FORCES

1. FORCES • Inertia, Mass, Weight • Newton’s Law • Types of Forces • Free-body diagram • Friction

2. FORCE • Push/pull • Causes an object to accelerate or change its velocity. • Net force: sum of all forces • Two types of forces: a) Contact forces b) Field forces • Gravitational …objects • Electromagnetic…Charges • Nuclear…subatomic particle • Weak…radioactive decay • Vector

3. Inertia, Mass, and Weight • Inertia • Resistance to change in its state of motion • Depends on mass • Example • Pushing heavy things • When moving…difficult to stop • Seatbelts • Galileo and inertia • Incline plane: initial height = final height

4. Inertia, Mass, and Weight • Mass • Amount of matter it has • Measures inertia • Units: kg • Remains constant • Weight • Changes with gravity • Measures force • Units: Newton

5. Inertia, Mass, and Weight • Examples • Mac and Tosh are arguing in the cafeteria. Mac says that if he throws his jello with a greater speed it will have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. With whom do you agree? Why? • If you were in a weightless environment in space, would it require a force to set an object in motion? • Mr. Wegley spends most Sunday afternoons at rest on the sofa, watching pro football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia? Explain. • Ben Tooclose is being chased through the woods by a bull moose which he was attempting to photograph. The enormous mass of the bull moose is extremely intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion.

6. Newton’s First Law • Law of inertia • Two parts • Object at rest, remains at rest • Object in motion, remains in motion • Unless an unbalance force acts upon it • No force needed to keep an object in motion • Resists acceleration

7. Newton’s First Law • Contradicted: • Aristotle: all objects have natural tendency come to rest • Newton: all objects come to rest due to friction; w/o friction object continues to move • Balanced and unbalanced forces

8. Newton’s First Law http://www.physicsclassroom.com/Class/newtlaws/U2L1a.html

9. Newton’s First Law

10. Newton’s Second Law • A net force or unbalanced forces causes an object to accelerate in the direction of the force. • Acceleration is directly proportional to the force

11. Newton’s Second Law • Acceleration is inversely proportional to the mass • Fnet = ma • Units: Newton (N) = kg·m / s2 • Vector sum of all forces • FORCES CAUSE ACCELERATION!!

12. Newton’s Second Law Equilibrium means “Zero” acceleration

13. Newton’s Second Law • Free Fall • All objects will fall with the same rate of acceleration, regardless of their mass • Air Resistance • Decreases the acceleration • Depends on cross-sectional area and speed • Terminal Velocity • Weight equals force due to air resistance; a = 0 m/s/s

14. Newton’s Second Law

15. NEWTON’S SECOND LAW

16. NEWTON’S SECOND LAW

17. Problems: Pg 92 • 1) When a shot-putter exerts a net force of 140 N on a shot, the shot has an acceleration of 19 m/s/s. What is the mass of the shot? • 7.4 kg • 2) Together a motorbike and rider have a mass of 275 kg. The motorbike is slowed down with an acceleration of –4.50 m/s/s. What is the net force on the motorbike? Describe the direction of this force and the meaning of the negative sign. • - 1.24 x 103 N; direction of force is in opposite direction of the velocity.

18. Problems: Pg 92 • 3) A car, mass 1225 kg, traveling at 105 km/h, slows to a stop in 53 m. What is the size and direction of the force that acted on the car? What provided the force? • - 9.8 x 103 N; road surface pushing against the car tires • 4) Imagine a spider with mass 7.0 x 10-5 kg moving downward on its thread. The thread exerts a force that results in a net upward force on the spider of 1.2 x 10-4 N. a) What is the acceleration of the spider? b) Explain the sign of the velocity and describe in words how the thread changes the velocity of the spider. • 1.7 m/s/s

19. Newton’s Third Law • Two different objects • Action-reaction pair • For every action force there is a equal and opposite reaction force • F object A on object B = - F object B on object A

