Introduction
This study focused on an object in motion with uniform acceleration. Using the Motion Encoder System and LoggerPro, the position, velocity, and time were taken and analyzed with the goal to determine linear and quadratic acceleration. Interpreting the graphs allowed the discovery of the effect of acceleration due to Earth’s gravity. This was represented by the value of the average acceleration of 9.8m/s^2 when the sine of theta was equal to 1 (90 degrees).
The significance of this experiment was to represent how acceleration changes in relation to an incline’s angle to determine freefall acceleration. With Galileo’s restricted method to determine acceleration with inclined planes, the data collected from the trials with the inclined planes were used to determine the freefall experiment using a graph of the collected average acceleration versus sine of theta. It was hypothesized that the acceleration would be directly proportional to the angle of the incline and that the acceleration would approach 9.8m/s^2 as the angle of the incline approached 90 degrees.
Method
Using a Lab Quest and Motion Encoder System, a cart was pushed up at various angles (increased amount of stacked books) on a dynamics track. A position versus time and velocity versus time graph was plotted on the computer using LoggerPro for all three trials for each angle of incline. Using linear fit on the velocity versus time graph and a quadratic fit on the position versus time graph, the linear acceleration, and quadratic acceleration, respectively, were collected for each trial. An average linear acceleration and average quadratic acceleration were calculated at the end of the trial’s execution.
Data
| Number of riser blocks | Height
h (m) | Length of incline, x (m) | Sin(theta) |
Trial 1 (m/s^2) |
| Acceleration |
Trial 2 (m/s^2) |
Trial 3 (m/s^2) | Average acceleration (linear, L)
(m/s^2) | Average acceleration (quadratic, Q) (m/s^2) | |||
| Acceleration | ||||||||||||
| Acceleration | |||||||||||||
| 1.21 | 0.003 | 0.005 | 0.007 | 0.005 | |||||||||
| 1 | 0.007 | 1.21 | 0.006 | L0.062
Q0.062 | 0.058
0.058 | 0.059
0.058 | 0.06 | 0.06 | |||||
| 2 | 0.019 | 1.21 | 0.016 | L0.146
Q0.146 | 0.143
0.144 | 0.143
0.144 | 0.144 | 0.144 | |||||
| 3 | 0.028 | 1.21 | 0.023 | L0.212
Q0.212 | 0.212
0.212 | 0.217
0.216 | 0.214 | 0.214 | |||||
| 4 | 0.037 | 1.21 | 0.031 | L0.286
Q0.290 | 0.294
0.294 | 0.294
0.294 | 0.291 | 0.292 | |||||
| 5 | 0.05 | 1.21 | 0.041 | L0.392
Q0.394 | 0.393
0.394 | 0.394
0.390 | 0.393 | 0.392 |
Analysis
The value of the acceleration when sin(theta) equals 1(freefall) is about 9.57 which is relatively close to the value of 9.8 which is the value of freefall acceleration. The percent error for this experimental value of freefall acceleration versus the actual is represented below.
Conclusion
Acceleration is directly related to the angle of an incline. When an angle is 90 degrees, the object is in freefall and acceleration is equal to the acceleration due to the Earth’s gravity, 9.8m/s^2. Reasons for the mild percent error are issues of rounding numbers and slight inaccurate selection of graph segments when collecting data for linear and quadratic acceleration.
