How to improve force-vector lab?

[bcrowell]

I have a lab I teach that has evolved over a long period of time. It's described on p. 14 of this pdf: http://www.lightandmatter.com/lab_205.pdf . Briefly, it involves setting up four force sensors around the circumference of a circular table. We tie strings to their hooks, and they all pull on a point at the center of the table. Students add the four force vectors and verify that their sum is zero. I'm not very happy with how this lab is working, and I'm wondering if anyone else has taught or done a similar lab and might be able to give suggestions for improvement.

One problem is that it seems to take students an inordinate amount of time (often as much as 1-2 hours) to get the strings tied, tension on the strings, and an appropriate amount of force on each sensor. My current lab manual describes the easiest and most efficient method I've found, which involves tying some knots and using screws to apply tension. Even so, some lab groups really seem befuddled by the whole process. To some extent, this may actually entail good learning, e.g., some students seem to expect that all four forces will be equal in magnitude, regardless of the angles; or they may not understand that if the forces are all too small, one can scale them all up by the same factor. Some of the delays, however, seem not to be physics related, but just due to issues such as their unfamiliarity with knots or the limited travel in the screws.

Another problem is that the Vernier force probes we're using seem to have unstable calibrations. The readings on the probes simply drift over time. This is a real pain. It means that the students can't just calibrate the sensors and then build the setup. They have to build the setup, take data, and then retrospectively determine and apply a calibration. The calibration often drifts by a huge amount, like 1 Newton. I have them do a quick graphical addition on the uncalibrated data (which I think has some educational value of its own) to make sure the results are reasonable before they take final data, cut the strings, and do the calibrations. But the calibrations are usually so whacked that even if they're doing everything right, the uncalibrated graphical addition comes out terrible.

If it was me doing the experiment, I'd get everything set up and tensioned properly, back off the screws by, say, five full turns, tare the sensors, and then put the tension back on. However, I'm afraid that if I asked my students to do this, they would spend another hour getting the tension back on and rebalancing all the forces.

A final problem is that these Vernier force probes just seem to be junk in general. We have about 30 of them, but about 5-10 of them die each year and need to be replaced, at $100 a pop. Also, many of them flake out during lab, when it's too late to substitute another sensor. E.g., we get sensors whose readings vary erratically by half a Newton or a Newton. Are there better sensors on the market?

We used to do this lab with weights hung from pulleys rather than electronic sensors. The problem with that version was that it was a pain to balance the forces, and we had to do complicated stuff to eliminate the effect of friction in the pulley. In theory the electronic version should be superior, but in practice it seems just as painful.

I'd be grateful for any suggestions for improvement.

 

[voko]

I would reduce the number of forces from four to three. I would also combine your old method (weights) with your new method (sensors). Two of the strings would have known weights attached to them, and one would be attached to a sensor (no screws). The weights could in fact be one and the same weight to simplify things further.

I would also eliminate knots. For example, the center assembly could be a solid ring and the strings could have hooks permanently attached to them.

 

[bcrowell]

I would reduce the number of forces from four to three. I would also combine your old method (weights) with your new method (sensors). Two of the strings would have known weights attached to them, and one would be attached to a sensor (no screws). The weights could in fact be one and the same weight to simplify things further.

I would also eliminate knots. For example, the center assembly could be a solid ring and the strings could have hooks permanently attached to them.

Thanks for your suggestions. The problem with using any weights at all is that you then get static friction in their pulleys, which requires laborious procedures to eliminate. We used to use a setup in which we had four weights and a solid ring, and that setup was roughly as problematic as the current one. I actually eliminated the ring recently in order to cut the number of knots from eight to four. My current setup uses four knots, and I don't think that number can be reduced without switching back to hanging weights, since we need a way to put tension on the strings.

 

[Dale]

You could eliminate knots all together by using lightweight chains and jewelery clasps.

If you have a good reliable sensor for measuring tension then you can easily couple the chains with those sensors to do a force vector type of lab. The easiest, IMO, would be to suspend a weight at the bottom of a Y configuration of chains and measure the angles and tensions.

 

[bcrowell]

You could eliminate knots all together by using lightweight chains and jewelery clasps.

If you have a good reliable sensor for measuring tension then you can easily couple the chains with those sensors to do a force vector type of lab. The easiest, IMO, would be to suspend a weight at the bottom of a Y configuration of chains and measure the angles and tensions.

Interesting idea about the chains -- I'll have to see if I can get some cheap ones and play around with that.

