FOR MANY, IT’S the start of a new semester of physics labs. That means there are new students in that introductory course. Of course, no one is really 100 percent ready to start these labs—but that’s OK. Here are three big ideas that I find students need to work on to be successful in lab.
This is a pretty easy problem to fix, but I think I should go over it. How do you convert units? Let’s say some students find the mass of an object as 123 grams—but to get the weight in Newtons, they need this mass in kilograms. Here’s what some students might say:
OK, we need to convert this mass from grams to kilograms. I know we have to do something with 1,000 but I can’t remember if we divide or multiply by 1,000. Wait, I got it. A kilogram is bigger than a gram so we need to multiply by 1,000 to get kilograms. Wait, that doesn’t make sense. Maybe it’s divide.
This is the process many students use to convert values. There’s an easier way. In short, you just multiply by one. Let me just start with the above example converting a mass in grams to kilograms. Suppose I have 123 grams and I multiply by the fraction 4/4, like this:
Yes, (4/4) is the same as the number 1. If you multiply a number by 1, you get the same thing. So, in this case you would just end up with 123 grams. Boring.
Any time you multiply by 1, you don’t change that value. Also, 4/4 is the same as 1 because you are dividing a number by the same thing. What if I replace the denominator with (2*2)? Nothing happens because 2 times 2 is still 4.
There is another fraction that is equivalent to 1. Here it is.
1,000 grams and 1 kilogram are the same thing, so this fraction is equal to 1. Now I can multiply my original mass by this fraction.
Now for the magic. I can treat the unit of grams just like a variable. Grams divided by grams is one. These units cancel and I am left with the unit of kilograms.
Boom. That’s it. Unit converted. In short, all you have to do is multiply by 1. Choose a fraction such that the numerator and denominator are equivalent (even if different units) and arrange it so the unit you want to convert cancels. It’s that simple.
OK, let me include one problem that pops up quite often. Suppose I have a volume of 3213 cm3 and I want to convert this to cubic meters. Here’s how I would do that (remember that there are 100 centimeters in 1 meter).
If I just multiplied by the fraction (1 m/100 cm), the cm3wouldn’t actually cancel. I need cm3 in the denominator. The only way to do this is to cube the fraction—but that’s what I get.
One last thing. You might be in introductory physics and you might be a carpenter. However, it’s not cool to use imperial units. It’s just going to cause problems. Stick to metric units. Trust me on this one. Trust me.
Converting units isn’t a super big problem—but that’s not true for graphs. Just about every introductory lab needs to make a graph. Why? Here is my short answer.
With a graph, you can show a functional relationship between two quantities. If that relationship is linear then you can find the slope of the best fit line and this slope probably means something.
Let’s just make a graph and then I will have something to talk about. Suppose I take a meter stick and a spring. I will hang the spring from some vertical mount and then hang some masses from it. I can record both the mass and the position of the bottom end of the spring. Here’s what that data might look like.
What is the relationship between position and mass? Students are often tempted to just find the ratio of mass and length—but that doesn’t work in this case (because I made the data so it would fail). No, the first step is to just plot the data on actual tree-based graph paper. I encourage students to use paper instead of a computer-based plotting tool so that it’s clear that they understand what’s actually going on. If you use a program to make a graph, sometimes the program will fix some things for you such that you don’t make mistakes. Mistakes are good if you are trying to learn.
Now for the graph. I did this on graph paper, just for you.
I didn’t just plot the data points from above—I also added a “best fit” line. On plain graph paper, you can add this line by using a straight edge to just approximate a line that comes the closest to all the points. This best fit line doesn’t even have to hit any of the points—it is absolutely not just connecting the dots.
Once I have a best fit line, I can then find the slope. There are two points on this best fit line (I circled them in red) that I am going to use to find the slope. Remember to use points on the line that you created and not the points you plotted. Also, the further away the points are from each other, the better it will be.
Now I can find the slope.
Let me make some important comments on this calculation as well as some errors students make.
- The slope means something. In this case, it’s just the ratio of mass to stretch, but you could also relate this to the force per meter stretch—the spring constant.
- The slope has units—usually. If the vertical axis has units and the horizontal axis has units then the slope would have units. The one case that’s a little different is if you plot distance vs. distance (both in meters). Then the slope would be unitless.
- Graphs can obviously be more than just x vs. y. I hate to say this, but it’s important. I find that some students make x-y graphs in their math classes and never realize that it doesn’t have to actually be x and y. Yes, I know that the math class goes over this idea, but the students don’t always get it.
- Notice that the axis doesn’t have to start at the value of zero. You can start at whatever number you like.
- The slope of this line is not the average value of mass divided by position. In this case, there is a non-zero y-intercept so you can just divide the two numbers. The slope tells you how the two numbers change—not the ratios of their values.
That’s enough notes to at least get you started.
Seeing Beyond the Instructions
This last tip is difficult because it really depends on the instructor’s ideas for the lab. So, in this case I’m giving student advice for the way I run lab classes.
Here are some things students say that make me worry.
“How many data points do you want me to take?”
“What else do you want me to do in lab?”
“Do you want me to make a graph for this data?”
I think you get the idea. Many students treat the lab as something that they (the students) need to do for me (the instructor). But I don’t want minions that do lab work, I want scientists that build experiments. The lab isn’t about following instructions, it’s about building a model.
Yes, it’s true. I do give some instructions before lab—but that’s just to get students started. What I really want is for students to play around with stuff, build a model and then find some way to use that model in an interesting way. That’s the way science works and that’s how I want my lab to work.
source and big thanks for the wonderful article : wired