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17 March 2013

Staci's solution: finding the speeds of two different carts on the same track

Quantitative demonstrations for collision problems seem so easy to set up -- pick a problem in a text, scale the problem for lab carts (i.e. make the mass of each object between 250 g and about 1500 g; be sure the speeds aren't much bigger than 100 cm/s), solve the problem, check the answer with motion detectors.  Done.

Not so fast.  Two major difficulties usually come up:

(1) controlling the initial speed of the carts

(2) measuring the speed of two carts on the same track simultaneously

While I haven't solved issue (1), I can usually finesse it away by keeping one cart at rest initially, and then perhaps asking for the final speed of the carts as a fraction of the initial speed of one cart.  Or, I can use brute force: I use a motion detector to measure the speeds of the carts before and after collision, but I hide the detector reading from the class, only revealing enough to make the solution necessary and interesting.

Issue (2) comes about because two standard Vernier detectors pointing toward each other on the same track interfere with one another, causing nonsense readings.  What to do?

Well, if the carts stick together after collision, no problem.  Keep one cart at rest initially, and a single detector can read the speeds before and after collision.

Brute force solution: if the carts bounce, then one motion detector can still read the before- and after- speeds of one of the carts.  For the cart that was initially at rest, a meterstick and stopwatch can get an after- speed measurement.    

Finessed solutions: after the collision, pick up the near cart so that the detector can "see" the far cart.  This was a student-inspired idea.  Or, if you have photogates and "picket fences", you're in good shape.

Deep finesse solution:  Don't use the motion detectors in the standard configuration.  Regular reader Staci Babykin suggested turning the motion detectors upside down, as shown in the picture.  She told me that the detectors set up like this read independently and accurately, without the interference issue.  I tried this setup this morning, and it worked like a charm.  

Staci noted that she tells the logger pro software to reverse the positive direction for one of the detectors.  Default for Vernier is that away from the detector is positive, toward the detector is negative.  But in this case, we want "toward the window" to be the positive direction for both detectors.  So say "reverse direction" for one detector, and now both probes have the same mathematical orientation.


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