Dr. AH Tabrizi (Online COVID-19 version) Engineering Processes & Tools (Engr. 10) Laboratory Experiment Dynamics of Gravity Powered Cars In this lab speed and acceleration of several cars are measured...

I need the calculations of the velocity in the lab


Dr. AH Tabrizi (Online COVID-19 version) Engineering Processes & Tools (Engr. 10) Laboratory Experiment Dynamics of Gravity Powered Cars In this lab speed and acceleration of several cars are measured and also calculated using a mathematical model based on energy balance. The cars start from rest on a race track at some height and coast down the track picking up speed. Sensors measure the speed of the cars at various points along the track and the total time lapse at the end of the run. Also, the drag force on the cars at some speeds is measured in a wind tunnel. To model the dynamics of the cars using energy principles we need to identify all the possible energy quantities that are at work in this problem, e.g. potential, kinetics, friction, drag, etc. The calculated speed should be compared to the measured value and discrepancies are noted and justified. The learning outcomes of this lab are: 1. Learn how to set up an experiment and collect data 2. Learn how to foresee potential problems in measurement 3. Learn how to create a mathematical model appropriate to the experiment being conducted 4. Learn how to post-process the collected information, i.e. perform comparison and evaluation of the experimental and mathematical data Please refer to the information provided in the lab for the particulars of the experiment. Test Procedure: 1. Get familiar with your team members. 2. Weigh your racecar using the electronic balance provided. See the given data below. 3. Measure all the dimensions of your car. See the given data below. 4. Take photos of your car from various angles as well as the measuring tools used. Write down the accuracy of the measurements. See the given picture below. 5. Measure the length of the track, release height of the car, and the slope of the track. See the given data below. 6. Place your car on the track, release it, and write down the total time lapse. IGNORE this item. Dr. AH Tabrizi (Online COVID-19 version) 7. Place your car on the track and place the photo-gate system at the pre-marked locations. Release your car and record the velocity of your car at the photo-gate location. Make sure you measure the distance traveled to the photo-gate. Refer to the lab discussion. 8. Repeat part 7 for various distances along the track as marked. 9. Place your car on the section of the track that is horizontal and using the force sensor push on the car gently until the car moves. Record this force, which is the rolling friction force. Refer to the lab discussion and use the data given below. 10. Place your car in the wind tunnel and run the tunnel at the airspeeds of about 30 and 20 mph. Record the drag force as well as the front and back lift force on the car. The lift forces will not be used in computation but they could allow for some discussions. Using these drag forces you will calculate the velocity of your car at various locations along the track. Note that you have already measured velocities at these locations so hopefully your calculations and the measurement will compare favorably. Refer to the lab discussion and use the data given below. 11. Write a report to document your work. You need to make calculations of your car’s velocity using the energy equations and data obtained. Compare your calculated velocities with the measured values and discuss discrepancies. Note on the Written Report: You should use the report template posted online. You may include pictures, graphs, tables, etc. as appropriate. Make sure all your dimensions are accurate. Please remember that you are communicating with your customer (or your company’s official) so make sure your report is properly done! Table 1. Data for the car experiment Car mass (kg) Friction force (N) Drag force (N) Distance between stations (m) Number of stations Car Material Track Material 0.5 0.02 7.5 1.5 10 Steel Aluminum 1 0.025 7.5 1.5 10 Steel Aluminum 2 0.03 7.5 1.5 10 Steel Aluminum 4 0.035 7.5 1.5 10 Steel Aluminum Dr. AH Tabrizi (Online COVID-19 version) Table 2: Station heights from the floor for the car experiment Station 1 Height 170 mm Station 2 Height 150 mm Station 3 Height 110 mm Station 4 Height 80 mm Station 5 Height 60 mm Station 6 Height 40 mm Station 7 Height 20 mm Station 8 Height 10 mm Station 9 Height 0 mm Station 10 Height 0 mm Slide 1 * Potential Energy Kinetic Energy Frictional Losses Aerodynamic Losses Images from: highlandtoday.com, ag-derby-cars.com, derbytalk.com * * Weight (use electronic scale) Dimensions (use caliper and ruler) Start Height (use measuring tape) Time of Travel (use stop watch etc.) Speed (measure at 4 places using photo-gates) * Friction Body Shape (why?) Release Height Weight Any other? * Error in Measurement Human Factors Inaccuracies in Mathematical Model Error in Computation * Let’s do some calculations to see if we could predict the car speed from the measured data * List the computed values and discuss * 2 (J) m = mass of object (kg) g = gravitational acceleration (9.81 m/s ) h = height of object (m) PEmgh = 2 1 (J) 2 v = velocity of object (m/s) KEmv = . d (J) f = rolling friction of wheel (m) - 0.00 027 for plastic on steel w = force on the surface (wheel weight + external force) (N) R = radius of wheel (m) d = distance traveled w FEf R = d (J) F = Friction force (measured using force gauge) d = distance traveled f f FEF = 2 2 3 1 (N) 2 C = Drag Coefficient A = Projected Frontal area (m) v = velocity (m/s) = Air density (kg/m) dd d FCAv r r = : Wind tunnel measurement (gram) = F * g/1000 (N) d F F 2 2 1 (N) 2 C = 1 2 Measured in wind tunnel v = Wind tunnel air speed dd d d d FCAv F Av F r r = = 2 ** 1 ** 2 distance traveled (meter) mass (kg) car height (meter) car velocity (m/s) & friction force (Newton) df df df PEKEFdFd mghmvFdFd d m h v FF =++ =++ = = = = =