20. Newton’s Third Law

21. Newton’s Third Law

22. Newton’s Third Law

23. Types of Forces • Applied Force (FA) • Applied to an object by another object • Force of Gravity (Fg or W) • W = mg • Perpendicular to the Earth • Normal or Support Force (Fn or N) • Exerted by contact with a surface • Perpendicular to the surface • Tension (T) • Force exerted by strings, ropes, and wires • Spring Force (Fs) • Force exerted by compressed or stretch spring • Friction Force (Ff) • Opposes motion of object

24. FRICTIONAL FORCE • Fluids or surface drag • Opposes motion • Two types: • Static friction…friction at rest • Ff sFn • Maximum value • Kinetic/sliding friction…friction in motion • Ff= kFn

25. FRICTIONAL FORCE • Coefficient of static friction () • Measures how difficult it is to slide one material over another. • Dimensionless • Independent • surface area • speed (except when v =0) • temperature • roughness/texture • Dependent • nature of the surfaces (material) • Proportional to normal force • k < s

26. FRICTIONAL FORCE

27. FREE-BODY DIAGRAM • Diagrams showing all forces that are found on the object with direction and magnitude • Arrows start from the center of the object. • Each arrow is labeled.

28. FREE-BODY DIAGRAM EXAMPLES • The force of gravity on a wagon is 230 N. The force of friction between the tires and the ground is 10 N. Sheila is pulling the wagon with a force 15 N. Draw the free body diagram showing the forces on the wagon. • A book is at rest on a table top. • A girl is suspended motionless from a bar which hangs from the ceiling by two ropes. • An egg is free-falling from a nest in a tree. Neglect air resistance. • A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance.

29. FREE-BODY DIAGRAM EXAMPLES • A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. • A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. • A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. • A skydiver is descending with a constant velocity. Consider air resistance. • A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration.

30. FREE-BODY DIAGRAM EXAMPLES • A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. • A car is coasting to the right and slowing down.

31. FREE-BODY DIAGRAM • Write a Fnet equation • Fx and Fy equations. • Fnet = ma • Balanced Forces • At rest • Constant velocity…a = 0 m/s/s • Fnet = ma = 0 • Unbalanced Forces • a  0 • Fnet = ma

32. Free Body Diagrams Calculations Fx = Fa – Ff = ma Fy = Fn – Fg = ma

33. Free Body Diagrams Calculations Fx = Ff = ma Fy = Fn – Fg = ma

34. Free Body Diagrams Calculations Fx = Fa - Ff = ma Fy = Fn – Fg = ma

35. Free Body Diagrams Calculations Fy = A – Fg = ma = 0

36. Free Body Diagrams Calculations Fx = Fa - A = ma Fy = Fn – B = ma

37. Problems: Pg 94 • 5)What is the weight of each of the following objects? a) 0.113 kg hockey puck b) 108 kg football player c) 870kg automobile • 1.11 N; 1.06 x 103 N; 8.50 x 103N • 6) Find the mass of each of these weights. a) 98 N b) 80 N c) 0.98 N • 10 kg; 8.2 kg; 0.10 kg

38. Problems: Pg 94 • 7)A 20 N stone rests on a table. What is the force the table exerts on the stone? In what direction? • 20 N, upward • 8) An astronaut with mass 75 kg travels to Mars. What is his weight a) on Earth b) What is the weight on Mars where g = 3.8 m/s/s? c) What is the value of g on top of a mountain if the astronaut weight 683 N? • 740 N; 290 N; 9.1 m/s/s

39. Problems: Pg 99 • 9)Suppose Joe, who weighs 625 N, stands on a bathroom scale calibrated in Newton. a) What force would the scale exert on Joe? In what direction? b) If Joe now holds a 50 N cat in his arms, what force would the scale exert on him? c) After Joe puts down the cat, his father comes up behind him and lifts upward on his elbows with a 72 N force. What force does the scale now exert on Joe? • 625 N, upward; 675 N; 553 N upward • 10) A 52 N sled is pulled across a cement sidewalk at constant speed. A horizontal force of 36 N is exerted. What is the coefficient of sliding friction between the sidewalk and the metal runners of the sled? • 0.69

