Velocity and Table
You have probably watched a ball roll off a table and strike the floor. What determines where it will land? In this experiment, you will roll a ball down a ramp and determine the ball’s initial velocity with a pair of photogates. You will use this information and your knowledge of vectors to predict where the ball will land. You will also learn how to determine percent difference between an expected value and measured value.
Measure the initial velocity of a ball using two photogates and computer software for timing. Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion. • Take into account trial-to-trial variations in the velocity measurement when calculating the impact point. MATERIALS Power Macintosh or Windows PC LabPro or Universal Lab Interface Logger Pro two Vernier photogates ball (1- to 5-cm diameter) masking tape ramp carbon paper plain paper meter stick. Set up an inclined tunnel made of paper on a table so that a ball can roll down it, across a short section of table, and off the table edge as shown in Figure 1.
Note: You do not need to make the ramp very high. A smaller gradient works better. Physics with Computers 1 Projectile Motion 2. Position the photogates so the ball rolls through each of the photogates while rolling on the horizontal table surface. Approximately center the detection line of each photogate on the middle of the ball. Connect photogate 1 to the DIG/SONIC 1 of the LabPro and photogate 2 to the corresponding second port. To prevent accidental movement of the photogates, use tape to secure them. 3. Mark a starting position on the ramp so that you can repeatedly roll the ball from the same place.
Roll the ball down the ramp through each photogate and off the table. 4. Do a few trial runs to make sure the ball does not hit either photogate. Reposition the photogates as necessary. Estimate the position on the floor that the ball hits. Once you are satisfied, anchor a piece of plain paper on the floor and position carbon paper on top of it such that after each run you can lift the carbon paper and measure the position of the mark left by the ball on the bottom paper. Now you are ready to begin the experiment. 5. Open the file in the Experiment 8 folder of Physics with Vernier.
A data table and two graphs are displayed; one graph will show the time required for the ball to pass through the photogates for each trial and the other will display the velocity of the object for each trial. 6. You must enter the distance, ? s, between photogates in order for Logger Pro to calculate the velocity. The program will divide this distance by the time interval ? t it measures to get the velocity (v = ? s/? t). Carefully measure the distance from the beam of photogate 1 to the beam of photogate 2. (It may be easier to measure from the leading edge of photogate 1 to the leading edge of photogate.
To successfully predict the impact point, you must enter an accurate measurement. Enter the distance into Logger Pro by selecting User Parameters from the Data menu, then clicking the gate_spacing tab. Change the number in the Distance Between Gates field to the correct distance in meters. Click . plumb bob floor origin Figure 2 7. Click . Check to see that the photogates are responding properly by moving your finger through photogate 1 and then photogate 2. Logger Pro will plot a time interval (? t) value for each instance you run your finger through photogate 1 or photogate 2.
Click , then click again, to clear the trial data and prepare for data collection. 8. Roll the ball from the start point you marked. Let it roll over the table and hit the floor. It will leave a mark on the paper under the carbon sheet. Take care not to bump any of the photogates, or your velocity data will not be precise. 9. Lift the carbon paper and measure the horizontal distance from the edge of the table to point of impact. Record it in your Data Table as dx (see example below) 10. Repeat step (8-9) for a total of 10 runs. You should have 10 entries for dx. Note: Do not click stop after each run.
Do so only after the tenth run or else you will lose all previous data. The ball may not land on the same spot each time but they should be close. Physics with Computers 2 Projectile Motion 11. After the last trial, click to end data collection. You will need to print out a copy of the graph velocity per trial and attach to your report. 12. Carefully measure the distance from the table top to the floor and record it as the vertical distance dy in the data table. There should be only one entry for this. 13. You should see 10 data points on the screen, one corresponding to each run.