Hanging Mass on an Incline lab

Mr. Johnson shows off his hanging mass setup

In my general physics labs, we follow a familiar formula each week.:

(1) Students collect data, constructing a linear graph as they go.

(2) They take the slope of a best-fit line using far-separated points on the line that are not data points, including units on the slope.

(3) They use a relevant equation to relate the physical meaning of this slope to a measurable physical quantity.

That's it.  I keep things as simple as possible so as to work on just these three skills.  The trick is, of course, finding straightforward yet interesting experiments which lend themselves to this approach.  Oh, and these experiments must stick within the topic areas in general- (approximately Regents-) level physics.

The procedure is essentially the same each lab day.  I demonstrate a method of data collection.  I write on the board the graph that students are to make.  Students collect and graph their own data in groups of two.  Once I've approved a group's graph, then I hand them a two-page homework assignment for them to work on either the rest of the lab period, or that night if they need more time -- no one leaves early.

Ideally, I'm designing an experiment such that I know what the value of each group's slope should be, but the students do not.  This is a bastardized version of the "recurrent lab" as described by Mikhail Agrest.  Students earn credit either for predicting something using their slope, or for matching their slope to an independent measurement.

So, Greg, give us an example of such a laboratory activity.  Sure -- see the picture.  I have students set up an inclined track, on which they place a Pasco cart.  The cart is connected over a pulley to a hanging mass.    The hanging mass is adjusted until the system hangs in equilibrium.  The angle of the incline is what they are eventually going to predict; I surreptitiously come around during the period to measure each incline with my iPad clinometer app.

We graph the mass of the hanging stuff on the vertical, with the mass of the Pasco cart on the horizontal.  Some mass is added to the Pasco cart, the hanging mass is adjusted to equilibrium, and another data point goes on the graph.  Rinse and repeat for an easily obtained straight-line graph in about 30-60 minutes (including setup and cleanup).

The homework assignment based on this lab activity is available here.  In sum, students take the slope, and then are guided to identify the slope as the sine of the incline's angle.  Most groups easily match my measurement.  

This is one of my better lab exercises, because (a) it fits the formula we've been using all year with no deviation, (b) it allows for accurate prediction of a measurable but initially unknown quantity, and (c) it reinforces the content in the problem solving portion of the course.  Try it... post comments or questions.

GCJ