PHYS 253: University Physics I Lab Prelab #1: Determining Parameters with Proportionality Background In many lab experiments, we are interested in determining a proportionality relationship from our data, e.g. y x x or y x x . This is a nice method for comparing a theoretical equation to real-world measurements, allowing us to verify if the model is useful and to determine the value of a physical parameter in the model. For example, from the constant acceleration equations, we know that the relationship between the time elapsed and the distance an object falls when dropped from rest is Ay = 2 9At , or AyoAt. If we experimentally measure distances and times and then plot the variables Ay vs. At , the data will be linear and the slope of the line, /, will be the value of the physical constant g/2. Problems x 0.70 1.1 1.5 2.5 3.5 y (x) 0.20 0.50 0.90 2.5 4.9 0.49 1.21 2 25 6.25 12.25 0 . 04 0 . 25 0' 81 6.25 24.01 1. Complete the table above, then carefully plot three combinations of variables on the following sheet: xvs. y; x vs. y; and x vs. y (x is the independent variable). Use a ruler to draw by hand a best-fit straight line from the origin through the data on each plot, and measure the slope of the line. K 2 K2 2. If x represents velocity in [m/s], and y represents force in [kg.m/s ], what are the units of the slope in each of the three cases? * (...near the surface of Earth, in the absence of drag)