Mass and Force

1. Mass and Force

2. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

3. Mass • SI unit kg • Weight is a force, unit N • Mass is involved in multiple engineering principles! What is the mass of your calculator? How about its weight on Earth? And on Mars?

4. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

5. Density • Density=mass/volume • SI units Kg/m3 • US units slugs/ft3 [ρ] = M/L3 • Important in e.g. material selection • Note: Density can change due to e.g. temperature and pressure Which one of these three materials would you choose for a part (size 0.001m3) of an airplane interior decor? How about as a counter weight for an elevator?

6. Lava Lamp Example http://www.youtube.com/watch?v=DL3Ez9bxMTo&feature=related How does the lava lamp work?

7. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

8. Mass Flow • Mass flow = mass/time • m’ = dm/dt = Δm/Δt • m’ units Kg/sec (SI) slugs/sec (US) • Volume flow = volume/time • V’ = dV/dt = ΔV/Δt • V’ units m3/sec ft3/sec • m’ = dm/dt = ρdV/dt = ρV’

9. M’ m’ • V’ v’ • For an incompressible fluid, M’ = m’ • V’ = v’ • Therefore velocity is greater in narrow pipe and slower in fat pipe.

10. Volume or mass flow? • Depends on application • Volume flow preferred • when filling a tank of a specific volume with liquids of different densities • when a process can accept only a limited volume at a time • Mass flow preferred • in chemical reactions, where the number of reactant molecules (mass) is important • when measuring gas flow • When goods sold based on weight

11. Mass Flow - Task Estimate the mass flow of a gas pump. Density of regular gasoline is 720 kg/m3.

12. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

13. Mass Moment of Inertia m2 r2 • Measure of how hard it is to rotate something with respect to the center of rotation, or resistance to rate of change of rotation • For a single mass particle: • For a system of mass particles: z-axes r m

14. Mass moment of inertia - example Which one of the following object is harder to rotate around the z-axes? Both are made of steel (r=7860 kg/m3). z-axis R=5 cm h1=30 cm Ø=20 cm h1=4 cm

15. How are these related to mass moment of inertia? flywheel

16. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

17. Momentum • Momentum p (or L) • p = mv L = mv • Momentum is directional • Velocity (a component of momentum) is directional

18. Momentum - Example www.aerospaceweb.org/question/investigations/columbia/foam-impact.jpg Investigators into the Columbia accident have estimated that the dislodged foam was about 48 x 29 x 14 cm (19 x 11.5 x 5.5 in) , weighed about 0.75 kg (1.7 lb) and impacted the Shuttle at nearly 850 km/h (530 mph). For the sake of a rough comparison, this block of foam would be about the same size and weight as a large loaf of bread. (www.aerospaceweb.org/question/investigations/q0131.shtml) p (or L) = mv = 0.75kg * 850,000m/3600s = 177 kg m/s Same momentum as a 5 kg (11 lb) brick hitting you driving 127.5km/h (80mph) !

19. Momentum - Task • Which has greater momentum? • An Olympic 100m runner at speed 10 m/s • A 1000kg car pulling out of a parking lot at 2 km/h

20. Mass and Weight • Mass - scalar (SI unit kg) • Weight – vector, it’s force (SI unit N)

21. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

22. Basics • Force is the interaction of two objects, typically one pushes or pulls the other • Direct contact: you pulling a door open • No direct contact: gravity pulling you toward the center of the earth • Force causes objects to move, lengthen, shorten, twist, bend, etc. • SI Unit: Newton [F]=N • F=ma  N=kg·m/s2 • U.S. Customary unit: pound force lbf • F=ma  lbf = 1slug·ft/s2 (1lbf=4.448 N)

23. Applications

24. Force is a vector quantity(on whiteboard) F1 F2

25. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

26. Spring Forces www.motorsportscenter.com/uploads/suspension.jpg www.pleasanthillgrain.com/bag_clip_bag_clips_stainless.asp http://rclsgi.eng.ohio-state.edu/~gnwashin/me481/mech_sys.html www.pharma-pen.com • Springs widely used in engineering • Store energy • Return to original position • Dampen vibration • Spring types: • Linear, torsional

27. Hooke’s law • Applicable in the elastic range of the spring • Elastic means there is no permanent deformation after the force is removed F = applied force (N) k = spring constant (N/mm, N/m) x = deformation of the spring (mm, m) x F

28. Whiteboard example • A compression spring is 10 cm long when no force is applied. When a force is applied, the deformed length is 8 cm. The spring has a spring constant of 10 N/m. Calculated the applied force.

