Looks like there are a few things going on here. 1) Student clearly takes units seriously, although that might have contributed to some of the errors. 2) A lack of real consideration of direction of force and acceleration vectors. 3) Possible confusion between force and acceleration and/or confusion about the mechanics of solving an equation involving physical quantities with respective units and all.

In my first year my class bombed on a very similar question due largely to #2 above. As a result I’ve become a huge fan of asking questions like “Which force is bigger, the tension or the gravitational force?” or equipping the class with clickers and posing it as a multiple-choice question with a series of possible force diagrams as the choices, where (A) tension > weight (B) tension = weight (C) tension < weight (D) not enough info. That way you get the class thinking about the problem without having to go all the way through the math. That's my $0.02 for #2.

This is so interesting! When I first started reading, I thought the student was hooked on equations and going to ignore the direction of the acceleration. That did happen, but way more, not-focused-enough-on-equations stuff happened in between. Definitely a bad algebra mistake happening with subtracting the “acceleration” from g. Depending on whether the student would be (a) ashamed of making the (algebra) mistake upon seeing it again or (b) confused about why it is wrong, I might take different paths with my advice to the student (with students I know from class, that’s easy to predict in advance, but impossible to tell from one piece of evidence like this). Oh gosh, just saw the next algebra mistake (subtracting a negative number, one of those negatives just conveniently disappears!).

Also really, really interesting is the use of entire words (“Tension”) instead of using a variable to represent it in the equation. The line where Tension is actually in parens is even more interesting.

Okay, I guess one of the first things I’d start to address is the direction of motion and direction of acceleration. Usually, on N2L problems, I try to encourage them to draw an arrow on the picture of the problem (either the one given or their own sketch) that shows the direction of the acceleration (not necessarily the motion). That helps orient where the axes should be if we want to tilt them, or helps keep track of the direction in problems like this. It might also prompt them to make their FBD more qualitatively correct, if they are thinking in that direction. Then I might try to get the student to do their mathematical representation in symbols instead of in words and numbers so that we can more easily see what the relationship they are stating.

In these types of questions I often see students take the following short cut:
Tension = (15 kg) (9.8 + 1.1 m/s/s)
They are basically doing all of the algebra in their head and just writing down this one statement. I try to discourage this as much as possible but for some of the brighter students it is obvious that they grasp the concept. Others however are just looking for the path of least resistance. They memorize solutions to question types and just regurgitate them. I’m not saying this student has done this but when they subtract the ‘accelerations’ it reminds me of this shortcut.

On line 3 the student writes the difference between the two forces is equal to acceleration but then adds the mass back into the equation on the next line. I’m not sure when the thought process was here. For some reason they include the units for every quantity except the mass on the right side of the equation leading to the incorrect statement of 16.5 m/s/s instead of 16.5 N. They then make the error of subtracting the ‘accelerations’.

I would ask the student to look at the two lines where they have Force – Force = Acceleration and ask them what is wrong with that statement.

Looks like there are a few things going on here. 1) Student clearly takes units seriously, although that might have contributed to some of the errors. 2) A lack of real consideration of direction of force and acceleration vectors. 3) Possible confusion between force and acceleration and/or confusion about the mechanics of solving an equation involving physical quantities with respective units and all.

In my first year my class bombed on a very similar question due largely to #2 above. As a result I’ve become a huge fan of asking questions like “Which force is bigger, the tension or the gravitational force?” or equipping the class with clickers and posing it as a multiple-choice question with a series of possible force diagrams as the choices, where (A) tension > weight (B) tension = weight (C) tension < weight (D) not enough info. That way you get the class thinking about the problem without having to go all the way through the math. That's my $0.02 for #2.

This is so interesting! When I first started reading, I thought the student was hooked on equations and going to ignore the direction of the acceleration. That did happen, but way more, not-focused-

enough-on-equations stuff happened in between. Definitely a bad algebra mistake happening with subtracting the “acceleration” from g. Depending on whether the student would be (a) ashamed of making the (algebra) mistake upon seeing it again or (b) confused about why it is wrong, I might take different paths with my advice to the student (with students I know from class, that’s easy to predict in advance, but impossible to tell from one piece of evidence like this). Oh gosh, just saw the next algebra mistake (subtracting a negative number, one of those negatives just conveniently disappears!).Also really, really interesting is the use of entire words (“Tension”) instead of using a variable to represent it in the equation. The line where Tension is actually in parens is even more interesting.

Okay, I guess one of the first things I’d start to address is the direction of motion and direction of acceleration. Usually, on N2L problems, I try to encourage them to draw an arrow on the picture of the problem (either the one given or their own sketch) that shows the direction of the acceleration (not necessarily the motion). That helps orient where the axes should be if we want to tilt them, or helps keep track of the direction in problems like this. It might also prompt them to make their FBD more qualitatively correct, if they are thinking in that direction. Then I might try to get the student to do their mathematical representation in symbols instead of in words and numbers so that we can more easily see what the relationship they are stating.

This work is a really great one!

In these types of questions I often see students take the following short cut:

Tension = (15 kg) (9.8 + 1.1 m/s/s)

They are basically doing all of the algebra in their head and just writing down this one statement. I try to discourage this as much as possible but for some of the brighter students it is obvious that they grasp the concept. Others however are just looking for the path of least resistance. They memorize solutions to question types and just regurgitate them. I’m not saying this student has done this but when they subtract the ‘accelerations’ it reminds me of this shortcut.

On line 3 the student writes the difference between the two forces is equal to acceleration but then adds the mass back into the equation on the next line. I’m not sure when the thought process was here. For some reason they include the units for every quantity except the mass on the right side of the equation leading to the incorrect statement of 16.5 m/s/s instead of 16.5 N. They then make the error of subtracting the ‘accelerations’.

I would ask the student to look at the two lines where they have Force – Force = Acceleration and ask them what is wrong with that statement.