This question has been edited since first posting.]

74. A satellite moves in an elliptical orbit around Earth, from position A closest to Earth to position B farthest from Earth.  Does the kinetic energy of the satellite increase, decrease, or remain the same when moving from A to B?

75. A satellite moves in an elliptical orbit around Earth, from position A closest to Earth to position B farthest from Earth.  Does the angular momentum of the satellite about the satellite's center increase, decrease, or remain the same when moving from A to B?

76. Write the formula for rotational kinetic energy, defining each term briefly.

77. A string pulls at angle of 30 degrees above the horizontal with tension 100 N.  What is the horizontal component of the tension in the string?

78. A normal force is the force of ____ on ____.

79. An object is 3 m above a table, and 6 m above the floor.  The object is moved horizontally from a position directly above the table to a position above the floor without the table in the way.  Has the potential energy of the object-earth system increased, decreased, or remained the same?

80. A person of mass 75 kg stands on a platform scale in an elevator which is moving down and speeding up.  Is the reading in the scale greater than, less than, or equal to 750 N?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 7

These fundamentals checks are excellent for exam prep.  You've been solving problems all year!  With the exam approaching, you know how to finish a problem, as long as you know how to start.  Well, on the AP exam, you can't ask a friend or a teacher how to start.  These fundamentals checks will help remind you where to start.

I know it might not FEEL like doing a five-minute "quiz" each day isn't quite the studying that your friends, teachers, and parents expect.  They talk about holing yourself up in a quiet cell doing practice problems for many hours.  

They are wrong.  

You're doing plenty of practice problems in your class.  Outside of class, just do these fundamentals checks each day, and make sure you pay attention to the answers to whatever you get wrong.  Have fun with them - challenge a friend or your classmates to see who gets the highest scores.  Ask your teacher if they'll give a homework exemption for top scores.  Bet a milkshake with some friends on your performance.  Anything to make the process enjoyable.

Fundamentals Check #7

61. How do you find instantaneous angular velocity from an angular position vs. time graph?

62.  The diagram to the right shows a ball of mass m moving at speed v toward point P.  The ball is a distance x from point P.  What is the angular momentum of the ball about point P?

63. An airplane has been cruising at a speed of 200 m/s for 10 s.  What is the airplane's acceleration?

64. Write the equation for translational kinetic energy.

65. How do you determine the location of an object from a velocity-time graph?

66. An object on a vertical spring oscillates in simple harmonic motion.  It's highest position is 30 cm above the ground; its lowest position is 20 cm above the ground.  At what position above the ground is the object's speed largest?

67. Define "mechanical energy".

68. The equation for the weight of an object on earth's surface is GMm/r^2.  How does the variable G in this equation change on the moon's surface, which is about 1/3 the diameter and 1/100 the mass of earth?

69. Write two expressions for angular impulse.

70. Under what conditions are the forces on an object balanced?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 6

Continuing on the baseball theme... our JV coaches talk about pitchers who throw great bullpen practice sessions, but can't even throw the ball within a radian of the catcher on game day.  I'm sure you know students who similarly do fine on practice problems, then wilt on the AP exam.

The only partial solution - partial because there are no magic bullets in physics teaching, just ways of attaining incremental improvements - is to make practice seem like a game.  Scrimmage every day.  Make the pitcher experience the consequences of walking back-to-back hitters during practice.  Let them fail!  Then, when the game comes, small failures are less likely to produce downward spirals.

In physics, I give quizzes like this every single day, with no questions allowed, and a strict time limit.  That means lots of chances to screw up - good!  Because everyone is used to communicating their knowledge (or lack thereof) under pressure.  Then the AP exam doesn't feel as much like a high stakes event, but rather like just another day at the office.

FUNDAMENTALS CHECK 6:

51. Write the equation for the potential energy stored in a spring

52. Two carts collide and stick together.  (a) Was momentum conserved in the collision? (b) Was mechanical energy conserved in the collision?

53. Two carts collide and bounce off one another.  (a) Was momentum conserved in the collision? (b) Was mechanical energy conserved in the collision?

54. Define the period of simple harmonic motion.

55. Planet X has a gravitational field that is 1/8 that on earth.  Joel has mass 100 kg on earth.  What is his mass on Planet X?

56. What is found by the area under a force vs. displacement graph?

57. A system consists of two objects, and experiences no net external force.  Describe the motion of the system's center of mass.

58. An object experiences only two forces: 20 N to the east, and 20 N to the north.  What is the magnitude of the net force on the object?

59. What are the units of rotational kinetic energy?

60. Sketch a free body diagram for a car that is moving to the right and skidding to a stop.  

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 5

A big THANK YOU to major league baseball for finally enforcing a pitch clock.  I've watched more games already this year than in the last four years combined.  It's not a complicated game.  Pick a pitch and throw it.  If you give up a home run, another 20 seconds of thought would not have changed that.