40. Problems: Pg 100 • 10b)Suppose the sled now runs on packed snow. The coefficient of friction is now only 0.12. If a person weighing 650 N sits on the sled, what force is needed to slide the sled across the snow at constant speed? • 84 N • 11) The coefficient of sliding friction between rubber tires and wet pavement is 0.50. The brakes are applied to a 750 kg car traveling 30 m/s, and the car skids to a stop. a) What is the size and direction of the force of friction that the road exerts on the car? • -3.7 x 103 N

41. Problems: Pg 100 • 11b)What would be the size and direction of the acceleration of the car? Why would it be constant? c) How far would the car travel before stopping? • -4.9 m/s/s; frictional force is constant; 92 m • 12) If the tires of the car in Practice Problem 11 did not skid, the coefficient of friction would have been 0.70. Would the force of friction have been larger, smaller, or the same? Would the car have come to a stop in a shorter, the same, or a longer distance? • Larger; shorter distance

42. Problems: Pg 102 • 13)A rubber ball weighs 49 N. a) What is the mass of the ball? b) What is the acceleration of he ball if an upward force of 69 N is applied? • 5.0 kg; 4.0 m/s/s • 14) A small weather rocket weighs 14.7 N. a) What is its mass? b) The rocket is carried up by a balloon. The rocket is released from the balloon and fired, but its engine exerts an upward force of 10.2 N. What is the acceleration of the rocket? • 1.5 kg; -3.00 m/s/s

43. Problems: Pg 102 • 15)The space shuttle has a mass of 2.0 x 106 kg. At lift-off the engines generate an upward force of 30 x 106 N. a) What is the weight of the shuttle? b) What is the acceleration of the shuttle when launched? c) The average acceleration of the shuttle during its 10 minute launch is 13 m/s/s. What velocity does it attain? d) As the space shuttle engines burn, the mass of the fuel becomes the same, would you expect the acceleration to increase, decrease or remain the same? Why? • 2 x 107 N; 5.0 m/s/s; 7.8 km/s; increase

44. Problems: Pg 102 • 16)A certain sports car accelerates from 0 to 60 mph in 9.0 s (average acceleration = 3.0 m/s/s). The mass of the car is 1354 kg. The average backward force due to air drag during acceleration is 280 N. Find the forward force required to give the car this acceleration. • 4.4 x 103 N

45. Free Body Diagrams Calculations • A rightward force is applied to a 6-kg object to move it across a rough surface at constant velocity. The object encounters 15 N of frictional force. Use the diagram to determine the gravitational force, normal force, net force, and applied force. (Neglect air resistance.) • A rightward force is applied to a 10-kg object to move it across a rough surface at constant velocity. The coefficient of friction, µ, between the object and the surface is 0.2. Use the diagram to determine the gravitational force, normal force, applied force, frictional force, and net force.

46. Free Body Diagrams Calculations

47. Free Body Diagrams Calculations

48. Free Body Diagrams Calculations A force of 55 N[E] acts on a combination of two boxes that are next to each other on a frictionless surface.                                                                                                                   Find: • the acceleration of the boxes. • the force exerted by box A on box B. • the force exerted by box B on box A.

49. Free Body Diagrams Calculations Three toboggans are connected by a rope. The first toboggan has a mass of 75 kg, the second a mass of 55 kg and the third a mass of 10 kg. If the force exerted on the first toboggan is 310 N and surfaces are considered to be frictionless.                                                                                                                    Find: • the acceleration of the toboggans • the force exerted by toboggan one on toboggan two. • the force exerted by toboggan two on toboggan three.

50. Free Body Diagrams Calculations