29. Determining the spring constant • In-class task: determine the spring constant of one of the scales in the back of the room • Plot your data in Excel, explain all the steps you take • Prepare to present in front of the class • See EF example 10.1 for help F = applied force (N) k = spring constant (N/mm, N/m) x = deformation of the spring (mm, m)

30. Homework and Teardown • Homework – due Thursday 04/01 before the class • From the course book: 9.5 (10p), 9.6 (less than 1 page typed)(20p), 9.12 (10p), and 9.23 (10p) • Look for (broken) products to take apart later • good product will replace one bad assignment grade • Bring products early!

31. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

32. Friction Forces www.garageboy.com www.respo.net/respo_school/respo_school_006/pics/pour_oil_01.jpg • “Frictionless” systems, commonly used in physics, do not really exist • Friction can be useful • Types of friction: • Dry friction • Static friction • Dynamic (kinetic) friction • Viscous friction (fluid friction)

33. Applied force and friction Maximum static friction force Friction force (N) Dynamic friction force Applied force (N)

34. Whiteboard Example • The static coefficient of friction between an object and a horizontal surface is 0.85. The object’s mass is 0.550 kg. If the object is pushed on the surface (force horizontal) of 5N, will the object move?

35. Friction In-Class Task How would you calculate the static coefficient of frictionof your calculator starting to slide on your course book?

36. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

37. Free body diagrams • Free body diagram shows all external forces acting on the body. • Commonly used in statics, dynamics, and mechanics of materials • Steps to draw the free body diagram • Make a simplified drawing of the body in question • Draw all force vectors acting on it • Do not forget weight, unless gravitational forces are ignored • Label all forces • Define fore coordinate system

38. Practice (white board) • Steps to draw the free body diagram • Make a simplified drawing of the body in question • Draw all force vectors acting on it • Do not forget weight, unless gravitational forces are ignored • Label all forces • Define fore coordinate system

39. In-class task • Draw a free body diagram for the two pipes in a v-shaped channel. 40 20

40. Newton’s Laws • Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it • For every action there is an equal and oppositereaction

41. Newton’s Laws • Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it This also applies to an object in rest – they will not move unless acted upon by an unbalanced force Remember what happened to the cannon ball in both x and y-directions? 11m v0 vy0 a vx0 1.5m a 100m

42. Newton’s Laws • , Notice the relation between the magnitudes and directions of F and a! m

43. Newton’s Laws • , m

44. Newton’s Laws • S • s • For every action there is an equal and oppositereaction Both the magnitude and direction of the two forces are equal N m Why are the absolute value signs on N and g, not mg or m? mg

45. Force Basics - revisited • Force is the interaction of two objects, typically one pushes or pulls the other • Direct contact: you pulling a door (from the handle) open  the door pulling the handle so it does not come off • No direct contact: gravity pulling you toward the center of the earth  the surface of the earth (pavement?) pushing you so you do not sink in the earth

46. Team Assignment – Due Tue 4/7 8:00 am • Problem/Design project: • Design a mass-spring system that can be taken to Mars to measure the acceleration due to gravity at the surface of Mars. • Explain the basis of your design • The governing equations & law’s of physics and how they relate to your design • Decisions on materials, components, attachment methods or working principle • Decisions that relate to the ability to take it to Mars • Include a drawing of your design • Include rough dimensions • Include a parts list. The level of detail can be “spring, glue, screw, metal plate”, so no need to find the actual part numbers and exact materials for the components. • Explain how your design should be calibrated and used • No need to build the system. • Hand in a report including equations and figures. The length can be anything from 2-4 pages typed. The length will not be graded. Only content is graded. Max 50p.

47. Assignment • Individual assignment (=homework) • Due Thu 4/9 8:00am • Problems: • 10.11, 10.15, 10.19, 10.21, 10.22 (10p each) • Follow format in course book EF chapter 4

48. Reminders • Look for (broken) products to take apart later • good product will replace one bad assignment grade

49. Agenda • Mass • Mass • Density • Mass Flow • Mass Moment of Inertia • Momentum • Force • Force basics and applications • Spring forces • Friction forces • Newton’s laws • Pressure

50. Newton’s Law - Application F Free Body Diagram: FBX FA FBY • Equilibrium of forces and moments F System: If F is 50N, what is FA+ FB, why?