Monday pre-activity: acceleration from rest for a moving object. Acceleration as a change in velocity with respect to time.
Acceleration is the change in velocity divided by the change in time. As an example, a RipStik was accelerated from rest to 1.34 m/s in 3.43 seconds, and then accelerated to 1.78 m/s in the next 2.59 seconds. The chart shows the time versus distance, velocity, and acceleration curves for the RipStik.
In this activity we will explore the shape of the path through the air made by a sphere. The path is a path in two-dimensional space. The graph will be a space versus space graph using the MKS system. The path reflects the influence of the acceleration of gravity on the sphere. The acceleration of gravity accelerates masses towards the center of the Earth at 980 centimeters per second squared. The result is a parabolic path.
We will be working outside to measure the arc of the sphere. The set-up and variables to be measured are seen in the following diagram.
Where k is the height of the y-intercept above the x-axis
and r is the distance from the axis of symmetry to one x-intercept (root).
| Task | n | Position title | Student name | x | y |
|---|---|---|---|---|---|
| Right x-intercept | 1 | Ball underhand pitcher | |||
| 2 | Meter stick holder | ||||
| 3 | Recorder | ||||
| right mid arc height | 4 | Tape measure holder | x | y | |
| 5 | Tape base holder | ||||
| 6 | arc height observer | ||||
| 7 | Data recorder | ||||
| Vertex height k | 8 | Tape measure holder | Same as 4 | x | y |
| 9 | Tape base holder | Same as 5 | |||
| 10 | Vertex position observer | ||||
| 11 | Data recorder | ||||
| left mid arc height | 12 | Tape measure holder | x | y | |
| 13 | Tape base holder | ||||
| 14 | arc height observer | ||||
| 15 | Data recorder | ||||
| Left x-intercept | 16 | Ball catcher | x | y | |
| 17 | Meter stick holder | ||||
| 18 | Recorder | ||||
| x-intercept to x-intercept | 19 | Wheel roller | distance = 2r | ||
| 20 | Recorder | ||||
Does our data agree with the theory? Use a spread sheet to plot the data. Set up a table like the seen below for spring 2008. Make an xy scattergraph of all three columns. Use the k and r from the activity to calculate the predicted path. The function below is an example based on the spring 2008 data. Your values of k and r will be different. Spring 2008 k was 2.2 m and r was 3.0 meters. The presumes that the column titles are in row 1 and that the first x-value is in cell A2. This formula would be in C2 and can be "filled down" for the next four rows.
=-(2.2/(3.0^2))*A2^2+2.2
Data from spring 2008
| location x (m) | y1 actual height (m) | y2 predicted height using the equation(m) |
|---|---|---|
| -3.0 | 0.0 | 0.00 |
| -1.5 | 1.3 | 1.65 |
| 0.0 | 2.2 | 2.20 |
| 1.5 | 1.4 | 1.65 |
| 3.0 | 0.0 | 0.00 |
