1. Equilibrium and Elasticity Ch 12 (all)

2. Equilibrium An object is in equilibrium when: - The vector sum of all the external forces that act the body must be zero. F net = 0 - The vector sum of all the external torques that act on the body, measured about any possible point, must all be zero. T net = 0 Objects in Equilibrium: 1) A book resting on a table 2) A hockey puck sliding with constant velocity across a frictionless surface 3) The rotating blades of a ceiling fan 4) The wheel of a bicycle that is traveling along a straight path at constant speed An object is in static equilibrium if it follows the rules of equilibrium, and the linear momentum of the body must be zero. Objects in Static Equilibrium: 1) A book resting on a table An object is in equilibrium when: - The vector sum of all the external forces that act the body must be zero. F net = 0 - The vector sum of all the external torques that act on the body, measured about any possible point, must all be zero. T net = 0 Objects in Equilibrium: 1) A book resting on a table 2) A hockey puck sliding with constant velocity across a frictionless surface 3) The rotating blades of a ceiling fan 4) The wheel of a bicycle that is traveling along a straight path at constant speed An object is in static equilibrium if it follows the rules of equilibrium, and the linear momentum of the body must be zero. Objects in Static Equilibrium: 1) A book resting on a table

3. Center of Gravity The gravitational force F g on a body effectively acts at a single point, called he center of gravity (cog) of the body. If g is the same for all elements of a body, then the body’s cog is coincident with the body’s center of mass (com). The gravitational force F g on a body effectively acts at a single point, called he center of gravity (cog) of the body. If g is the same for all elements of a body, then the body’s cog is coincident with the body’s center of mass (com).

4. Elasticity All real “rigid” bodies are to some extent elastic, which means that we can change their dimensions slightly by pulling, pushing, twisting, or compressing them. A body is placed under eithe stress or strain, which are proportional to each other because stress=module x strain. All real “rigid” bodies are to some extent elastic, which means that we can change their dimensions slightly by pulling, pushing, twisting, or compressing them. A body is placed under eithe stress or strain, which are proportional to each other because stress=module x strain.

5. Tension and Compression For simple tension or compression, the stress on the object is defined as F/A, where F is the magnitude of the force applied perpendicularly to an area A on the object. The strain, or unit deformation, is then the dimensionless quantity ∆L/L, the fractional change in a length of the specimen. The modulus for tensile and compressive stresses is called the Young’s modulus and is represented in engineering practice by the symbol E. F/A = E ∆L/L For simple tension or compression, the stress on the object is defined as F/A, where F is the magnitude of the force applied perpendicularly to an area A on the object. The strain, or unit deformation, is then the dimensionless quantity ∆L/L, the fractional change in a length of the specimen. The modulus for tensile and compressive stresses is called the Young’s modulus and is represented in engineering practice by the symbol E. F/A = E ∆L/L

6. Shearing In the case of shearing, the stress is also a force per unit area, but the force vector lies in the plane of the area rather than perpendicular to it. The corresponding modulus, which is given the symbol G in engineering practice, is called the shear modulus. F/A = G ∆x/L In the case of shearing, the stress is also a force per unit area, but the force vector lies in the plane of the area rather than perpendicular to it. The corresponding modulus, which is given the symbol G in engineering practice, is called the shear modulus. F/A = G ∆x/L

7. Hydraulic Stress The stress is the fluid pressure p on the object, and pressure is a force per unit area. The strain is ∆V/V where V is the orginial volume of the specimen and ∆V is the absolute value of the change in the volume. The corresponding modulus, with symbol B, is called the bulk modulus of the material. p = B ∆V/V The stress is the fluid pressure p on the object, and pressure is a force per unit area. The strain is ∆V/V where V is the orginial volume of the specimen and ∆V is the absolute value of the change in the volume. The corresponding modulus, with symbol B, is called the bulk modulus of the material. p = B ∆V/V

8. 20 Questions

9. Which of the following is not a requirement for an object to be in equilibrium? A) linear momentum is constant B) energy is conserved C) angular momentum is constant  B) energy is conserved

10. Explain what each symbol in the formula p = B ∆V/V stands for and when this formula might be used Used to determine the hydraulic stress experienced by an object p = pressure B = the bulk modulus of the object ∆V = the change in volume from the force V = the original volume

