Picket Fence Free Fall Lab

Experiment 5 Picket Fence Free Fall We say an object is in free fall when the only force acting on it is the Earth’s gravitational force. No other forces can be acting; in particular, air resistance must be either absent or so small as to be ignored. When the object in free fall is near the surface of the earth, the gravitational force on it is nearly constant. As a result, an object in free fall accelerates downward at a constant rate. This acceleration is usually represented with the symbol g. Physics students measure the acceleration due to gravity using a wide variety of timing methods. In this experiment, you will have the advantage of using a very precise timer connected to the computer and a Photogate. The Photogate has a beam of infrared light that travels from one side to the other. It can detect whenever this beam is blocked. You will drop a piece of clear plastic with evenly spaced black bars on it, called a Picket Fence. As the Picket Fence passes through the Photogate, the computer will measure the time from the leading edge of one bar blocking the beam until the leading edge of the next bar blocks the beam. This timing continues as all eight bars pass through the Photogate. From these measured times, the program will calculate the velocities and accelerations for this motion and graphs will be plotted. P ic ke t fence Figure 1 OBJECTIVE  Measure the acceleration of a freely falling body (g) to better than 0.5% precision using a Picket Fence and a Photogate. Experiment 5 MATERIALS computer Vernier computer interface Logger Pro Vernier Photogate Picket Fence clamp or ring stand to secure Photogate PRELIMINARY QUESTIONS 1. Inspect your Picket Fence. You will be dropping it through a Photogate to measure g. The distance, measured from one edge of a black band to the same edge of the next band, is 5.0 cm. What additional information will you need to determine the average speed of the Picket Fence as it moves through the Photogate? - You would need to know what the entire length of the picket fence is and how long it takes for your partner to pass the entire fence from one end to the other. You also need to know the slope of the picket fence and the photogate along with what the changes in velocity will be. 2. If an object is moving with constant acceleration, what is the shape of its velocity vs. time graph? - The object that is moving with a constant acceleration should be demonstrated as a linear line on a velocity vs. time graph. The slope of a graph such as this will be constant as well. 3. Does the initial velocity of an object have anything to do with its acceleration? For example, compared to dropping an object, if you throw it downward would the acceleration be different after you released it? - If an object has an initial velocity of zero its acceleration will start slow then speed up exponentially, so yes initial velocity does effect an objects acceleration. In the scenario of dropping an object toward the ground versus throwing it at the ground the acceleration would be the same as when throwing the ball due to the fact that slope is indepent of the distance vs. time graph. PROCEDURE 1. Fasten the Photogate rigidly to a ring stand so the arms extend horizontally, as shown in Figure 1. The entire length of the Picket Fence must be able to fall freely through the Photogate. To avoid damaging the Picket Fence, make sure it has a soft surface (such as a carpet) to land on. 2. Connect the Photogate to the DIG/SONIC 1 input of the Vernier computer interface. 3. Open the file “05 Picket Fence” in the Physics with Computers folder. 4. Observe the reading in the status bar of Logger Pro at the top of the screen. Block the Photogate with your hand; note that the GateState is shown as Blocked. Remove your hand and the display should change to Unblocked. 5. Click to prepare the Photogate. Hold the top of the Picket Fence and drop it through the Photogate, releasing it from your grasp completely before it enters the Photogate. Be Picket Fence Free Fall careful when releasing the Picket Fence. It must not touch the sides of the Photogate as it falls and it needs to remain vertical. Click to end data collection. 6. Examine your graphs. The slope of a velocity vs. time graph is a measure of acceleration. If the velocity graph is approximately a straight line of constant slope, the acceleration is constant. If the acceleration of your Picket Fence appears constant, fit a straight line to your data. To do this, click on the velocity graph once to select it, then click Analyze menu and select ‘Curve Fit’, select a linear fit, to fit the line: y = mt + b to the data. Record the slope in the data table. Do the same with the position versus time plot but fit with a quadratic. Record the two times the A-value for the quadratic fit in the data table along with twice it’s uncertainty. 7. To establish the reliability of your slope measurement, repeat Steps 5 and 6 five more times. Do not use drops in which the Picket Fence hits or misses the Photogate. Record the slope values in the data table. DATA TABLE Trial 1 2 3 4 5 6 Slope (m/s ) 9.623 9.744 10.08 9.560 9.706 9.734 uncertainty -.02026 2 -.01784 -.03136 -.004410 -.02354 -.02463 A value *2 9.638 9.746 10.04 9.552 9.708 9.746 Uncertainty*2 -.013634 -.015734 -.0243 -.003964 -.01234 -.013472 RESULTS TABLE 2 Acceleration (m/s ) Minimum Maximum Average Avg Dev 9.552 10.08 9.73975 0.02 Acceleration due to gravity, g Precision 9.80 ±± 0.02 m/s 2 0.2 % ANALYSIS 1. From your six trials, determine the minimum, maximum, and average values for the acceleration of the Picket Fence. Record them in the data table. -Completed as seen above. 2. Describe in words the shape of the position vs. time graph for the free fall. -The graph looks like the shape of the letter U, also known in algebraic terms as a purabola. 3. Describe in words the shape of the velocity vs. time graph. How is this related to the shape of the position vs. time graph? Experiment 5 -The velocity vs. time graph is a straight line. The slope of the distance vs. time graph at a point is equal to the velocity. 4. The average acceleration you determined represents a single best value, derived from all your measurements. The minimum and maximum values give an indication of how much the measurements can vary from trial to trial; that is, they indicate the precision of your measurement. One way of stating the precision is to take half of the difference between the minimum and maximum values and use the result as the uncertainty of the measurement. Check to see that this estimate of the uncertainty is roughly in agreement with your uncertainties from fitting the velocity or position. Express your final experimental result as the average value, ± the uncertainty. Round the uncertainty to just 3-4 digits and round the average value to the same decimal place. For example, if your minimum, average and 2 2 maximum values are 9.12, 9.93, and 10.84 m/s , express your result as g = 9.9 ± 0.9 m/s . Record your values in the data table - Completed above in the data table. 5. Express the uncertainty as a percentage of the acceleration. This is the precision of your experiment. Enter the value in your data table. Using the example numbers from the last step, the precision would be 6. Compare your measurement to the generally accepted value of g (from a textbook or other source). Does the accepted value fall within the range of your values? If so, your experiment agrees with the accepted value. - Our value does fall in the accurate range, because it falls below the 9 percent it is extremely accurate. 7. Inspect your velocity graph. How would the associated acceleration vs. time graph look? Sketch your prediction on paper. Now change the upper graph to acceleration vs. time. Do this by clicking on the y-axis label. Select Acceleration. Comment on any differences. You may want to rescale the graph so that the acceleration axis begins at zero. - Since the velocity graph is linear with a constant slope, the acceleration graph should be a constant function is a horizontal line above the time axis. Our data appears irregular. This is because the small variations in the timing measurement. When the acceleration vs. time graph is selected, it autoscales, magnifying these variations. When the origin is included on the vertical axis, the data appear consistent, as in the graph below. 8. Using the acceleration vs. time graph on the screen, click on the Statistics button, , to determine the average acceleration. How does this compare with the acceleration value for the same drop, determined from the slope of the velocity graph? - The trace values from our acceleration graph are around the value of the slope of the velocity graph.