The first activity utilized the ULI, photogate and Logger Pro systems to analyze graphs for free fall. The photogate system was first assembled and connected to the computer using the ULI. Three graphs were analyzed by the Logger Pro program namely distance vs. time, velocity vs. time, and acceleration vs. time graphs. A chopper was dropped in between the photogate, and data of various components such as acceleration were recorded and plotted on the different graphs in the program. After data collection, a linear fit and a quadratic curve was tested upon the graph of distance vs. time. It was found out that a quadratic curve would fit better for the distance vs. time graph rather than a linear fit. This shows that the distance follows a parabolic curve as time progress during a free fall. This is shown by the equation X = X0 + V0t – 1/2gt2, or D= V0t – 1/2gt2 .A quadratic equation has a form ax2 + bx + c = 0, where ax2 is –1/2gt2 , bx is V0t, and c is X – X0 which is also the displacement or as scalar quantity, the distance D. The graph of velocity vs. time is a linear equation, in which a slope may be taken by the equation y = mx + b. Our equation is V0 = gt. If the derivative of the graph of distance vs. time were taken, the resulting derivative would be the linear graph of velocity vs. time. Furthermore, if the derivative of the graph of velocity vs. time were taken, we would have the graph of acceleration vs. time, which has the equation y = m, or a horizontal graph. This graph is logical for acceleration, since in a free fall, the acceleration of the object is at a constant 9.8m/s2.
The average slope of the graph of velocity vs. time in five trials was taken to compare with the theoretical acceleration of gravity (9.8m/s2). In computing, we had a value of 9.428 m/s2, which was 3.79% off from the theoretical. We computed for the percentage error by the equation (theoretical – actual) / theoretical * 100. This is a large percentage error as compared to percentage errors acquired by other groups. Several causes of error may be attributed to this. Mechanical errors, or errors in the equipment may have caused this. The photogate wasn’t working at first and had to be replaced. We even had to work with another computer, since the computer assigned to our table was malfunctioning.
The second activity utilized an accelerometer to measure the amount of acceleration of an object at various heights/point from the ground. A representative wore the accelerometer with the indicator arrow facing upward, and then positioned himself in a trampoline. He would then jump up in down within a certain time of about five seconds. The acceleration was then graphed in the computer by a series of crests and troughs. The pattern of the graph was somewhat uniform all throughout, with crests and troughs at close to regular intervals paralleled to the different points at the jump of the representative. It was noticed that at a higher point during the jump, the graph shifted downward. Inversely, when the representative landed in the trampoline, the graph shot upward. This was reasonable. The force of gravity increases as an object is closer to the ground. This why the graph moved upwards when the representative landed on the trampoline. Crests represented high rates of acceleration. Similarly, crests indicate that the representative nearer to ground. The troughs, on the other hand, indicate lower rates of acceleration. The force of gravity decreases as an object is farther from the ground. At the peak of the representative’s jump, the graph would move downward, creating the low points of the graph.
However, the orientation of the graph may be changed. Remember that before jumping, the indicator arrow was flipped upwards. The effect on the graph was it shot downwards at peaks of the jump, and it moved upwards whenever the representative landed. If the indicator arrow is flipped downward, the previous graph will also be flipped. Instead of an increasing positive value as one descends, the meter will read an increasingly negative value. This is simply an indication of the direction of the acceleration., which going down.
In this activity, we have learned the relationships between time, distance, velocity and acceleration. In addition, we are also able to confirm the presence of acceleration due to gravity. Even if the theoretical is 9.8m/s2 , the presence of factors like air resistance lessens this value.
