07A Velocity and Acceleration 07A - Page 1 of 6

Velocity and Acceleration

Introduction

This lab uses a Motion Sensor to measure the motion of a motorized cart and a fan cart. Graphs of position and velocity are analyzed for constant velocity, and constant acceleration. The output from the 850 interface is used to control the speed of the motorized cart.

EquipmentQty Items Part Number 1 Motion Sensor PS-2103A 1 Dynamics System ME-6955 1 Motorized Cart ME-9781 1 Fan Cart ME-6977 1 Elastic Bumper ME-8998

Set-up

1. Set up the track as shown in Figure 1 with the elastic bumper and feet. Note that the motion sensor is on the end of the track that is the zero point for the yellow rule. Connect the motion sensor to the 850 and make sure the range switch is on the "Cart" icon.

2. Plug the motorized cart power cord into Output #1 on the 850, and make sure it is on the OFF/EXTERNAL SETTING. The fan cart will not be used until later in the experiment.

Written by Jon Hanks

Figure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized CartFigure 1: Motion of the Motorized Cart

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3. Make a graph of Position versus Time.

4. In the Recording Conditions on the Sampling Bar at the bottom of the page in Capstone, select the Stop Condition and make the Condition Type Measurement Based. Select Position as the Data Source. Make the condition: Is above 0.80.

Procedure – Motorized Cart

1. Position the back of the Motorized Cart at the 20 cm mark. Always start the cart from this position.

2. Confirm that the 850 Output #1 is set on DC with a voltage of 2 Volts. Turn the Output ON and OFF to ensure that everything works.

3. Start recording data. Turn the Output ON and OFF to ensure that you are getting good position data.

4. You can delete unwanted runs using the Delete Run feature in the Control Palette at the bottom.

5. When everything looks good, click on Auto in the Output Control. This will cause the output to automatically turn on when you start recording. You can stop recording anytime you wish, but there is also a stop condition built-in that will stop the cart before it reaches the bumper.

6. Get a single good run of position vs. time, then open the Data Summary window and label this run Motorized Cart.

Velocity

If x(t) is a function that describes the position of an object as a function of time, then the velocity of the object is given by v(t) = dx/dt, the first derivative of the position function. Graphically, the velocity is the slope of the position graph.

1. For your position graph of the Motorized Cart, how does the slope vary during the run?

2. Select a linear Curve Fit from the graph tool palette.

3. What is the physical meaning of the slope? Does it have units?

4. How linear is your data? Was this constant velocity?

5. What is the physical meaning of the y-intercept on the graph? Does it have units?

Written by Jon Hanks

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Setup - Fan Cart

1. Place the fan cart on the track as shown in Figure 2. The fan can swivel on its base: It should be pointed back towards the motion sensor with the angle indicator set to zero degrees.

2. Adjust the level of the track so that the cart is rolling slightly downhill, to compensate for frictional drag. Give the cart a slight push to the right (away from motion sensor). If it speeds up, the track is too steep.

3. Turn on the fan cart by pressing its power button. The fan cart is now in Standby mode, and the fan speed should be set on Low. Press the power button again to start and stop the fan.

4. Press the fan speed button to change the speed to the Medium setting. Press the power button again to start and stop the fan.

Figure 3: Fan Power Figure 4: Adjusting Fan Speed

5. In Capstone, create a Start Condition: Position is above 0.20. Make the Stop Condition: Position is above 0.50.

Written by Jon Hanks

Figure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan CartFigure 2: Motion of Fan Cart

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Procedure – Fan Cart

1. Position the back of the fan cart at the 15 cm mark

2. Make sure the fan speed is on the Medium setting. Press the power button to start the fan, but hold on to the cart to keep it at the 15 cm mark.

3. Start recording data, and then release the cart. There will not be any data plotted on the graph until the cart has reached the 20 cm mark due to the start condition. This allows the cart to start moving before actual data collection begins, and gives a better looking graph. You can stop recording anytime you wish, but there is also a stop condition built-in that will stop recording before the cart reaches the bumper.

4. You can delete unwanted runs using the Delete Run feature in the Control Palette at the bottom. Get a single good run of position versus time data, and then rename this run “Fan Cart”.

5. For your position graph of the Fan Cart, how does the slope vary during the run? Was this constant velocity?

Velocity Graph

6. Use the same Start Condition but change the Stop Condition to Position above 0.70.

7. In the graph, click on the Add a Plot Area tool in the toolbar. On the second plot area below the Position plot, select Velocity on the vertical axis.

8. Click on the position graph to make that graph active, then select the Slope tool from the graph tool palette.

9. Move the slope tool to 0.2 seconds on the graph.

10. What is the slope at this point (including units)?

11. How does this compare to the speed on the velocity graph for this same time?

12. Repeat for 0.4 s and 0.6 s.

Written by Jon Hanks

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Constant Acceleration

If v(t) is a function that describes the velocity of an object as a function of time, then the acceleration of the object is given by a(t) = dv/dt, the first derivative of the velocity function. Graphically, the acceleration is the slope of the velocity graph.

1. Make a velocity vs. time graph. For your velocity graph of the Fan Cart, how does the slope vary during the run?

2. Select a linear Curve Fit from the graph Tool palette.

3. What is the physical meaning of the slope? Does it have units?

4. How linear is your data? Was this truly constant acceleration?

5. What is the physical meaning of the y-intercept on the graph? Does it have units?

Fan Cart with Short Pulse: Non-Constant Acceleration

1. Remove the Start Condition and keep the Stop Condition as before.

2. On the fan cart, press the Pulse Duration button as shown in Figure 5. With the "1s" LED lit, the fan will run for 1 second and then turn off. When you press the Power Button, there is a 2 second delay before the fan turns on.

3. Press the Power Button, and immediately start recording data. You can stop recording anytime you wish, but there is also a stop condition built-in that will stop recording before the cart reaches the bumper.

4. Get a single good run of velocity versus time data, and then rename this run “Fan Pulsed”.

Written by Jon Hanks

Figure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of PulseFigure 5. Setting Time of Pulse

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Velocity Analysis

5. Label the points on the graph where the acceleration of the cart was zero.

6. Label the points on the graph where the acceleration of the cart was constant, but not zero.

7. How do these points coincide with where the fan was on?

8. Use the Area tool in the graph tool palette to calculate the area under the velocity vs. time graph. What is the physical meaning of the area? What are the units?

9. From the shape of the velocity vs. time graph, predict the shape of the position vs. time graph.

Position Analysis

10. Make a Position versus Time graph.

11. Did you correctly predict the shape of the position vs. time graph?

12. Can you identify the points on the graph where the fan turned on and off?

13. Use the Coordinates tool (from the graph tool palette) to measure the last position data point. How does that point correspond to the area you took on the previous page?

14. When the Coordinates tool has been selected, you can right click on the cursor (on the graph) to activate the Delta tool. Using the Delta tool, measure the total displacement of the cart. How does this value correspond to the area you took on the previous page?

Written by Jon Hanks