Teacher’s Guide - Activity P03: Acceleration on an Incline (Acceleration Sensor)

|Concept |DataStudio |ScienceWorkshop (Mac) |ScienceWorkshop (Win) |
|Linear motion |P03 Acceleration.ds |(See end of activity) |(See end of activity) |

|Equipment Needed |Qty |Equipment Needed |Qty |
|Acceleration Sensor (CI-6558) |1 |Dynamics Cart (inc. w/ Track) |1 |
|Angle Indicator (inc. w/ Track) |1 |Meter stick |1 |
|Base and Support Rod (ME-9355) |1 |1.2 m Track System (ME-9429A) |1 |

What Do You Think?

When a sled accelerates down a snow-covered hill, on what does its acceleration depend? You may want to consider the height of the hill, the slope of the hill and the mass of the sled. How does its acceleration depend on the variable(s) you selected?

Take time to answer the ‘What Do You Think?’ question(s) in the Lab Report section.

Background

A cart on an incline will roll down the incline as it is pulled by gravity. The direction of the acceleration due to gravity is straight down as shown in the diagram. The component of the acceleration due to gravity which is parallel to the inclined surface is gsinθ where θ is the angle of the incline. Neglecting friction, this is the acceleration of the cart.

|SAFETY REMINDER |[pic] |
|Follow all safety instructions. | |

For You To Do

Use an Acceleration Sensor to measure the motion of a cart as it moves down an inclined track. Use an angle indicator to measure the angle of the inclined track or determine the sine of the angle (sin θ) from the height of the track and the length of the track.

[pic]

Use the slope of a graph of the cart’s acceleration versus sin θ to determine the value of “g”, the acceleration due to gravity.

• NOTE: This activity is easier to do if you have a partner to run the computer while you release the cart.

PART I: Computer Setup

1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer.

2. Connect one end of the cable to the Acceleration Sensor and connect the other end into Analog Channel A on the interface.

3. Open the file titled as shown:

|DataStudio |ScienceWorkshop (Mac) |ScienceWorkshop (Win) |
|P03 Acceleration.ds |(See end of activity) |(See end of activity) |

• The DataStudio file has a Workbook display. Read the instructions in the Workbook. The file has a Graph display of Acceleration versus Time, a Table display of Acceleration and ‘sin (theta)’, and a Graph display of Acceleration versus ‘sin (theta)’.

• Data recording is set for 50 measurements per second (50 Hz).

• See the pages at the end of this activity for information about creating a ScienceWorkshop file.

PART II: Sensor Calibration and Equipment Setup

• You do not need to calibrate the sensor for this activity.

1. Carefully measure and record the overall length of your track.

2. Level the track by setting the cart on the track to see which way it rolls. Adjust the leveling screw at the end of the track to raise or lower that end until the cart placed at rest on the track will not move toward either end. Record the height of the end of the track that does not have the end-stop.

3. Mount the Acceleration Sensor onto the cart.

• Use the large thumbscrew to attach the ‘short’ leg of the bracket to the sensor.

• Use the small thumbscrew to attach the ‘long’ leg of the bracket to a threaded hole in the top of the cart.

4. Set the ‘SENSOR RESPONSE’ switch to ‘SLOW’.

5. Use the base and support rod to raise the end of the track without an end-stop so that it is 20 cm higher than its position when level.

6. Mount the angle indicator onto the raised end of the track.

7. Use a pencil to put a mark near the midpoint of the track.

• Let the midpoint mark be your starting point for the cart release during data recording.

Preparing to Record Data

Recording data involves the following steps:

• Measure and record the height of the track (or record the angle of the track).

• Tare the sensor. Start data recording.

• Release the cart.

• Catch the cart and stop recording data.

Repeat the process for several heights (several angles).

PART III: Data Recording

1. Determine the angle of the track. (Hint: Use the angle indicator, or measure the height of the track and use the height and length of the track to calculate the sine of the angle.)

2. Put the cart at the starting point on the inclined track. Press the ‘TARE’ button on the sensor to zero the sensor.

3. Start recording data (hint: click ‘Start’ or click ‘REC’) and then release the cart so it moves down the track.

4. Catch the cart when it reaches the end of the track and stop recording data.

5. Lower the raised end of the track by four centimeters.

6. Repeat the procedure at the new height.

7. Continue to repeat the procedure until the raised end is at 4 centimeters.

Analyzing the Data

The first part of analyzing the data involves the following steps for each different height:

• Determine the sine of the angle. (Hint: Use the measurement from the angle indicator and then find the sine of the angle or calculate the sine of the angle based on the height and length of the track.)

• Examine the Graph display of Acceleration versus Time to determine the average acceleration.

• Enter the average acceleration and the sine of the angle into the Table display of ‘Acceleration’ and ‘sin (theta)’.

Repeat the analysis procedure for the each height.

1. Determine the sine of the angle and record the value in the Lab Report section.

2. In the Graph display, click-and-drag the cursor to highlight that section of the data that corresponds to the motion of the cart down the track.

