Dedra Demaree ORAAPT, Oct 2010

Goal-based reform: Representing information, conducting experiments, thinking divergently, collecting and analyzing data, constructing, modifying and applying relationships and explanations, being able to coordinate these abilities

 Observe: Watch a magnet move within a coil ASK students what else they’d like to see  Model: Students brainstorm a quasi-mathematical statement for induced current BASED ON THE OBSERVATIONS  Test: Try with different coils, alignments…  Refine model then apply: problem solving, generators…

1. Understand the problem and devise a plan a. Read and translate the problem statement. b. Determine applicable concepts/laws and assumptions/simplifications. 2. Represent the problem physically and mathematically a. Represent physically. b. Represent the concepts/laws mathematically. 3. Carry out the solution a. Work through the mathematics. 4. Look back – was your answer as expected, does it make physical sense? a. Evaluate the result.

Points: a. Read and translate the problem statement No problem statement is written A clear re-statement of the problem is given 1 b. Determine applicable concepts/laws and assumptions/ simplifications No information is given about assumptions, concepts or laws that apply Trivial or incorrect assumptions are listed or only the concepts/laws are listed Correct assumptions are given with no information about how they relate to the concepts/laws that will be used, or an important assumption is missing Correct assumptions are listed along with information about how they relate to the concepts/laws that will be used to solve the problem 2 a. Represent physically No physical representation is given An incorrect physical representation is given, or one that is correct, but does not include any labels or defined quantities A reasonable physical representation is given, but is not clearly labeled, does not define all quantities, or a clear representation is given but it contains a mistake A clearly labeled, correct physical representation is given, with all quantities and symbols clearly defined 2 b. Represent the concepts/laws mathematically No mathematical representation is given A mathematical representation is given 3 a. Work through the mathematics No solution is given Only a partial solution or an incorrect solution is given There is some small mistake in the solution, or units are neglected, or the mathematical steps are unclear A complete solution with clear mathematical steps is given, and the answer has correct units 4 a. Evaluate the result No evaluation is given Very little information is given to evaluate the result A partial explanation is given for why the result makes sense (or does not make sense if the incorrect answer was reached), and what it tells us about the physics of the situation A clear and complete explanation is given for why the result makes sense (or does not make sense if the incorrect answer was reached), and what it tells us about the physics of the situation

Read the problem carefully. What are the key words? What information is given and what will you need to find? Visualize the situation for yourself, what physically might happen? Explicitly state what the problem is asking including clarifying the problem statement. For example, if the problem states when will the two cars collide, you can state when will the two cars have the same coordinates for x and t. Points: a. Read and translate the problem statement No problem statement is written A clear re- statement of the problem is given

Think what physics concepts/laws are involved and what assumptions you can make about the physical situation in order to apply those concepts/laws. What assumptions are reasonable: can you ignore the size of the objects and consider them particles? Can you ignore friction? In your homework you must explicitly state how the assumptions simplify the problem and are consistent with what concepts apply– for example if you are using momentum conservation for the system of two cars in a collision it means you will be ignoring friction from the road since that is an external force and you have simplified the system to no external forces in order to apply a conservation law. Points b. Determine applicable concepts/laws and assumptions/ simplification s No information is given about assumptions, concepts or laws that apply Trivial or incorrect assumptions are listed or only the concepts/laws are listed Correct assumptions are given with no information about how they relate to the concepts/laws that will be used, or an important assumption is missing Correct assumptions are listed along with information about how they relate to the concepts/laws that will be used to solve the problem

Translate the text of the problem into an appropriate type of physical representation (this may be a picture, a free-body diagram, an energy bar chart, a ray diagram….). Record all given quantities in the diagram and identify symbolically (define your symbols!) the relevant variables and unknowns. Choose and show the coordinate axes. For example, a force diagram should have labeled axes, correct force arrows of representative length and direction with defined labels (i.e. if you label an arrow F eb, you must state that e is the earth and b is the box, or if you label and arrow G you must state that it is the force of gravity acting on the box). 2 a. Represent physically No physical representatio n is given An incorrect physical representation is given, or one that is correct, but does not include any labels or defined quantities A reasonable physical representation is given, but is not clearly labeled, does not define all quantities, or a clear representation is given but it contains a mistake A clearly labeled, correct physical representation is given, with all quantities and symbols clearly defined

