Activity 425 Maximum Velocity and Acceleration：活动425的最大速度和加速度

Activity 425 Maximum Velocity and Acceleration：活动425的最大速度和加速度 Activity 4.2.5 – Maximum Velocity and Acceleration Introduction Velocity is a vector quantity as opposed to scalar quantities; vectors have both magnitude and direction. For example, + 10 miles/hour could indicate that a rocket is (ascending) traveling upward, parallel to the launch pad at 10 miles/hour; where -10 miles/hour could indicate that the rocket is descending at a rate of 10 miles/hour. Acceleration is a vector quantity. Accelerating or “speeding up” by convention is a positive quantity, whereas decelerating or “slowing down” is a negative quantity. This method is a theoretical calculation that ignores drag. Therefore, the calculations will not be entirely accurate (will differ than actual results depending on various experimental conditions) but should give a good indication of the velocity of the rocket. In this activity the equations have been simplified so the emphasis is on working with simple equations to determine velocity rather than using complicated mathematics. You will calculate the velocity of rockets that you and your team members have launched in previous activities and answer questions related to various model rocket engines and rocket performance. Even though mathematical calculations are required, the emphasis is on applying the formulas rather than developing a deep understanding of each formula. Engineers often use mathematical formulas from physics and tables of specifications to calculate values that describe physical phenomena. Equipment , Scientific Calculator (optional) , Computer , Excel spreadsheet program , Max Calc Excel file , Engine Specs Excel file Procedure In this activity, you will calculate the maximum velocity and maximum acceleration a model rocket will obtain during a launch using various size model rocket engines. The maximum velocity of a model rocket occurs at the moment just before the rocket engine’s propellant “burns out.” After the propellant is exhausted, the rocket Project Lead The Way, Inc. Copyright 2010 AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 1 continues to travel upward due to momentum (the coast phase); however, gravity is gradually slowing the rocket during its vertical assent. Eventually the force of gravity will return the rocket to earth. Smoke that is coming from the model engine during the coast phase is the tracking smoke; it is not smoke from burning propellant. Use the following formulas and the table of Model Rocket Engine Specifications found in Activity 4.2.5 Rocket Engine Specs.xls, which is used to calculate the maximum velocity and maximum acceleration of the flight of an Alpha model rocket with an A8-3 engine. This is the rocket and engine type that was flown earlier. Maximum Velocity ThrustAvgMaximumVelocity,(,1)(gravity)(time)WeightAvg TAvg,1)gtV,(WAvg V = Maximum velocity of the rocket TAvg = Average thrust of the rocket engine WAvg = Average weight of the rocket before launch and at the moment when the propellant is exhausted g = acceleration of gravity (32 ft./sec.2) or (9.8 m/s2) t = thrust duration of the engine The thrust duration of the engine can be obtained from the table of Model Rocket Engine Specifications. However, the average thrust of the rocket engine and the average weight of the rocket before launch and at the moment the propellant is exhausted must be calculated using the table of Model Rocket Engine Specifications and the weight of the rocket. Average Thrust, T Avg To calculate the average thrust of the rocket engine, T., use the Model Rocket Avg Engine Specifications and the following equation. TotalImpulse16oz.T ,xAvgThrustDuration1lb. This equation calculates the average thrust of the rocket engine and converts the thrust from ounces (oz.) to pounds (lb.). Average Weight, W Avg To calculate the average weight of the rocket before launch and at the moment when the propellant is exhausted, use the following equation, the weight of the rocket, and the Model Rocket Engine Specifications. Project Lead The Way, Inc. Copyright 2010 AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 2 rocketweightandengineweightpriortoliftoff，weightofrocketatmomentwhenpropellantisexhasedW,Avg.2 rocketweightandengineweightpriortoliftoff，(weightofrocketandengine,propellantweight),WAvg.2 Maximum Acceleration The acceleration of the rocket expressed in terms of the number of “g”s a rocket experiences is given by the following equation. (Note the acceleration equation is one of the factors in the maximum velocity equation above.) TAvgAcceleration,a,(,1) WAvg Calculations can be made in either English units or metric units. Remember to show units of measure in your calculations. In order to change parameters and to answer questions that require numerous routine calculations, engineers look for short cuts to save time. Using a spreadsheet program allows an inquirer to change conditions and view results instantaneously to answer questions. 1. Open the Excel spreadsheet file, Max Calc, to calculate the maximum velocity in feet/second and miles/hour and to calculate the g force of the maximum acceleration. For example, you will learn that if the velocity of the rocket is 3g, then the acceleration is three times as strong as gravity. 2. The rocket’s weight and required engine specifications can be found in the Excel spreadsheet file, Engine Specs. Use the spreadsheet to calculate the maximum velocity and acceleration for the Alpha model rocket with an A8-3 engine and compare the results with your calculations from Step 1. Note: The calculations made with a calculator and with a spreadsheet maybe slightly different due to rounding. 3. The following five engines are recommended for use with the Alpha model rocket: 1/2A6-2, A8-5, B4-4, B6-4, and C6-5. Use the spreadsheets Max Calc and Engine Specs, and the table of Model Rocket Engine Specifications to calculate the maximum velocity and maximum acceleration of the Alpha rocket for each of the five engines. 4. Compare maximum velocity and acceleration data for the five engines. Project Lead The Way, Inc. Copyright 2010 AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 3 5. Which engine provides the maximum velocity? 6. Which engine provides the maximum acceleration? 7. Does the engine that has the maximum velocity also have the maximum acceleration? If yes, give evidence. If no, provide an explanation. 8. The B8-5 engine is not recommended for use in the Alpha model rocket. Calculate the maximum velocity and maximum acceleration for the Alpha model rocket if a B8-5 engine were used. 9. Compare the results from the B8-5 engine and the engines that are recommended. 10. Provide reasons why the B8-5 engine is not recommended for use in the Alpha rocket. 11. Now go back and use your data to calculate your maximum velocity and acceleration for each launch of your rocket. (If you have not yet measured the mass - do so! Fill out the table below (add more columns if necessary. Launch # Maximum Velocity Maximum Acceleration 1 2 3 Project Lead The Way, Inc. Copyright 2010 AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 4 Conclusion 1. Print your spreadsheet data and compare your data with other groups. 2. Write a short summary of your results and implications for future model rocket flights. 3. Do you think your calculated values for velocity and acceleration are correct? Why or why not? 4. Why do you feel that model rocket manufactures state that no live payload should be used on a model rocket? Comment on this advisory using your data on velocity and acceleration. Be prepared to discuss results with the class. 5. Since the data generated by the spreadsheet neglects drag, are the calculations for maximum height and maximum velocity too large or too small? Explain your reasoning. Project Lead The Way, Inc. Copyright 2010 AE – Unit 4 – Lesson 4.2 – Activity 4.2.5 – Maximum Velocity and Acceleration – Page 5