Accel equals Decel

Challenge:  To design a simple sled and hanging mass system that will accelerate and decelerate at similar rates autonomously.

Parameters: Your system should accelerate for half the available run distance while the hanging mass is falling towards the floor.  Once it hits the floor, the sled portion should decelerate to a stop over the remaining distance available on the table.  You will need a ticker-tape and timer to record the position and time data, which you should record for every third dot.  (3/60 of a second is 0.05 seconds).  With that data, create a spreadsheet, calculate velocities over each interval, graph position and velocity vs. time.  Separate the acceleration and deceleration portions and find the magnitude of each by finding the slopes of the fit lines.  Measure masses, and draw scale FBDs for each part of the system for both the acceleration and deceleration portions of the trip.  These should be done before competition day, so they can be done with data from a representative trial you did in preparation for the competition.

Scoring:  Your system will be scored based on the distance it travels and the agreement between the magnitudes of acceleration and deceleration, as follows:

Score = D^2 /(a/d)   or   D^2 /(d/a)

D is the distance your sled moves in metres, as measured with the ticker tape.  The acceleration / deceleration ratio will be calculated with the larger magnitude one as the numerator.  These will be from the graphs produced from the same ticker tape.  You will have a maximum of three runs with ticker tape ink pads during the competition day.

Rank will be based on score, with highest score earning highest rank.

Physics:  Although not perfectly linear due to sag in the middle of the table, we will be using this challenge to review all one-dimensional kinematics and dynamics topics from grade 11.  I will detail these requirements as we proceed in class.

Extensions: The surfaces involved in the sled/table interaction give rise to a force of kinetic friction.  We can estimate the coefficient of friction from our data.  This should be the same for both portions of the trip as it is the same surfaces, but does the data support this conclusion?  What might cause discrepancy, if any exists?    

Help/Hints: Make some parameters of your system adjustable so that you can do trial and error practice runs without the ink pad in the days leading up to the competition.  Quick video analysis can be done by assuming constant acceleration (and deceleration) and having meter sticks on the table for distance estimates.  Once you set up your spreadsheet and graphs, I recommend duplicating the page for subsequent trials. You can then easily compare different runs.  Use a naming system like F3a, F3b, F3c, and be sure to label your ticker tapes with the same system, and keep them safe!  You will need to submit the ticker tape that gave you the best result for the contest.

Quiz Topics: One-Dimensional Kinematics, FBD, Newton’s Laws, Measurement, Graphing

Online Text: College Physics chapters 2, 3, 4, 5 (one dimension only)