`Reaction TimeRoy Coleman                    Morgan Park High School                               RetiredObjective:Each student will be able to obtain his/her reaction time by making simple measurements.  Each student will also be able to find the constituent parts of their overall reaction time.     Materials needed: Each group of two will need one 30 cm (12 inch) ruler to find their reaction time.  For the more advanced activities, each group will need a meter stick, a stopwatch and two funnels connected together by more than two meters of rubber tubing. Suggested Strategy:The time that it takes you to react to a particular situation is called your reaction time.  Your reaction time depends on many factors including the stimulus and the particular part of the body that is to react, i.e., it takes longer to move your foot from the gas to the brake pedal than it does for your fingers to grab something simply because your leg is heavier and it has to move farther. Today we will be finding the time required for you to grab a dropped object, namely a 12 inch ruler.  Brace your hand on the edge of a desk so that the fingers are over the edge ready to grab the ruler as it is dropped.  Have your partner hold the ruler such that its zero centimeter mark is even with the center of your fingers and, at some random time, drop it.  Record the distance that the ruler fell (where you caught it), during the time that your body was reacting.  Do this at least 10 times.  It is important that the ruler is held even with your fingers (not above or below them) and that it is dropped (not thrown down).  ALL readings MUST be recorded but any readings that are way out of line can be crossed out and ignored.  (In general, your measurements should be between 10cm and 30cm.)  Average your readings and then determine your reaction time. The reaction time can be determined in several ways.  You can use the standard equation for freely falling bodies Sf=1/2at2+vot+So. Where Sf is the average distance that the ruler fell, a is the acceleration of gravity (980 cm/sec2),t is the time that it takes the ruler to fall (the reaction time), vo is the initial velocity (zero) and So is the initial distance (zero).  Substituting in zero for vo and So simplifies this to Sf=1/2at2.  Solving this equation for t yields                           dt=sqrt(2Sf/a) An alternate method would be to use the following chart to look up the time corresponding to the average distance that the ruler fell.       DISTANCE     TIME       DISTANCE     TIME       DISTANCE     TIME       DISTANCE     TIME        (cm)       (sec)        (cm)       (sec)        (cm)       (sec)        (cm)       (sec)                                                            0.012  --  0.005        8.281  --  0.130       31.862  --  0.255       70.756  --  0.380        0.049  --  0.010        8.930  --  0.135       33.124  --  0.260       72.630  --  0.385        0.110  --  0.015        9.604  --  0.140       34.410  --  0.265       74.529  --  0.390        0.196  --  0.020       10.302  --  0.145       35.721  --  0.270       76.452  --  0.395        0.306  --  0.025       11.025  --  0.150       37.056  --  0.275       78.400  --  0.400        0.441  --  0.030       11.772  --  0.155       38.416  --  0.280       80.372  --  0.405        0.600  --  0.035       12.544  --  0.160       39.800  --  0.285       82.369  --  0.410        0.784  --  0.040       13.340  --  0.165       41.209  --  0.290       84.390  --  0.415        0.992  --  0.045       14.161  --  0.170       42.642  --  0.295       86.436  --  0.420        1.225  --  0.050       15.006  --  0.175       44.100  --  0.300       88.506  --  0.425        1.482  --  0.055       15.876  --  0.180       45.582  --  0.305       90.601  --  0.430        1.764  --  0.060       16.770  --  0.185       47.089  --  0.310       92.720  --  0.435        2.070  --  0.065       17.689  --  0.190       48.620  --  0.315       94.864  --  0.440        2.401  --  0.070       18.632  --  0.195       50.176  --  0.320       97.032  --  0.445        2.756  --  0.075       19.600  --  0.200       51.756  --  0.325       99.225  --  0.450        3.136  --  0.080       20.592  --  0.205       53.361  --  0.330      101.442  --  0.455        3.540  --  0.085       21.609  --  0.210       54.990  --  0.335      103.684  --  0.460        3.969  --  0.090       22.650  --  0.215       56.644  --  0.340      105.950  --  0.465        4.422  --  0.095       23.716  --  0.220       58.322  --  0.345      108.241  --  0.470        4.900  --  0.100       24.806  --  0.225       60.025  --  0.350      110.556  --  0.475        5.402  --  0.105       25.921  --  0.230       61.752  --  0.355      112.896  --  0.480        5.929  --  0.110       27.060  --  0.235       63.504  --  0.360      115.260  --  0.485        6.480  --  0.115       28.224  --  0.240       65.280  --  0.365      117.649  --  0.490        7.056  --  0.120       29.412  --  0.245       67.081  --  0.370      120.062  --  0.495        7.656  --  0.125       30.625  --  0.250       68.906  --  0.375      122.500  --  0.500Another alternative would be to draw a graph from the above chart and have the students read the time from the graph. The experiment could be stopped at this point but there are several more things that can be calculated.  The time obtained in the first part (call it reaction time-tr) is really the sum of three other times: 1) the time that it takes for your brain to realize that the object has been dropped (call it processing time-tp); 2) the time for the nerve signal to travel from your brain to your fingers (call it nerve time-tn); and 3) the time that it takes for your fingers to close (call this dynamic time-td).  (i.e., tr=tp+tn+td) The easiest of the three to calculate is the nerve time (tn).  Since nerve signals travel at an approximate speed of 30,000 cm/sec, we can measure the distance from your brain to your fingers and use the equation time=distance/rate to find the nerve time. The next easiest is dynamic time (td).  Dynamic time can be found by using a timer with a second hand or stopwatch to time 25 complete pinches (open and close) and then dividing that time by 50 (since each open and close is two actions). Processing time (tp) can be found two ways.  One method is to work backwards from the reaction time.  Given tr, tn and td, you can subtract the sum of tn and td from tr to get the processing time.  An alternate way that should produce aresult that is within the same order of magnitude is to take the tubing with a funnel in each end.  Mark the center of the tubing.  Have a student sit with onefunnel over each ear and the tubing spread behind them.  Have the partner tap the tubing at various places and ask the listener to indicate which ear/side the tapwas on.  There will be a dead spot near the middle where the listener cannot tellwhich side the tap was on.  Mark the approximate locations (left side and right side) of the limits of the dead spot.  The length of the dead spot can be used to find the processing time.  Knowing the speed of sound is about 34,000cm/sec,  time=distance/speed can be used to determine th brain's processing time.  In addition, some anatomy can be determined because, for most people, the dead spotwill not be centered but slightly off to one side.  That is due to the fact thatthe brain's auditory processing area is located on one side and it takes a tinybit longer for the signals to travel from the ear furthest from the autitory center. Performance Assessment:Several large sheets of paper should be hung on the wall of the classroom about knee level.  Each sheet should have the outline of a gas pedal and brake pedal drawn on the sheet.  Each group of students should be able to determine their reaction time and dynamic time for moving their foot off of the gas to the brake.  First hint: Hold the meterstick even with the top of the brake pedal and dropit.  Students can then move their foot to 'catch' the meterstick with their footsimilar to dropping the ruler between the fingers.  Second hint: make sure the classroom wall is sturdy enough to take some kicking.Multicultural Note:All of the equations and symbols used in this lesson are the same, regardless of the language of instruction.  Ukranian, German, Italian and Japanese physics books all have their physics equations in 'English'. `