11. Because forces are applied to the end points of a rod in opposite direction, the stress experienced is _______. Tension

12. A steel rod has a radius R of 9.5 mm and a length of 81 cm. A 62 kN force F stretches it along its length. What is the stress experienced by the rod? stress = F/A stress = F/ πR 2 stress =(6.2x10 4 )/ π(9.5x10 -3 ) stress = 2.2 x 10 8

13. To find the tension of T1,where would the best pivot point be? To find the tension of T1,where would the best pivot point be? A AB C T1

14. Which disks are in equilibrium? F FF 3F 2F F F F A B C B only

15. Which way will the seesaw tip? Towards B 5 kg3kg2 kg 1 m 2 m A B

16. Since the constant of proportionality is called a modulus of elasticity, stress equals… modulus x strain

17. The bending of a wave as it enters a new medium is called______: Refraction

18. Find the tension in T. The box has a mass of M and the bar has a mass of 3M. Find the tension in T. The box has a mass of M and the bar has a mass of 3M. t net = Fr T y = T (sinØ) M 1 r 1 + M 2 r 2 = T y r 3 M2d + 3M3d = T(sinØ) 6d 11/6 M = T(sinØ) T = 11M/6(sinØ) 2d 6d Ø

19. A 50 kg man is on one side of a seesaw and is 2 meters away from the pivot point, a 40 kg man wants to balance the force, how far from the pivot point should he stand? t 1 = t 2 x 1 m 1 g = x 2 m 2 g (2)(50)(9.8) = (x 2 )(40)(9.8) X 2 = 2.5

20. Find the tension in T2. (blue beam is mass less) Find the tension in T2. (blue beam is mass less) t net = RF t net =-(r1xmg)+(Fxr2) r1 x mg = F x r2 3 x 5 x 9.8 = F x 7 F = 21N 5kg T1T2 3m 4m Pivot Point

21. Is the center of mass near A, B, or C? Is the center of mass near A, B, or C? The center of gravity is closest to C. 5 kg 3kg 2 kg A B C

22. Which of the following are in equilibrium? A)A car accelerating B) A hockey puck at constant speed C) A book resting on a desk Which of the following are in equilibrium? A)A car accelerating B) A hockey puck at constant speed C) A book resting on a desk Both B and C. A is not because it is not at constant speed.

23. If a 10 kg mass is placed on a rod 5 meters away its pivot point, when is the torque experienced? t = x F g t = x m g t = (5) (10) (9.8) t = 490 Nm

24. When force is applied to a bridge, it results in: A)Tension B)Compression C)Both When force is applied to a bridge, it results in: A)Tension B)Compression C)Both Both

25. The stress with is force per unit area and the force vector lies in the plane is the case of _________. Shearing

26. Which equation is the modulus for tension and compression? A) F/A = G ∆x/L B) p = B ∆V/V C) F/A = E ∆L/L

27. Which equation is the modulus for shearing? A) F/A = G ∆x/L B) p = B ∆V/V C) F/A = E ∆L/L

28. Which equation is the modulus for hydraulic stress? A) F/A = G ∆x/L B) p = B ∆V/V C) F/A = E ∆L/L

29. 10 Questions

30. A book resting on a table is in _______ equilibrium. Static

31. The single point in which gravity is effectively acting on for any object is called the __________. Center of Gravity

32. When an object is being pulled apart by two forces in opposite direction parallel to its plane, the object is under ______. Tension

33. An object being acted on by two opposite forces perpendicular to its plane is said to be under a _________ stress. Shearing

34. When a object being acting upon by a surrounding fluid is said be to under a ________________. Hydraulic Compression

35. If g is the same for all elements of a body, then the body’s center of gravity is coincident with the body’s ___________. Center of Mass

36. All real “rigid” bodies are to some extent _________. Elastic

37. For simple tension or compression, the stress on the object is defined as ____. F/A (Force / Area)

38. The translational motion of a body is governed by Newton’s _______ law in its linear momentum form. Second (F net = dP/dt)

39. Name the three elastic moduli used to describe the elastic behavior of an object. Tension and CompressionTension and Compression ShearingShearing Hydraulic StressHydraulic Stress