This activity is intended to help you practice solving problems using the A*R*C*S format introduced in Figure 2.16.1. This will serve as a touchpoint you can come back to if you need any assistance on working through an A*R*C*S activity. You will work through each section of the A*R*C*S format, watch a video, and reflect on your work. The videos are a little bit long, but there is a lot to explain in an A*R*C*S activity!
Shown below are two blocks connected by an ideal string that passes over a massless, frictionless pulley. The mass of the larger block sits on a flat, frictionless table, and has a larger mass than the smaller block, which hangs vertically. Determine the speed of each block when the larger block reaches the edge of the table, a distance of 0.75 m.
Figure12.2.1.Two blocks, connected by a rope.
1.Analyze and Represent.
(a)Understand and Plan.
First, identify all known and unknown quantities. For all known quantities, you should estimate an appropriate numerical value.
(b)Identify Assumptions.
Next, identify any simplifications or assumptions you will make to solve the problem.
(c)Represent Physically.
Draw a free-body diagram for mass 1 and mass 2. Make sure to accurately label each force, and indicate your coordinate system.
(d)Observe.
Review what you wrote for the Analyze and Represent parts above, and compare it with the video below.
(e)Reflect.
Describe any similarities and differences. Were there any other assumptions you made? Are there other representations that might be helpful?
2.Calculate.
(a)Represent Principles.
Make a list of the important concepts, laws, or ideas that you will use to solve the problem. (Hint: You have probably seen more than one way to approach a situation like this one. This is a good place to consider the advantages and disadvantages of each approach.)
(b)Find Unknowns Symbolically.
Now you are ready to solve for the unknown symbolically. Don’t plug any numbers in yet!
(c)Plug in Numbers.
Plug in numbers into your symbolic expression found in the previous step.
(d)Observe.
Review what you wrote for the Calculate parts above, and compare it with the video below.
(e)Reflect.
There are many ways to solve this problem. Can you think of a way to perform this calculation that is different from the one in the video? Do you think that way would be easier or harder? What parts of the calculate portion did you find most difficult?
3.Sensemake.
(a)Units.
Conduct an explicit unit check on your final symbolic answer to determine if the units are correct.
(b)Numbers.
(i)
Convert your final numerical answer into a unit that is more familar to you (miles per hour, kilometers per hour, etc.). What else travels this fast? You may need to use Google to help you answer this question. Is this a reasonable speed for a falling block?
(ii)
Consider the situation where mass 2 falls on it’s own, under the force of gravity. What is the velocity of mass 2 after it falls a distance of 0.75 m? How does this compare with your numerical answer found above? Does this make sense? Why or why not?
(c)Symbols.
(i)
How does the speed change if you increase L? What is physically happening that explains this behavior?
(ii)
Predict what would happen if the second block has zero mass and explain why that happens.
(iii)
Now turn to your symbolic answer. Does your symbolic answer confirm your expectations?
(d)Observe.
Review what you wrote for the Sensemake parts above, and compare it with the video below.
(e)Reflect.
What other sensemaking strategies might you be able to use? Do you have any questions about sensemaking after completing this section?
