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Skill 2.B
Science Practice 2 is about using mathematical routines to describe and explain phenomena, as well as to solve problems. Skill 2.A is calculating or estimating an unknown quantity with units from known quantities by following a logical computational pathway.
This skill will be 20-25% of the multiple-choice section of the AP Physics 1 exam and will be only part of 30-40% of the free response dedicated to all of science practice 2. The individual skills do not have a % breakdown provided for the free-response section.
How will you recognize when to use this skill?
How will you recognize when to use this skill?
The words calculate or estimate in the prompt will typically be used on a free response question, but multiple-choice questions will use a variety of prompts.
Example FR promtps:
"Calculate an experimental value for the unknown mass using the best - fit line that you drew in part (c)."
"Estimate the value of the acceleration of the system."
Example MC Prompts:
"Given L = 1.0 m, μ = 0.1, and θ = 30°, which of the following is most nearly the speed v of the block as it reaches point A?" [answer choices are numerical values with units]
"What is the speed of the block after sliding a distance of 5 meters?" [answer choices are numerical values with units]
How will I be assessed on a calculation problem?
How will I be assessed on a calculation problem?
The word calculate, as defined in our course, means to perform mathematical steps to arrive at a final answer, including
algebraic expressions,
properly substitited numbers,
and correct labeling of units and significant figures*.
We can see in the scoring rubrics that there are often points assigned to each of these steps with exception of significant figures. So, when you are calculating values, whether for your homework (even PositivePhysics)
*We love that Chemistry stresses on the rules of significant figures so you can get good at that because it is important in precision work. In our course, where we often ignore friction and air resistance so we can practice general relationships and science practices, we will simply report 3 significant figures as a norm while fully acknowledging that we should be more careful about that.
Foundational Skills Resources
Foundational Skills Resources
The rest of this page is about how to document and earn credit for a calculation question, but you may need to learn or brush up on some foundational skills to ensure you can be successful on all the problems you will be asked to solve. Check the following calculation subpages for focused help on the following topics:
How to approach a calculation?
How to approach a calculation?
Don't guess what to type in your calculator, use the GESSSCE method! Just kidding. That is not a catchy acronymn and will not be using that in class. But seriously, my students that think they are being efficient by not following these steps end up wasting a lot of time in frustration when they make mistakes because they have to completely redo things.
Recommended steps are in green and steps that are required for credit are in blue and underlined.
Givens: Organize your given values with appropriate symbols that will represent them in equations. This can be a list, but sometimes a table or a diagram can be more helpful in chunking values based on the scenario.
Equation/Expression: Write the most general form of the equation you will be using as found on the formula chart (or based on the definition of the principle or term being used).
Simplify: If there are any terms that are zeros or need to be altered to different symbols, apply them now to make your algebra easier.
Solve algebraically: Use your algebra skills re-arrange to solve for the variable you need, and if applicable, to combine this equation with others.
*It will be tempting to plug in numbers and start solving for small chunks here but trust the man who has been teaching this longer than you have been alive; you need the practice deriving and once you get good at that it will be much more efficient to do things this way. So, do not subtitue those given values until step 5. See Skill 2.A Derivation if you need help with this.Substitute: replace all the variables with the given values you organized in step 1
Calculate the answer: Now it is time to grab your calculator! Check out my page on Calculator Info/Skills to make sure you are using your calculator right.
Evaluate the units: Make sure answers that need units have them evaluated and attached to the number. Without the unit the answer will be considered wrong.
Units not working out can be a tip that you have an error in your calculation process, so it is a great idea to check through the process of combining units. Check out my page on Unit symbols & use for a list of what units should be used for each quantity and rules for/examples of combining units during calcualtions.
Calculation Example1
Calculation Example1
The first examples show two ways of showing work for the same positive physics problem.
You do not need to annotate each step, as is done in green for optional steps and blue for required steps, but it is a great idea to complete each of the steps.
The bottom example takes much less space and still gets the key elements of equation, substitution, and answer with correct units.
Calculation Example 2
Calculation Example 2
Example 2 shows how to document calculating a value from a best fit line.
A great example is shown to the left
equation 1 is an interpretation of the equation for slope = rise/run that connects to the physics values on the y and x axes.
equation 2 is a standard kinematics equation solved to match the rise/run relationship.
the substitution does not use data points, but easily read points on the line
units are analyzed and reported properly.
Example of common mistake
Example of common mistake
Here is an example of how many students might fail to earn any points on this question.
No original equation, so the division shown is not a substitution.
The answer is not correct because the slope is not properly connected to the equation showing the slope is equal to twice the acceleration.
There are no units, so even if the answer were correct, points may not be earned for being incomplete.
What is different about estimating than calculating?
What is different about estimating than calculating?
In an estimation a greater amount of liberty is in making assumptions (especially about comparative values) in order to either simplify the calculation to approximate the value or generalize for a variety of similar situations.
Compare the processes of calculating vs estimating the acceleration of block 1 in a system of two masses connected by a lightweight string over a massless pulley.
Calculating in this example involves these steps, shown at right:
writing a net force equation for block 1 and realizing you do not have the tension, so you need a 2nd equation with tension in it.
writing a net force equation for block 2.
combining the 2 equations (knowing the acceleration magnitudes are the same and assuming the tension is the same since the pulley has no mass)
solving the equation for a
substituting the values of the problem and solving (not shown in this example.
Estimating can be done conceptually or mathematically. You may be asked to both explain and show how the equation can be used to estimate.
For cases where the mass of block 2 is nearly equal to the mass of block 1
conceptually we know that if the 2 blocks are equal they can balance each other out, so the tension must get closer to the weight for each block. This would make the net force approach 0 as their masses approach equality, and therefore the acceleration would be approximately zero.
building on the calculation work done, if m1 and m2 are the same the final equation would become (mg-mg)/(m+m) = 0/2m, so the acceleration would be approximately zero.
For cases where the mass of block 2 is much greater than the mass of block 1 (when estimating "much greater" go with something ridiculous, like 100x greater, not something like 2x greater)
Conceptually, the more different the masses, the more different the tension and weight will be on each mass, to the point of the tension being nearly 0% of the weight of block 2. In that case, object 2 is essentially in freefall
building on the calculation work done, the weight of block 1 is negligible compared to the weight of block 2 as are the mass, so the equation can be simplified to m2g/m2 = a, or a=g.
In the example shown at right an alternative approach is shown making the mass of block 2 100x greater than mass 1.
Practice
Practice
This is the easiest practice to find. The chapter questions in your textbook, homework assignments, and most Physics websites will offer calculation practice. Ask me if you need help finding the right resource.
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