I would anticipate a couple of problems with a vertical setup: (1) The sensors are only sensitive to the component of the force that acts along their axes. This makes it important to get them accurately lined up with the central point, and I don't see how one would do that with the vertical setup. Possibly our existing circular tables could just be tipped up vertically, but we would need to figure out appropriate hardware for that. (2) If using the chains, then you have complications due to their weight. I guess you could simply add their weight to the hanging weight. But also, the chains would be catenary curves rather than straight lines. The curvature could be reduced by putting lots of tension on, but I doubt that this can be done without damaging the chains. The nice thing about doing the lab in a horizontal plane is that the force of gravity on the strings/chains/ring is perpendicular to the sensors and therefore has no effect.

In general, I think the vertical "Y" setup would be easier mainly because one would automatically get some equilibrium, and tension would automatically happen. But the central point or object would reach its equilibrium position at some random point. If you want accurate angles, you probably need to use the circular table in a vertical plane, but then it becomes necessary to adjust everything so the central point is at the center of the table -- which eliminates the main advantage of the vertical setup.

Such a setup also only simplifies things if you limit yourself to three forces -- with four forces, you don't automatically get an equilibrium. The thing I don't like educationally about using only three forces is that when I've done the lab that way, I've seen students make lots of conceptual errors that are based on their expectation that the resulting figure will be a triangle. E.g., they assume it's going to be a triangle, and then they start doing the law of sines and law of cosines. Often this is because they're uncomfortable with the concept of the components of a vector, so they want to avoid that.

We actually do a lab sort of similar to this one in a vertical plane, where they verify that both force and torque cancel. (It's on p. 34 of the pdf linked to above.) It works, but it's extremely low precision, like 10% error bars. Our current setup for the force lab, done by students who are careful and using sensors that aren't acting finicky, gives error bars more like 0.2%. I'd hate to increase our error bars by a factor of 50 if I could avoid it.

 

[bcrowell]

I googled to try to figure out what other people were doing, and I came across this: http://physics.appstate.edu/laboratory/quick-guides/vector-addition-0 They simply hold the force sensors on top of a piece of paper and trace the lines onto the paper. I think if one held each sensor at the back and allowed it to "wiggle" into equilibrium, it would naturally align itself with the axis of the force. It should work with either 3 or 4 sensors.

 

[Andy Resnick]

It's not clear from the diagram on page 14 (edit... page 15 confirms this)- are you looping a string connecting sensors 3 and 4 around a string connecting sensors 1 and 2? I have to check what we do, but I would have all 4 'force sensors' (and I agree 3 would be a lot easier than 4) connected individually to a central object, like a ring, and have the students explore under what conditions the ring does not move. I can envision lots of problems associated with that loop sliding back and forth along one string. Also, the way you have it set up the tension forces on (say) sensors 3 and 4 are not independent..

Also, I'm not clear on what a 'force sensor' is- are you trying to generate 4 independent forces and determine conditions for equilibrium or something else? What is generating the tension forces- do the sensors hang off the table?

 

[voko]

The thing I don't like educationally about using only three forces is that when I've done the lab that way, I've seen students make lots of conceptual errors that are based on their expectation that the resulting figure will be a triangle. E.g., they assume it's going to be a triangle, and then they start doing the law of sines and law of cosines. Often this is because they're uncomfortable with the concept of the components of a vector, so they want to avoid that.

From this I infer that the purpose of the lab is not only to get your students to establish experimentally that zero resultant force is a necessary condition for an equilibrium, but also teach them something about vectors. Which may not be bad in itself, but it is perhaps this sort of multiple purposes that the lab is so complicated.

 

[bcrowell]

It's not clear from the diagram on page 14 (edit... page 15 confirms this)- are you looping a string connecting sensors 3 and 4 around a string connecting sensors 1 and 2? I have to check what we do, but I would have all 4 'force sensors' (and I agree 3 would be a lot easier than 4) connected individually to a central object, like a ring, and have the students explore under what conditions the ring does not move. I can envision lots of problems associated with that loop sliding back and forth along one string.

We used to use a central ring, but that required 8 knots rather than 4, and it introduced a separate source of error because the knots had to be slid into a position along the rim of the ring so that they were aligned with the center. This setup is IMO far superior. We do not generally have problems with the strings slipping, because there is a lot of friction where the strings go around each other at the center.

Also, the way you have it set up the tension forces on (say) sensors 3 and 4 are not independent..

This would be true if there were no friction at the center. In reality friction makes these two forces independent. They can differ by about a factor of 2 before any slipping occurs. This is discussed briefly in a footnote in the lab manual.

Also, I'm not clear on what a 'force sensor' is- are you trying to generate 4 independent forces and determine conditions for equilibrium or something else? What is generating the tension forces- do the sensors hang off the table?

The sensors are electronic black boxes that interface to a computer. They're basically digital spring scales. They're oriented horizontally.