Similarly, don't take more than five minutes for one of these fundamentals checks!  This is recall, not problem solving.  If you don't know the answer, more time isn't going to change that.  Just do your best, and learn from what you get wrong.  

FUNDAMENTALS CHECK #5

41. Under what conditions are the kinematics equations valid?

42. How do you determine instantaneous speed from a curved position-time graph?

Questions 43-45: In the velocity-time graph shown, the positive direction is right.

43. Which way is the object moving?

44. Is the object speeding up or slowing down?

45. What is the direction of the object's acceleration?

46. Write the standard kinematics equation for displacement.

47. An object moves in a circle.  What is the magnitude and direction of the object's acceleration?

48. Cart A moves east with momentum 30 Ns; cart B moves north with momentum 40 Ns.  What is the magnitude of the momentum of the two-cart system?

49. Write the equation relating torque to angular momentum.

50. What is determined from the area under a force vs. time graph?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 4

Time for a new fundamentals check!  Note that some questions may be similar or even identical to past checks - that's absolutely normal.  Try this without looking at notes!  If you truly understand, then you should be able to get it right the second time even if you missed it the first time.  :-)

FUNDAMENTALS CHECK #4:

31. What are the units of power?

32. Write the formula to find the gravitational field at a planet's surface.

33. Define angular acceleration.

34. (a) Can angular momentum be converted to linear momentum?  (b) Can rotational kinetic energy be converted to translational kinetic energy?

35. I stand at rest on a platform scale.  What is the Newton's third law companion force to my weight?

36. What are the units of acceleration?

37. A coconut falls from a tree onto a person's head, where it stops.  The equation J = Ft is used to calculate the force of the coconut on the person.  Describe in words what the variable t represents.

38. In a satellite's circular orbit, is the gravitational potential energy of the planet-satellite system constant or changing throughout the orbital path?  Explain very briefly why.

39. A lump of clay is stuck to a meterstick, which rotates about the meterstick's center of mass.  The rotational inertia of the meterstick is I, and the rotational inertia of the clay is MR^2.  What is the rotational inertia of the meterstick-clay system?

40. When is the equation speed = distance / time valid?

Answers Tuesday or Wednesday in the comments!

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 3

I said "daily" review, and I sorta mean it - I teach on Saturday mornings, so no reason not to post a fundamentals check today.  I'll post number 4 on Monday, though, 'cause even at boarding school we don't teach on Sundays.  :-)

FUNDAMENTALS CHECK #3

21.   Write the equation for the force of a spring.

22.   Write the equation for the potential energy of a spring 

23.   On a velocity-time graph, how do you determine the position of an object?

Questions 24 and 25:  A motor cart in the laboratory can be set to move at any steady velocity.  A student sets the cart into motion at many different steady velocities, each time measuring the distance the car travels in 5.0 seconds.  The student graphs this distance on the vertical axis, and the cart’s velocity on the horizontal axis.

24.   Is this graph a line or a curve? Briefly, why?

25.    If this graph is a curve, what could be graphed instead to get a straight line?  If this graph is a line, what is the physical meaning of the slope?

26.   Write the equation for the gravitational field at the surface of a planet.

27.   When a planet makes a circular orbit around a sun, say or show briefly how to solve for the planet’s orbital speed.

28.   In what kind of collision is mechanical energy conserved?

29.   In what kind of collision is linear momentum conserved?

30.   Write the equation for kinetic energy.

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 2

Here's the second of the daily fundamentals checks.  My answers will be in the comments either Sunday or Monday.  Enjoy!

11.   Give a specific example of a situation in which a moving object’s acceleration is NOT constant.

12.   Object A moves left with momentum 2.0 N·s; object B moves right with momentum 3.0 N·s.  What is the total momentum of the two-object system?

13.   Which type of coefficient of friction can take on any value up to a maximum that depends on the surfaces in contact? 

14.   Write the formula for gravitational potential energy.

15.   An object moves downward and slows down.  Which is correctly set equal to ma?  Choose one.

(A                     A)  (up forces) – (down forces)

(B                     B)  (down forces) – (up forces)

1616.   Define power.

1617.   Write the definition of torque.  (Not Newton’s second law for rotation, the equation that defines torque.)

Questions 18 and 19: A ball is thrown up and to the right with speed v at an angle of 30^o above the horizontal.

18.   What is the vertical component of the ball’s acceleration immediately after it’s released?

19.   What is the horizontal component of the ball’s velocity as it reaches the ground?

 

20.   A car speeds up while moving east.  The two horizontal forces acting on the car are the force of the engine and the force of friction.  What is the direction of the car’s acceleration?

