05 Motion with Constant Acceleration Page 1 of 8 Motion with Constant Acceleration Introduction Position and velocity vs. time are graphed for a Smart Cart with a Smart Fan Accessory moving with constant acceleration along a dynamics track. Software tools are used to find velocities at various times, and to find the acceleration of the cart. Then the cart’s motion is studied for the case of non-constant acceleration. Figure 1: Experimental Setup Equipment Qt y Items Part Number 1 Smart Cart (Blue) ME-1241 1 Dynamics Track Feet (Pair) ME-8972 1 Dynamics Track Endstops (Only 1 needed) ME-8971 1 1.2m Starter Dynamics Track ME-9493 1 Smart Fan Accessory ME-1242 1 Elastic Bumper (Elastic & 1 pair brackets needed) ME-8998 Required, but not included: 1 PASCO Capstone software Written by Stuart Loucks
Transcript
05 Motion with Constant Acceleration Page 1 of 4
Motion with Constant Acceleration
Introduction
Position and velocity vs. time are graphed for a Smart Cart with a Smart Fan Accessory moving with constant acceleration along a dynamics track. Software tools are used to find velocities at various times, and to find the acceleration of the cart. Then the cart’s motion is studied for the case of non-constant acceleration.
Required, but not included:1 PASCO Capstone software
Setup
1. As illustrated in Figure 1, install the two Track Feet on the underside of the Dynamics Track. Install the fixed End Stop at one end of the track (see Figure 1), and an Elastic Bumper (see Figures 1 & 2) at the other end.
2. Turn on the Smart Cart, and then wirelessly connect it in Capstone. On the bottom toolbar, change the Position Sensor sample rate to 40 Hz.
3. In Capstone, create a graph of Position vs. Time.
4. Place the cart on the track near the end stop, and make sure the +x-direction (printed on the top of the Smart Cart) is pointing toward the far end of the track where the elastic bumper is.
Smart Fan Setup
1. Attach the Smart Fan Accessory to the Smart Cart so the fan is facing the end stop, as shown in Figure 3.
2. Plug the cable from the fan into the side of the cart.
3. Adjust the level of the track so that the cart is rolling slightly downhill away from the end stop, to compensate for frictional drag when the cart is moving in that direction. Give the cart a slight push away from the end stop. If it speeds up, the track is too steep.
4. Turn on the Smart Fan Accessory by pressing and holding its power button briefly. The fan cart is now in Standby mode. (If the fan comes on, press and hold to turn the power off, and try again.)
5. In Capstone, open the Smart Fan tool. Set the thrust to +50. Under advanced options: Click On, and the fan should come on. Then click Off. Enable Auto, which makes the fan automatically turn on when recording starts.
6. Close the Smart Fan tool.
7. Recording conditions: In Capstone, on the lower toolbar, open Recording Conditions. Create a Start Condition: Position is above 0.20. Create a Stop Condition: Position is above 0.50. With these settings, the fan automatically comes on when you click Record. However, data recording begins only when the cart has traveled 0.20 m (by which point the acceleration will be steady, making for a nicer graph), and ends when the cart is at 0.50 m (at which point the fan is turned off). You can adjust these Recording Conditions as needed to suit your experiment.
1. Make sure the cart is at rest by the end stop. Start recording. The fan should automatically turn on, accelerating the cart. When the cart reaches 0.50 m, the fan and recording should automatically stop. Repeat as needed until you get a smooth run. Use the Delete run button at the bottom toolbar if needed.
2. How does the slope of the position graph change during the run? Look very carefully. To help, you can try a linear curve fit and a quadratic curve fit to see which one best fits the data. What does this tell you about how the velocity was changing during the motion?
Velocity Graph
1. 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.
2. Measurements for Time = 0.2 s:
Click on the position graph to make that graph active. Select the Slope tool from the graph tool palette. Move the slope tool to 0.2 seconds on the graph. Record the slope at this point (including units).
Click on the velocity graph, and add a Coordinates/Delta tool. Move the tool to 0.2 seconds on this graph, and record the velocity. How does this compare slope of the position graph at this same time?
3. Repeat for 0.4 s and 0.6 s.
4. The velocity of the cart is equal to the rate of change of its position. On the graphs that means: At any time, the slope of the position graph is equal to the value of the velocity. How well does your data support this statement?
5.
Written by Stuart Loucks
05 Motion with Constant Acceleration Page 4 of 4
Acceleration
1. How does the slope of the velocity graph change during the run? Look very carefully.
2. Click on the velocity graph. Select a linear Curve Fit from the graph Tool palette. On the linear fit, the “r” value (the “correlation coefficient”) gives you a good idea of how close your data is to exactly linear. A nearly perfect line has r = 1.000. How linear is your data?
3. The acceleration of the cart is equal to the rate of change of its velocity. On the graphs, that means: At any time, the slope of the velocity graph should be equal to the value of the acceleration. Record the acceleration (slope of velocity graph), with units.
4. Based on the linear fit results, is the acceleration approximately constant?
5. What is the physical meaning of the y-intercept on this graph? Does it have units?
Non-Constant Acceleration
1. In Capstone, open the Smart Fan tool. Keep the thrust to +50. Under advanced options: Keep the Auto box checked. There should be no Start Condition. Add a Stop Condition, measurement based for Position above 0.4. This will make the fan shut off when the cart gets to 0.4 m.
2. Close the Smart Fan tool.
3. Recording conditions: In Capstone, on the lower toolbar, open Recording Conditions. Remove any Start Condition. Change the Stop Condition: Position is above 0.70. Now, when you click Record, it immediately begins recording data, and continues until the cart moves 0.70 m. You can adjust these Recording Conditions as needed.
4. Start with the cart at rest near the end stop. Record and get a single good run.
5. Notice that even though the fan turns on at 0 seconds, it takes some time to get the car moving and accelerating at a constant rate. On the velocity graph, use an Annotation from the toolbar, and label the point where the cart acceleration becomes constant. Explain your choice.
6. Also on the velocity graph, label the point where the fan shuts off. Explain your choice.
