Analysis

1. The graphs you have recorded are fairly complex and it is important to identify different regions of each graph. Click the Examine button  and move the mouse across any graph to answer the following questions.

a) Identify the region when the ball was being tossed but still in your hands:

· Examine the velocity vs. time graph and identify this region. Label this on the graph.

· Examine the acceleration vs. time graph and identify the same region. Label this on the graph.

b) Identify the region where the ball is in free fall (defined as when gravity is the only force acting on the ball):

· Label the region on each graph where the ball was in free fall and moving upward.

· Label the region on each graph where the ball was in free fall and moving downward.

c) Determine the distance, velocity, and acceleration at specific points.

· On the velocity vs. time graph, decide where the ball had its maximum speed (magnitude of velocity), just as the ball was released. Mark the spot and record the value on the graph.

· On the distance vs. time graph, locate where the ball reaches its the maximum height during free fall. Mark the spot and record the value (distance from sensor) on the graph.

· What was the velocity of the ball at the top of its motion?

· What was the acceleration of the ball at the top of its motion?

2. The motion of an object in free fall is modeled by y = y₀ + v₀t + ½ a_yt², where y is the vertical position starting at  y₀, initial velocity is v₀, time is t, and a_y is acceleration due to gravity (9.8 m/s²)(*Note that due to the setup down is measured as the positive direction). This is a quadratic equation whose graph is a parabola. Your graph of distance vs. time should be parabolic. To fit a quadratic equation to your data, click and drag the mouse across the portion of the distance vs. time graph that is parabolic, highlighting the free-fall portion. Select "Analysis/Automatic Curve Fit" select quadratic fit from the list of models. Examine the fit of the curve to your data and click "OK" to return to the main graph. Determine g from your quadratic fit (related to coefficient of x²). How closely does this g compare to expected?

3. The graph of velocity vs. time should be linear. To fit a line to this data, click and drag the mouse across the free-fall region of the motion. Click the Regression button . How closely does the coefficient of the x term compare to the accepted value for g?

4. The graph of acceleration vs. time should appear to be more or less constant. Click and drag the mouse across the free-fall section of the motion and select "Analysis/Statistics". How closely does the mean acceleration value compare to the values of g found in Steps 2 and 3?

5. From the three graphs, determine your average value for g. Compare your value of g with the expected value using absolute difference and percent error. Write a sentence for each way of doing the comparison.

6. List some reasons why your values for the ball’s acceleration may be different from the accepted value for g.