3. Use the Graph’s built-in analysis tools to determine the average (‘mean’) of the acceleration.

• Hint: In DataStudio, click the ‘Statistics menu’ button ([pic]) and select ‘Mean’. In ScienceWorkshop, click the ‘Statistics’ button ([pic]) to open the statistics area. In the statistics area, click the ‘Statistics menu’ button ([pic]) and select ‘Mean’.

4. Enter the sine of the angle and the average acceleration for that angle into the Table display.

For the second part of analyzing the data, use the Graph display of Acceleration versus ‘sin (theta)’.

1. Find the slope and y-intercept of the best-fit line through your data.

• Hint: In DataStudio, click the ‘Fit’ button and select ‘Linear’ from the menu. In ScienceWorkshop, click the ‘Statistics menu’ button and select ‘Curve Fit, Linear Fit’ from the submenu.

2. Record the slope as the acceleration due to gravity, “g”.

• Hint: In DataStudio, the slope ‘m’ is shown in the ‘Linear Fit’ legend on the Graph display. In ScienceWorkshop, the slope is the coefficient ‘a2’.

Record your results in the Lab Report section.

Lab Report - Activity P03: Acceleration on an Incline

What Do You Think?

When a sled accelerates down a snow-covered hill, on what does its acceleration depend? You may want to consider the height of the hill, the slope of the hill and the mass of the sled. How does its acceleration depend on the variable(s) you selected?

Answers will vary. For a slippery (frictionless) slope, the acceleration depends only on the slope of the hill, given by the angle of incline, θ.

Questions

1. What is the percent difference between your measured value for “g” and the accepted value for “g”?

Remember, [pic]

Answers will vary. For the heavier cart, the measured value is 1.9% less than the accepted value. For the lighter cart, the measured value is 2.2% less than the accepted value.

2. If the mass of the cart is doubled, how are the results affected? Try it.

The change in mass of the cart should not make a difference in the measured acceleration (but it obviously did in the example above). This may be because the force of friction is proportionally less for the heavier cart.

Appendix: Set Up ScienceWorkshop

Create a ScienceWorkshop file to measure acceleration.

Set Up the Sensor

In the Experiment Setup window, click and drag the analog sensor plug to Channel A. Select ‘Acceleration Sensor’ from the list of sensors. Click ‘OK’ to return to the Experiment Setup window.

Set the Sampling Options

Click the ‘Sampling Options’ button in the Experiment Setup window or select ‘Sampling Options’ from the Experiment menu to open the Sampling Options window. Under ‘Periodic Samples’ click the right arrow to set the sample rate at ‘50 Hz’ (50 measurements per second).

Set Up the Display

In the Experiment Setup window, click and drag the Graph display icon to the Acceleration Sensor icon.

Select ‘Acceleration (m/s/s)’ from the list of calculations and click ‘Display’.

Analyzing the Data

After you have recorded data and determined the sine of the angle and the average acceleration for each trial, use the ‘Experiment Notes’ window to enter your data into a new Graph display of Acceleration versus sin (theta).

Enter the Data

1. Open a ‘Notes’ window. Use the following format to enter your data pairs of the sine of the angle and the average acceleration for each angle:

‘sine of angle’ ‘average acceleration’

2. Pick ‘Select All’ in the Edit menu and then pick ‘Copy’ in the Edit menu. Result: The data pairs in the Notes window are highlighted.

3. Click the Experiment Setup window to make it active. Pick ‘Paste’ from the Edit menu to ‘paste’ the data into the Data list. Result: The ‘Enter Data Cache Information’ window opens.

Enter ‘Acceleration’ as the Long Name and ‘m/s/s’ as the Units and click ‘OK’. Result: ‘Import’ appears in the Data list in the Experiment Setup window.

Display the Data

1. In the Graph display, select ‘Data Cache, Acceleration’ from the ‘Data Input’ menu.

Result: The data pairs are plotted. Note that the horizontal axis label is ‘Time (s)’ but the ‘x’ values correspond to the sine of the angle.

|Time Estimates |Preparation: 30 min |Activity: 30 min |

Objectives

Students will be able to…

use the Acceleration Sensor to measure the motion of a cart as it moves down an inclined track for several different angles of inclination of the track

determine the sine of the angle of the inclined track for each different angle

use the software to determine the average acceleration for each trial

create and then plot ordered data pairs for the sine of each angle and the corresponding average acceleration

analyze a graph of acceleration versus sine of the angle to determine the slope and thereby determine the acceleration due to gravity, ‘g’

Notes

This activity is similar to Galileo’s experiment in which he let a ball roll a measured distance down an inclined plane and recorded the time. Instead of determining the relationship of d to t2 for various angles of the inclined plane, the student can make measurements to find the value of g.

The acceleration of the cart down the incline is due to the net force parallel to the surface of the incline. The net force is the difference between mg sin θ and the frictional forces, where m is the mass of the cart and θ is the angle of the incline.

If friction is neglected, the acceleration of the cart is:

a = g sin θ

The slope of the line on a graph of acceleration and sin θ is the value of the acceleration due to gravity, g.

DataStudio Sample Data

ScienceWorkshop Sample Data

The following is a Graph of sample data for a cart of mass = 1457.5 g (1.457 kg).

[pic]

The following is a Graph of sample data for a cart of mass = 464.4 g (0.464 kg).

[pic]