Use the physical representation to construct a mathematical representation. Make sure that this representation is consistent with the physical representation (for example, if you define your origin above the ground, an object on the ground will not have zero gravitational potential energy). You should have a symbolical mathematical statement that clearly shows what concept/law you are starting with to solve the problem. For example a 1-d kinematics equation could start with x f = x o + v o t + (1/2)at 2. 2 b. Represent the concepts/laws mathematically No mathematical representation is given A mathematical representation is given

Use the mathematical relationships from 2b to clearly solve for the unknown quantity (quantities). Make sure you include enough steps that someone can follow your work and that you use consistent units. If you have set up your problem properly, this step should be purely mathematics. However, you may find yourself stuck and unable to completely solve the problem. In that case, go back and check all above steps to make sure you haven’t overlooked some piece of physics implied by the situation, or some known relationship such as the fact that the kinetic friction is proportional to the normal force. Keep symbols in your solution as long as possible, and when appropriate, only put numbers in at the final step. Make sure you include units in your final answer. 3 a. Work through the mathematics No solution is given Only a partial solution or an incorrect solution is given There is some small mistake in the solution, or units are neglected, or the mathematical steps are unclear A complete solution with clear mathematical steps is given, and the answer has correct units

Is the final value you found reasonable? Are the units appropriate? Does the result make sense in limiting cases? Does the result make physical sense? Include a written explanation for why your result makes sense and what it tells you about what happens in the physical situation. 4 a. Evaluate the result No evaluation is given Very little information is given to evaluate the result A partial explanation is given for why the result makes sense (or does not make sense if the incorrect answer was reached), and what it tells us about the physics of the situation A clear and complete explanation is given for why the result makes sense (or does not make sense if the incorrect answer was reached), and what it tells us about the physics of the situation

 Observation Experiments Can students represent their observations Do students clearly distinguish observations and explanations? Can they find a model based on observations?  Testing Experiments Can they make a prediction based on the model? Can they draw solid conclusions based on experiment?  Application Experiments Can they apply knowledge to find something new two different ways – and judge whether the two methods are in agreement?

Bullets marked, for example, A3 refer to the application experiment rubric ability 3. Bullets without such designation are given as additional guidance. All bullets must be addressed in your lab write- up, and a random subset will be graded. Design at least two independent experiments to determine the coefficient of static friction between your shoe and the carpet strip provided. (You can use any of your group’s shoes, and either the front of the back of the carpet, whichever gives you ‘cleaner’ data) Equipment: Force probe, ruler, carpet, board. Include in your report the following: a. (A1) Identify the problem to be solved. b. (A2) Design two reliable experiments that solve the problem. c. Draw a sketch of your experimental designs. d. Draw a free-body diagram for the shoe. Include an appropriate set of co-ordinate axes.

e. (A7) Choose a productive mathematical procedure for solving the problem. Use the free-body diagram to devise the mathematical procedure to solve the problem for each experimental set-up. f. (A3) Discuss how you will use the available experiment to make the measurements. g. (A8) Identify the assumptions made in using the mathematical procedure. h. (A9) Determine specifically the way in which assumptions might affect the results. i. What are the possible sources of experimental uncertainty? How could you minimize them? Perform the experiments. j. Record the outcome of your experiments. k. (A4) Make a judgment about the results of your experiments. l. (A5) Evaluate your results by comparing the two independent methods. Use your uncertainty to make and explicit comparison of the two values you obtained for the coefficient of static friction. m. What are possible reasons for the difference? n. Which experiment was more accurate and why? o. (A6) Identify the shortcomings in the experiments and suggest specific improvements.

 (55 points) (THIS IS TWO PROBLEMS COMBINED SINCE THEY ARE ABOUT THE SAME SITUATION) A tall person pushes moves a box up a 10 m long ramp that makes an angle of 10 degrees with respect to the horizontal, by pushing on it with a push force of 70 N at an angle of 20 degrees below the horizontal (he’s pushing somewhat downward on the box). The box has a mass of 30 kg, and there is (lucky for you) NO friction between the box and the floor. (10 points) Draw a physical representation for the box for use with Newton’s laws (for part b), making sure to clearly label and define all quantities. (15 points) If the box starts from rest, find the speed of the box when it reaches the top of the ramp using Newton’s laws and kinematics. (You must have an initial equation(s) without numbers in it as a starting point for full credit.) (8 points) Draw a physical representation for the box for use with work and energy (for part d), making sure to clearly label and define all quantities. (16 points) If the box starts from rest, find the speed of the box when it reaches the top of the ramp using work and energy. (You must have an initial equation(s) without numbers in it as a starting point for full credit.) (6 points) State the assumptions you used FOR PART D and how they determined what concepts applied.