2.3.3 Lab Kinematics Acceleration of Falling Objects: Galileo Revisited

Materials:

Ring stand
Meter stick/metric ruler
Marble
1.75 meter dynamics track (or PVC pipe)
Protractor
Stopwatch
Calculator
Computer with graphing software
Materials for Exploring Further:

Ticker timer and ticker tape
Graph paper and scotch tape
Projectile apparatus
Carbon paper
White craft paper

Procedure

Use the protractor to set your track at a 5° angle. Use the ring stand to hold the track at this angle.
Hold the marble at the top of the track. Start the timer as you drop the marble. Stop the timer at the moment you hear the marble hit the table. Record the time in seconds (t1) in the data table below.
Repeat the experiment 4 more times, and record each result (t2, t3, t4, t5) in the data table.
Repeat steps 3 and 4 with your track set at angles of 10°, 15°, 20°, 25°, 30°, 35°, 40°, and 50°.
For each angle, find the average (mean) time it took the marble to drop (tavg). Record the averages in the data table.
Find the square of each average time (t2) and record these values in the data table.
Multiply the length of the track, determined in step 1, by 2 (2d) and record the result in the data table. (This result will be the same for every angle you used.)
For each angle, calculate the acceleration of the marble (a) using the equation . Record the results of your calculations in the data table.
Now use the computer to make a graph of acceleration versus the sine of the angle of incline (the angle at which you set your track). The sine of the angle is the independent variable, so it goes on the x-axis; put the acceleration on the y-axis.
Use the computer to find a line of best fit.
Since a freely falling object is falling at a 90° angle, you can use your graph to determine the acceleration of any falling object — that is, the acceleration due to Earth's gravity. Extend the line of best fit to the sine of 90°. The y-value for this point should be equal to the acceleration due to gravity.
Write a journal describing your experiment.
Write a journal communicating your conclusions, supported by the data.

Angle of incline 5° 10° 15° 20° 25° 30° 35° 40° 50°
t1 (s)

2.11 1.46 1.10 1.13 0.89 0.90 0.75 0.68 0.66
t2 (s)

2.10 1.50 1.11 1.04 0.87 0.94 0.77 0.79 0.59
t3 (s)

2.09 1.53 1.22 1.06 1.01 0.81 0.83 0.80 0.71
t4 (s)

2.01 1.42 1.20 0.98 0.97 0.83 0.81 0.82 0.70
t5 (s)

2.04 1.39 1.32 0.99 0.86 0.77 0.84 0.66 0.79
tavg (s)

t2 (s2)

2d (m)

(m/s2)

Analyze

1. What happened to the time it took for the marble to reach the table (t) as the angle of incline increased?

2. What is the relationship between the acceleration of the marble (a) and the time it takes the marble to reach the table (t)?

Draw Conclusions

1. According to your graph, what would be the acceleration of the marble at 90°?

2. Given what you know about the acceleration of Earth's gravity (g = 9.8 m/s2), is this number accurate? If not, explain why you think it is not accurate.

Explore Further

1. What factors might affect the accuracy of this experiment? Describe one way you could improve the experiment's design. List any equipment you might use, and explain how you would use it.

2. If the acceleration of gravity is 9.8 m/s2, then that means an object falling at 90° will be traveling 9.8 m/s after 1 second, 19.6 m/s after 2 seconds, and so on. Use the data values in your table to sketch a rough graph of velocity versus time for the 10° angle and another for the 40° angle. What value do the slopes of these graphs represent? Which graph has the greater slope? Why?