1. Created by the Faculty of the Mechanical Engineering Department in the Kate Gleason College of Engineering at RIT MECE 102: Engineering Mechanics Lab A First Year Course in Newtonian Mechanics, Experimentation, and Computer Tools

2. MECE-102 Course Grades Exam #1 Performance: Average Grade = 70%Max Grade = 100%

3. Week 7 Lecture Impulse and Momentum We will study: the impact of two carts moving along a horizontal path the tradeoff between Impulse and Momentum that occurs during the impact of the carts We will be using the Ultrasonic Transducer to determine distances travelled, velocities and momentums of the moving carts.

4. iCLICKER: The week 7 Lab Experiment studies the relationship between Impulse and Momentum of a system. Which one of the following is the definition of Impulse? Select your Answer: A.The distance integral of force. B.The time integral of force. C.The time derivative of acceleration. D.The time derivative of velocity. E.None of the above.

5. iCLICKER: The week 7 Lab Experiment studies the relationship between Impulse and Momentum of a system. Which one of the following is the definition of Impulse? Select your Answer: A.The distance integral of force. B.The time integral of force. C.The time derivative of acceleration. D.The time derivative of velocity. E.None of the above.

6. iCLICKER: Which of the following are units of Impulse? Select your Answer: A.[kg m/s] B.[kg m/s 2 ] C.[N s] D.[N m] E.None of the above

7. iCLICKER: Which of the following are units of Impulse? Select your Answer: A.[kg m/s] B.[kg m/s 2 ] C.[N s] D.[N m] E.None of the above

8. FORMULATE: State the Known Information Determine the speed of a vehicle with mass m 1 after its collision and attachment to a vehicle of mass m 2. Estimate the work done during the collision process by comparing the theoretical speed versus the observed speed of the combined vehicles, m 1 + m 2.

9. FORMULATE: Identify the Desired Information

10. iCLICKER: For our Week 7 experiment, which one of the following assumptions is FALSE? Select your Answer: A.Air resistance is negligible. B.Friction force is negligible. C.Mass of the system being analyzed is constant. D.Heat Transfer between the vehicles and track is negligible. E.Elastic Spring Energy is negligible.

11. iCLICKER: For our Week 7 experiment, which one of the following assumptions is FALSE? Select your Answer: A.Air resistance is negligible. B.Friction force is negligible. C.Mass of the system being analyzed is constant. D.Heat Transfer between the vehicles and track is negligible. E.Elastic Spring Energy is negligible.

12. FORMULATE: Identify Assumptions

13. Figure 7.1: Schematic Diagram of a first car colliding with and attaching to a second cart. CHART: Schematic Diagram

14. CHART: Free Body Diagrams

15. CHART: Data Tables Each row in the STATE TABLE corresponds to one unique position as the cart moves along the track. This Lab Experiment will analyze the impact of the two carts along a horizontal surface where we define our elevation datum, z = 0.

16. CHART: Data Tables The PROCESS Table describes the exchange of energy, work, heat, Impulse and Momentum as the system moves between states. For this experiment we are interested in the Impact “Process” which takes place starting at an initial state, i, and ending at a final state, f.

17. EXECUTE: Recall the Governing Equations

18. Newton’s 2 nd Law states the “The net external force acting upon a body is equal to the time rate of change of the linear momentum of the body.” Separating the differential and integrating between an initial time, t i, and a final time, t f gives:

19. EXECUTE: Recall the Governing Equations Recall that Impulse is defined as “The integral of force over time.” This generalized version of Newton’s 2 nd Law allows us to predict the motion of a system of interacting bodies.

20. iCLICKER: Based on the concepts of Impulse and Momentum from Week 7, we should expect that the velocity of cart 1 just prior to impact will be greater than the velocity of the combined carts after impact. Select your Answer: A.True B.False

21. iCLICKER: Based on the concepts of Impulse and Momentum from Week 7, we should expect that the velocity of cart 1 just prior to impact will be greater than the velocity of the combined carts after impact. Select your Answer: A.True B.False

22. EXECUTE: Recall the Governing Equations Analysis of the cart FBD’s confirms that action and reaction forces between the 2 carts are equal and opposite (Newton’s 3 rd Law). Applying the previous Assumptions to the analysis generates the following equations:

23. EXECUTE: Recall the Governing Equations Analysis of the Momentum equations associated with the initial mass m 1 and the final combined mass (m 1 + m 2 ) gives: Solving for the final velocity of the combined mass (m 1 + m 2 ) gives:

24. Consider the following Problem ………

26. Answer: m 2 = 7m 1

27. Figure 7.3: Apparatus and two body impact within the field of view of an ultrasonic transducer Lab Experiment Set-up

28. Now let’s talk about Asteroids … http://news.cnet.com/8301-11386_3-57564621-76/europes-space-agency-kicks-off- asteroid-collision-mission/

29. Homework Prior to LAB tomorrow Read section 7.2 of the textbook Watch LAB Videos Complete the on-line LAB quiz in myCourses Attempt to solve all assigned chapter problems in your logbook before RECITATION. WEEK 7 Problem Set: From Section 7.5: Problems 1, 10, 17, 18, 19 Lab Report is due Monday by 6pm! The Scribe must upload the LAB REPORT to the myCourses Dropbox.

30. Questions?

31. Consider the following Problem ………

32. Answer: m 2 = 3m 1