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Lab Report 3 Report by: student Purpose Lab 3A: For this lab we conducted an experiment that demonstrated graphs of motion and determining how the position correlates to time on a position versus time graph. The purpose of the lab was to graphically and mathematically understand how a position versus time graph behave based on a specific velocity, position, and time. Lab 3B: For this next test we conducted an experiment that demonstrated graphs of motion and determining how the velocity correlates to time on a velocity versus time graph. The purpose of the lab was to graphically and mathematically understand how a velocity versus time graph behave based on a specific velocity, position, time, and acceleration. Lab 3C: For this lab we conducted an experiment timing the distance it takes to reach the bottom of the incline plane calculating the instantaneous speed to find average velocity. The purpose of this experiment is to measure the average speed of an object over a decreasing distance and to capture the average speed to find the instantaneous speed. Lab 3D: For this lab we conducted an experiment measuring the acceleration on an inclined plane. We lowered the inclined plane after each measurement was taken starting the cart off at the midpoint. The purpose of this experiment was ultimately to use the slope off of the cart’s acceleration versus sin(θ) graph to find acceleration due to gravity and compare the results to the theoretical value. Apparatus Part A: • PASCO Interface (for one sensor) • Motion Sensor • Reflector board • Data Studio Part B • PASCO Interface (for one sensor) • Motion Sensor • Reflector Board • Data Studio Part C • PASCO Interface (for two sensors) • IDS Photogates and Fences • 2.2 m Dynamics Track • Dynamics Cart • Meter Stick • Data Studio Part D • PASCO Interface (for one sensor) • Acceleration Sensor • Angle Indicator • 2.2 m Dynamics Track • Dynamics Cart • Large Rod Base and 45-cm Rod • Data Studio Theory Part A: While observing a position vs time graph we are studying a few things. We are able to determine how far an object traveled, along with how long It took to get that far. Plus, you are able to identify the velocity it was traveling. In order to find velocity, you can calculate it by taking the slope of the line, which is determined by the simple formula ???????? = ∆????????(?) ∆????(?) Part B: While observing a velocity vs time graph we are studying a few things. We are able to determine how fast an object was moving, along with how long It took to get that far. Plus, you are able to identify the acceleration and position. In order to find acceleration, you can calculate it by taking the slope of the line, and you can calculate distance by taking the area under the line. They are determined by the formulas. ????????????(?/?2) = ∆????????(?) ∆????(?) Part C: As the cart goes down the incline plane to zero we find the average velocity, by finding the average distance it takes over the average time it takes to reach the bottom. ???????? = ∆????????(?) ∆????(?) Part D: After each trial, we used data studio to measure acceleration to show how it relates to gsin(θ). We then calculated acceleration with the use of the slope off of the cart’s acceleration versus sin(θ) graph to find acceleration due to gravity. We then compared the experimental value of acceleration due to gravity on an inclined plane with the theoretical value of acceleration due to gravity to find percent error. 1. a=gsin(θ) 2. percent difference=| ????????????−?ℎ????????? ?ℎ????????? |x 100% Procedure Part A: First, gather all materials—PASCO interface, motion sensor and reflector board. Open up data studio and click the file “04 Position_Time.ds”. After gathering materials and setting up the DataStudio an example of distance versus time graph will pop up for you to follow. Place the motion sensor aimed at mid-section and hold board steadily in front of you. The program will give you three seconds before recording data and provides a pointer that moves up and down depending on the movement in front of the sensor. This will automatically stop recording data after 10 seconds. Use the reflector board and stand in front of the PASCO sensor while moving forward and backward in an attempt to replicate the graph using the appropriate motion. To delete the previous trials off of the graph, click experiment and delete all data runs. You should attempt this until you get as close as possible to the original graph. Part B: First, gather all materials—PASCO interface, motion sensor and reflector board. Open up data studio and click the file “04BVelocity_Time.ds”. After gathering materials and setting up the DataStudio, an example velocity versus time graph will appear for you to follow. Similar to part A, place the