# GALILEO AND THE INCLINE PLANE

### Purpose:

To investigate relationships between distance, velocity, time and acceleration for a cart rolling down and incline plane.

### Equipment:

Dynamics Cart
Incline Plane
Flag
CBL / TI-82
Photogates

### Procedure

1. Set incline at a specific angle (5-10 degrees).
2. Set up two photogates for connection to CBL as described in CBL-PHOTOGATE Quick and Dirty.
3. Set cart even with first photogate so that it is just about to block the photogate.
4. Set second photogate 20 cm away from first photogate.
5. Prepare CBL for collecting data in the pulse mode. Release the cart and record time to travel between the two gates.
6. Repeat at the same distance until you are releasing the cart consistently and are able to produce repeatable data.
7. Repeat and record time for distances at 5.0 cm intervals until you run out of board.

### Data:

Angle:_____________

 DISTANCE TIME

### Analysis and Conclusion:

1. Enter your data in to L1 and L2 in your calculator.
2. Use StatPlot to graph distance versus time.
3. Use Stat - Calc and PwrReg mode to curve fit your graph.
4. Once the power of the data is clear you may want to change your curve fit to the appropriate power regression. (For example use CubicReg if it has been determined that the graph should have a power of three). Once you have your equation, substitute d and t in for y and x respectively and try to determine what each of the coefficients represents.
5. Manipulate t in order to make your curve a straight line. Calculate the equation of this line and again try to determine what each of the coefficients represents.

## CBL Photogate--- Quick and Dirty

Equipment Set-Up

1- Connect Photogates to photogate-CBL adapter

2- Connect CBL to TI-82

3- Select Prgm- Timer

4- Select Pulse mode for timing mode

Collecting Data

1- Hit enter to ready CBL for data collection.

2- Postion object at starting position (Just before it breaks the beam.)

3- Release object.

4- Record time in data table.

5- Hit enter and choose [2] yes, unless you are on last trial.

6- Repeat for each distance

## NOTES FOR THE INSTRUCTOR

This is just one example of how the classical Galileo's Incline Plane experiment may be completed using the CBL.

Some suggestions for other ways to collect data:

1) Use Gate mode, choose two gates and have a flag 5.0 cm long so that the two times recorded are the time it takes the flag to pass through the photogate at each position. Using this data the students can find the initial velocity and the final velocity.

2) Use Motion mode, and then use Smart Pulley selection in order to collect data for a cart sliding down an incline.

3) Use any of the first two methods for a ball rolling down an incline.

Some suggestions for analysis:

1) Instead of using the TI-82, the students can use any graphing or spreadsheet program in order to analyze the data including MS Excel, Vernier's Graphic Analysis or Logger Pro, or any other package.

2) The students could be given more instruction on what type of graph the are to get, for instance tell them it is a quadratic.

3) Another interesting approach use to have the students use the data to calculate the value for acceleration along the incline and compare that to the value = g * sin q or to the value of acceleration calculated for a different version of lab with incline at the same angle.

4) Students may also want to compare results using CBL to results calculated using a different method, stopwatch, waterclock, or ticker tape timer.

### Sample Data

 DISTANCE TIME TIME2 0.559 0.100 0.312 0.719 0.150 0.517 0.840 0.200 0.706 0.969 0.250 0.939 1.07 0.300 1.14 1.19 0.350 1.42 1.27 0.400 1.62 1.36 0.450 1.85 1.45 0.500 2.10 1.56 0.550 2.43 1.64 0.600 2.71 1.72 0.650 2.94 1.78 0.700 3.17 1.85 0.750 3.42 1.90 0.800 3.62 1.95 0.850 3.80 1.99 0.900 3.96

Written by Douglas Hutton, July 1997