2007-09-17- Test given back and g lab
L = length
T = time
What is the A in x = Acos(BT).
When you take the cosine, you take the cosine of the scalar so there's no units, so B will always have the reciprocal units of T, so if T is in seconds then B would be 1/seconds. So this has no units in the parameter ultimately. So whatever B is, T is the reciprocal units. A and X are going to have the same units. So whatever it is that X is representing (in this case, position), then A would have those units as well, which would be L for length.
v = C_{1}e^{-C_{2}T}.
So V is going to have the same units as C_{1} in this case as well.
g/cm^3 to kg/m^3 ?? So you do 1 * 100 * 100 * 100 / 1000.
A car making a 200 km journey travles 20 km/hr for the first 100 km. How fast must it go during the second 100 km to average 40 km/hr? 200/40 = 5 hr. So that's impossible.
Introduction
To determine the acceleration due to the force of gravity, taking the derivative of the position function provides the velocity function and the second derivative of the position function provides the acceleration, which should be experimentally confirmed to be -9.81 m/s^2 for constant acceleration.
Methods
The TI-84+ SE calculators were wired to the rangers which allow for motion detection. The bouncy ball was dropped directly below the ranger as in the following diagram:
It is important to note that the information that was collected with the detector was the distance per millisecond that the ball was starting from the detector.
Data
Plotted ideal position function
Experimental position data
(How do you plot points in gnuplot?)
Analysis
First we need to trace and find the maximum of the first parabola in order to start the construction of our equation. The maximum is (1.299, 0.310562), so: y_{1} = (x-1.299)^{2} + 0.310562.
The equation that matches the first bounce is -3.550(x-1.299)^{2} + 0.310562.
The equation that matches the second bounce is -5(x-1.79896)^{2} + 0.277808
The equation that matches the third bounce is -1(x-2.2986712)^{2} + 0.17
Conclusion