motion sensor aimed at your mid-section and hold the board steadily in front of you. The program will give you three seconds before recording data and provides a pointer that moves up and down depending on the movement in front of the sensor. This will automatically stop recording data after 10 seconds. Use the reflector board and stand in front of the PASCO sensor while moving forward and backward in an attempt to replicate the graph using the appropriate motion. To delete the previous trials off of the graph, click experiment and delete all data runs. You should attempt this until you get as close as possible to the original graph. Part C: First, gather all materials—PASCO Interface for two sensors, IDS photogates and fences, 2.2 m Dynamics track, dynamics cart and a meter stick. Open up Data Studio and click the file “05AverageSpeed.ds.” This should open up graphs of Average Speed versus Distance as well as a table display of distance, time between gates, and average speed. After gathering materials and setting up the ramp and PASCO interface, you first have to measure different points on the ramp. Find a midpoint on the ramp and set up the each interface 40 cm away from the midpoint on opposite sides. Before you start the experiment, make sure to put the five pattern picket fence, solid band side up, onto the cart. Then, adjust the heights of the two photogates so the beams are blocked as the cart moves down the track. Also, be sure the distance between the two photogates matches the first distance located in the Distance table. After you put the cart on the ramp and start the timer, keep the timer remaining continuous throughout the entire experiment. After the cart reaches the bottom of the ramp, save each trial onto the data table, and move the interface 5 cm in on both sides and reattempt the experiment to capture the time it takes to go through each interface as it approaches a distance of zero. Part D: First, gather all materials—PASCO Interface, acceleration sensor, angle indicator, 2.2 m Dynamics track, dynamics cart and large rod base and 45 cm rod. Open up Data Studio and click the file “10gsintheta.ds.” This should open up graphs of Acceleration versus Time and Acceleration versus ‘sin(theta)’, along with a data table provided. After gathering materials, setting up the PASCO interface, placing ramp at 20 cm high, and mounting the angle indicator onto the raised end of the track, we then attached the acceleration sensor to the cart, switching the setting to slow. We then put a mark where our midpoint was located, which was also our starting point. Before letting go of the cart on each trial, we used the angle indicator to help us calculate the sine of the angle, as well as making sure to zero out the sensor by pressing ‘TARE’. We pressed start each time we let go of the cart and stop after the cart reached the bottom of the track. After recording the data, we repeated the procedure using new heights. For each trial, we lowered the ramp 4 cm, until the ramp reached a height of only 4 cm, which was our stopping point. Data Tables Part C: Trial Distance “D” m Average Speed (m/s) 1 0.80 0.712 2 0.70 0.73 3 0.60 0.708 4 0.50 0.715 5 0.40 0.719 6 0.30 0.71 7 0.20 0.722 8 0.10 0.778 Part D: Analysis of Data In lab 3A and 3C, the equation below is used to find the slope of the line to find velocity. The slope of the graph in part C was -0.047 according to data studio. ???????? = ∆????????(?) ∆????(?) Ex: 0.719−0.715 0.4−0.5 = −0.04 In lab 3D, we used the equation, a=gsin(θ), to calculate the theoretical acceleration values and then plugged the answer into the equation, percent difference=| ????????????−?ℎ????????? ?ℎ????????? |x 100%, to find the percent difference between theoretical and experimental values. The remaining theoretical values are 0.85 for all sin(5) and 0.59 for sin(3.5). The remaining percent differences not including run one are 5.88, 17.65, and 50.5. Ex: a=gsin(θ) A=(9.8)(sin(5)) A=(9.8)(0.0872) A= 0.85 Ex 2: % difference=| ????????????−?ℎ????????? ?ℎ????????? |x 100%, % difference=| 1.1−0.85 0.85 |x 100% % difference= 29.4% During a lab experiment, there will always be experimental uncertainties. For this lab in particular, a lot of the experimental uncertainties probably have to do with human error. There was one person hitting stop and start while the other was pushing the cart. The student pressing the start and stop button could have a delayed reaction and stop/start it too early or too late. This also applies to the student letting go of the cart, as they could have released it too delayed or early. Another one of our experimental errors had to do with the actual equipment we were using. In lab 3D, after multiple attempts of graphing results not being accurate, we called the teacher over to see what we could have been doing wrong.