AP Physics 1 and AP Physics C - Mechanics Daily Review: Fundamentals check 1

Only four weeks until exam day for AP Physics students.  What should you do?

It's not all about working practice problems.  You can't scheme to solve any problem if you don't know the fundamental facts and equations underlying that problem, any more than you can scheme to stop the Chiefs offense if your tackling skills are poor.

So spend the next month working on fundamentals - items you must recall quickly and accurately if you're to have any chance at dealing with a complex problem on the AP exam.  

To help you out, I'm going to publish one five-minute fundamentals check each day until the exam.  Take no more than five minutes!  If you don't know how to do these, you ain't gonna figure them out by staring or thinking.  They're straight-up recall, or sometimes simple questions about common situations.  

And then a day or two later I'll publish my answers in the comments.  Feel free to use these as quizzes in class, or for your own review!  Don't look at my answers, though, until you've *written* - yes, I mean written down, not just thought about - your own answers.  

These questions are perfect review for BOTH AP Physics 1 and AP Physics C - mechanics.

FUNDAMENTALS CHECK NUMBER 1:

Questions 1-6: In the diagram, a rope connects two object of different masses, where m₁ > m₂.  The cart of mass m₁ is on a frictionless surface.  The mass of the pulley is negligible. 

1.       Is the tension in the rope greater, less than, or equal to m₂g?

2.       Is the acceleration of m₁ greater than, less than, or equal to g?

3.       Which object experiences a larger force of the rope on the object?

4.       Which object has a larger magnitude of acceleration?

5.       What is the direction of the acceleration of m₂?

6.       What is the direction of the velocity of m₁?

7.       Write two expressions for impulse.

8.       What is determined by the area under a force vs. displacement graph?

9.       When an object undergoes simple harmonic motion, what is the direction of the force that the object experiences?

10.   On a position-time graph, how is the location of an object determined?

That's all - my answers will be posted in the comments on April 14 or 15.

What's a "second squared," anyway?

Read any textbook*, and you'll see the units of acceleration written - correctly, if suboptimally - as m/s².  

*Okay, any *physics* textbook.  Probably "A Short History of the United States" doesn't write the units of acceleration this way.

Most practicing physicists understand that acceleration is defined as the change in velocity per unit time.* That makes the acceleration unit (m/s)/s.  Of course a practicing physicist, someone who is quite fluent in mathematics, resolves the improper fraction by turning division into multiplication-by-the-reciprocal: m/s x 1/s = m/s².

*By the way, new physics students are just as confused by the phrase "per unit time" as "per second squared."  Just say "per second" or "in one second."

But our students are certainly not fluent in mathematics, nor in the physical meaning of acceleration.  Years ago, I asked advanced upperclass students this multiple choice question, in which the distractors were taken verbatim from student responses:

Which of the following describes the meaning of an acceleration of 1.60 m/s²?

(A) The elevator gains or loses 1.6 meters per second of speed each second

(B)  The elevator gains or loses 1.6 meters each second

(C)  The elevator travels 1.6 more or fewer meters each second

(D) The elevator travels 1.6 m/s² more or less each second

(E)  The elevator is either speeding up or slowing down by 1.6 meters for every second squared.

Our students, our naïve padawans, hear "meters per second squared" and assume that a "second squared" must be a thing.  The fact that most of the class got this quiz question wrong showed me conclusive evidence that the typically-written units of acceleration are an unrepaired pothole on the road to progress.

What does acceleration really mean, anyway?  In language my students understand: acceleration tells how much an object's speed changes in one second.  

That's often written as a = Δv/Δt, though this equation further obscures meaning.  Our students aren't fluent in math!  Either they don't understand what the delta means, and read the equation as "acceleration is velocity over time"; or even if they do understand that the delta means "change in," they have to laboriously translate that language in their minds before comprehension sets in.  Watching students process the mathematics reminds me of my 1992 Russian language class, where I earned the worst scores in the class on oral exams.  I had to translate what I heard into English (sometimes using mnemonics or slow recall to attempt to figure out the meaning of newer vocabulary); formulate a response in English; and then translate back to Russian.  This is not a recipe for scintillating conversation, any more is it a recipe for expressing physics knowledge.

Use m/s/s as acceleration units.  This is a completely correct expression.  Every time a student writes the unit and mentally pronounces the abbreviation - "meters per second per second" rather than "em slash ess slash ess" - that student is reinforcing the physical meaning of acceleration until it becomes natural.

I've been using this expression for acceleration units for nearly a decade now.  Of course it's not foolproof!  There is no One Weird Trick for teaching the most difficult concept in all of first-year physics.  Yet, I get way, way better understanding now than I did in the days when I said "meters per second squared."  Try it - you will, too.