Introduction:

In this experiment you will conduct a quantitative analysis of a ball which falls under the influence of gravity and then bounces several times. In particular you will measure quantities such as its acceleration, the time between bounces and the height of each bounces.

Procedure:

The main instrument we will use for studying the motion of the ball is a motion detector connected to a Logger Pro. This instrument detects the position of an object as a function of time using sonar and can be used to obtain graphs of position vs. time, velocity vs. time and acceleration vs. time. Typically the acceleration vs. time graph is hard to interpret, so the slope of the velocity time graph is the best way to determine the acceleration due to gravity. Fix the motion detector at as high a position as possible and release the ball at a distance of about 0.5 m below the motion detector (it cannot reliable detect motion at a distance closer than 0.5 m.

The answers to the following questions will help you interpret your graphs. What direction does the motion detector take as the positive direction? Where is the zero position?
 
 

1. Drop a ball below the motion detector and obtain position, velocity and acceleration vs. time graphs which are reasonably clean of anomalous spikes and which show several bounces of the ball. Describe the form of each graph in your notebook, giving careful attention to the points on the graph when the bounces occur and when the ball reaches its maximum height.
2. From the slope of the velocity vs. time graph obtain the value of the acceleration of the ball. Is the acceleration constant? Compare the value you obtain to the accepted value for the acceleration due to gravity. Explain any differences you observe.
3. From the position vs. time graph determine the sequence of heights of each bounce. Include in your sequence the initial height of the ball. Does this sequence form a recognisable type of pattern? (i.e. is it approximately an arithmetic or a geometric sequence?)
4. From the position vs. time graph determine the sequence of times between each successive bounce. Does this sequence form a recognisable type of pattern? (i.e. is it approximately an arithmetic or a geometric sequence?)