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Impulse Lab 7 In this experiment you will verify the relationship between force and momentum through impulse. Using the short spring adapter, the iOlab will measure force as a function of time, as well as the velocity before and after, a collision. (1) (2) (3) Demonstration Video https://www.youtube.com/watch?v=ELLk7WrYuHg 1. Attach the hook to your iOlab. We will now measure the actual mass of the device. We will do this by picking the mass up and holding it steady, then measuring the applied force on the object as it balances out gravity. m Part 1 – Finding Mass of iOLab (skip if you have done this in previous experiments) 2. As always, first Calibrate both the accelerometer and the force sensor. 3. Choose the Accelerometer Sensor and select Ay. 4. Select the Force Sensor. 5. Click Record, then pick up the device, hold it for a second or two, then set it back down and stop recording. 6. Zoom in on the constant non-zero applied force after you have picked up the mass and before you set it down. 7. After zooming in, highlight a section of the graph. Your graphs should now look like... ...this. 8. Write down the average acceleration As your object is at rest, your device is directly measuring the acceleration due to gravity and not the actual acceleration. 9. Write down the average force. 10. Now calculate the actual mass of the device by... Include this value in your report. Part 2 – Impulse 1. Attach the short spring to your iOlab. 2. As always, first Calibrate both the accelerometer and the force sensor. 3. Choose the Wheel Sensor and select Velocity only. 4. Select the Force Sensor. 5. Find a smooth surface and somewhat sturdy object for your iOLab to collide with such as the iOLab box or your phone. 6. Practice pushing (wheels down) your iOLab into the box and allowing it to recoil. You do not want to push the device so hard that it may damage the device (or your wall). You want to make sure that there is time after your push before the collision to measure the velocity. 7. Click Record. Push the object into the wall and allow it to recoil. Repeat this process a total of three times. Stop recording. Your graphs should look like the graph below. Include a screen grab of your results in your report. 8. Next, zoom into one of the peaks. Your Force versus time, and velocity versus time, graphs should look as follows. 9. Create a table as below to collect the important date from the experiment. Include this table in your report. 10. Calculate the area under the Force versus time graph (J1). Place it in the table below under Trail 1. Include a screen grab of your graph in your report. 11. Make a note of your approximate initial and final time associated with the collision and include them in your table. 12. Using your t values and area under the curve (J1), calculate the average force. 13. Indicate the initial and final velocity of the collision in your table. As impulse is the change in momentum, which is a vector, direction matters (indicate positive/negative sign). Include a screen grab of your graph in your report. 14. As momentum is defined as p = mv, calculate the change in momentum (J2). 15. As you have now calculated impulse two separate ways, calculate the percent difference between the measurements. 16. Zoom out and repeat steps #8-15 for the remaining two collisions. Include their data under Trial 2 and 3 your table. 14. Discuss your results with your lab partners. Were your Impulse values close? What were sources of uncertainty? What could you have done differently in your experiment/analysis to improve your results. Extended Questions 15. 16. Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Slide 23 Slide 24 Centripetal Motion Lab 8 ω ac = ω2 r r Consider an object rotating at angular velocity ω. The centripetal acceleration at distance r from the rotation axis (here the center of the object) is given as ac = ω2 r. ω ac ax ay ac2=ax2+ay2 Just like any vector, ac can be decomposed into x and y components. ω ac = ω2 r r Accelerometer – measures the acceleration. Gyroscope – measures the angular velocity. r ω As the accelerometer is offset from the gyroscope by a distance r... ω ac ax ay As the accelerometer is offset from the gyroscope by a distance r, by measuring the centripetal acceleration and angular speed, you will verify this distance dynamically. ac = ω2 r Centripetal Acceleration 1. Say something nice to your lab partners. 2. As always, first Calibrate both the accelerometer and the force sensor. 3. Choose the Accelerometer, and select only Ax and Ay. 4. Select the Gyroscope, and select only ωz. 5. Find a smooth surface to spin your device on. 6. Practice spinning your iOLab (wheels up) on a surface. 7. Select Record, then spin your iOLab on the floor (wheels up) and allow the iOLab to come to rest. Repeat this step four more times. Stop collecting data. ***Here the object is rotated clockwise, hence ω is negative. You may rotate your iOLab either direction. 8. Zoom into one of the spins, they should look like below***. The areas highlighted correspond to your rotation. While the relationship between centripetal acceleration and angular velocity, is consistent throughout, we will choose the time right after your influence when the angular velocity is at a maximum. 9. Note the maximum angular velocity. Place your data in a table like the one below. 10. Note the corresponding x- and y-components of the centripetal acceleration. Place your data in a table like the one below. Table 1 Table 1 9. Note the maximum angular velocity. Place your data in a table like the one below. 10. Note the corresponding x- and y-components of the centripetal acceleration. Place your data in a table like the one below. Table 2 ac = ω2 r 11. Repeat steps 9 and 10 for the remaining spins and dill in Table 1. 12. As the relationship between centripetal acceleration and angular velocity is by graphing angular acceleration (y-axis) versus angular velocity squared (x-axis) you retrieve the distance between the accelerometer and gyroscope r as the slope. Use a spreadsheet program (Excel/Google Sheets/etc.) to create such a graph. Use XY-Scatter (i.e. no connecting line between the points) for the data, and then use a linear fit. Include a copy of this graph and Table 2 in your report. 13. Record the slope of your graph as the experimental distance rexp. y = ms x + b ac2=ax2+ay2 r 14. Using a ruler, measure the actual distance between the accelerometer and the gyroscope ract. 15. Calculate the percent error between the actual distance and the experimental value. 16. Compare your experimental value of rexp and your percent difference with your your lab partners. 16. What force (and corresponding torque) causes your iOLab to come to rest after you release the object? 17. How could you use the data you took to calculate the corresponding angular acceleration (deceleration) to 16? Bonus: What additional measurements/information would you need to calculate the moment of inertia of the iOLab device from this experiment? Extended Questions Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12