## Motion Down an Incline

Concept: linear motion

Time: 30 m

SW Interface: 700

Macintosh® file: P10a Changing Velocity

## EQUIPMENT NEEDED

• Science Workshop Interface
• base and support rod
• photogate with mounting bracket
• five-pattern picket fence (for cart)
• dynamics cart
• meter stick
• track, 1.2 meter, with end-stop

## PURPOSE

The purpose of this activity is to investigate how the velocity of an object down an incline depends on the angle of the incline, the mass of the cart, and the distance from the point of release (or change in height).

## THEORY

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. The component of the acceleration due to gravity which is parallel to the inclined surface is gsin ø where ø is the angle of the incline. Neglecting friction, this is the acceleration of the cart. Due to the non-zero acceleration, the speed of the cart will increase as function of time. The goal of this experiment is to determine how the velocity of the cart depends on:

• The mass of the cart
• The angle of inclination
• The change in height

## PROCEDURE

In this activity you will use a photogates to measure the motion of a cart as it moves down an inclined track. To find the velocity of the cart, the cart will be started from rest and a "picket fence" mounted on the cart will pass through the photogate beam. We will change parameters like position, height, and mass, and determine how the velocity of the cart

* 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 Science Workshop interface to the computer, turn on the interface, and turn on the computer.
2. Connect the first photogate's stereo phone plug to Digital Channel 1 on the interface. NOTE: the first photogate is the photogate closest to the release point of the cart.
3. Connect the second photogate's stereo phone plug to Digital Channel 2 on the interface.
4. Open the Science Workshop file titled as shown:
• Macintosh: P10a Changing Velocity

The document has a Graph and a Table display. The vertical axis of the Graph shows "velocity (m/sec)". The horizontal axis shows the time since the first photogate signal was intercepted.

5. The "Sampling Options..." for this experiment are as follows: Periodic Samples = Fast at 10 Hz, Digital Timing = 10000 Hz.
6. The Science Workshop program calculates the velocity of the cart based on the distance between the leading edges of the opaque bands of the picket fence. The top row of the "five pattern picket fence" has opaque bands that are 1 centimeter from leading edge to leading edge. This value for the distance has been entered in the setup window for the "Photogate & Picket Fence".
• If you are using a picket fence with a different distance between the leading edges of the opaque bands, change the value in the setup window for the sensor (as follows).
• Double-click the Photogate & Picket Fence icon in the Experiment Setup window to open the sensor setup window.
• Enter the correct distance for "Opaque Band Spacing" in the sensor setup window. Click "OK" to return to the Experiment Setup window.
7. The "Sampling Options..." for this experiment are as follows: Periodic Samples = Fast at 10 Hz, Digital Timing = 10000 Hz.
8. Make sure that the opaque band on top of the picket fence intercepts the LED signals.

### PART II: Sensor Calibration and Equipment Setup

1. You do not need to calibrate the photogate for this activity.
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. Put the picket fence in the slots on the top of the dynamics cart with the 2.5 cm wide band on top. Attach the photogates with mounting bracket to the track. Position the photogates so the cart will have room to begin to move before the picket fence passes through it. Adjust the photogate height so the 1 centimeter row of the picket fence will pass through the photogate beam.
4. Set up the track as shown in the diagram, raising the end of the track without an end-stop so that it is 10 cm higher than its position when level.

### PART III: Preparing to Record Data

1. Before recording any data for later analysis, you should experiment with the photogates, cart, and picket fence. Put the cart at the starting point on the track
2. Put the cart at the starting point on the track (use the end of the track as your starting point). Release the cart so it moves down the track.
3. Click "Stop Sampling" to end recording of your sample data. "Run #1" will appear in the Experiment Setup window.
4. Click the "Autoscale" button in the Graph display.
5. Erase your trial run of data. Select "Run #1" in the Data list in the Experiment Setup window ...... and press the "Delete" key.

### PART IV: Data Recording

1. Position the photogates at 25 cm and 55 cm from the end of the track and determine the angle of the track.
2. Click the "REC" button to begin data recording.
3. Put the cart at the starting point on the track. Release the cart so it moves through the photogate.
4. Increase the mass of the cart by adding one "black bar" to the top of the cart and repeat the measurement.
5. Increase the mass of the cart by adding a second "black bar" to the top of the cart and repeat the measurement.
6. Move the photogates to 35 cm and 65 cm and repeat the previous three measurements.
7. Move the photogates to 45 cm and 75 cm and repeat the previous three measurements.
8. Lower the raised end of the track by five centimeter.
9. Repeat the previous 9 measurements at this new angle.

## ANALYZING THE DATA

1. For each measurement carried out, determine the change in height of the cart.
2. Make a plot the velocity of the cart versus the change in height for each series of measurements during which the mass of the cart of kept constant. What type of dependence can describe the dependence of the measured velocity on the change in height? Consider the following relations: v^3 vs h, v^2 vs h, v vs h, sqrt(v) vs h, 1/sqrt(v) vs h, 1/v vs h, 1/v^2 vs h, and 1/v^3 vs h.
3. What is the relation between the measured velocity and the mass of the cart at a fixed distance?

© Frank L. H. Wolfs, University of Rochester, Rochester, NY 14627, USA

Last updated on Monday, February 26, 2001 6:33