Forces and the Laws of Motion

1. Forces and the Laws of Motion Chapter 4

2. Part 1 • Newton’s Laws explain why objects move (or don’t move) as they do • Newton’s First Law • Law of Inertia • Relationship between mass and inertia • Balanced vs. Unbalanced Forces • Drawing Free-Body Diagrams • Finding Net Forces and Using in Kinematic Equations

3. Part 1 • Newton’s Second Law • Net Force and Acceleration • Relationships between variables • Weight • How planets stay in orbit • Elevator Problems • Newton’s Third Law • Action-Reaction Pairs • Definition of Friction

4. 4.1 Forces • Force: a push or pull on an object which may change the object’s state of rest or motion (thus changing “a”) F=ma • Force is a vector • SI Unit: • Newton (N) or kg/ms2 • 1 N = 0.225 lb

5. Types of Forces • Contact forces – result from physical contact between two objects • Field forces – interaction of invisible fields between two objects

6. Types of Forces

7. Types of Forces • Classical physics deals with contact, gravitational, and electromagnetic forces.

8. Changes in Shape • Forces exert a change in an object’s shape, temporarily or permanently

9. 4.2 Newton’s First Law (Inertia) • An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force. (Objects want to keep doing what they are doing.)

10. Real-life Examples: • Walking around a track with a full cup of water. When does it spill? • Start………..change is velocity • Around curves……….change in direction • You are riding a bike and hit a curb. • You are riding an elevator to the first floor. As it stops, blood rushes to your feet. • To get the ketchup from the bottom of the bottle, you turn it upside down and have to bang on it.

11. Inertia • Tendency of an object to resist being moved from original course • Common misconception: • Popular belief is that objects will always eventually come to rest. • If a book is pushed across a lab table, it will eventually stop. • The force that causes it to slow is friction. • A force is not required to keep an object in motion, but to change it’s velocity.

12. Inertia’s Relationship to Mass • Mass: measure of “stuff” in an object • Scalar quantity (kg) • As inertia increases, mass increases! • Imagine teeing up with a bowling ball • Think of pitching a tennis ball vs. a baseball

13. Balanced and Unbalanced Forces Consider a book at rest on the table • What forces are in play? • Force of gravity (Fg) • Force of the table on the book (Fn) • Are these forces equal and opposite? • Yes, because the book does not change it’s motion. • This is said to be in EQUILIBRIUM. • It remains at rest or constant velocity (a=0) • Fnet=0

14. Balanced and Unbalanced Forces, contd. Consider the book sliding across the table • What forces are in play? • Force of gravity (Fg) • Force of the table on the book (Fn) • Force of friction between the book and table (Ff) • Are these forces equal? • No because there is no force to balance friction • The book slows; therefore, has an acceleration • There is an Fnet

15. Challenge Micah drops a fat cat (50.0 N) off the roof of his house into a pool. As the cat enters the pool, it experiences an upward force of 50.0 N. • Draw a velocity vs. time graph to describe the motion of the cat. • What does his velocity look like as he falls toward the pool? • What about once he hits the water?

16. Free-Body Diagrams • Used to show relative magnitude and direction of all forces acting on an object • Size of arrow reflects magnitude of force • Direction of arrow shows direction of force • Label each arrow as to the type of force • Represent the object by a box Fn Fapp Fg

17. Finding Net External Forces Net force: vector sum of all forces (resultant) • Remember algebraic sum of vectors!! • Split x and y components for each vector. • Find Rx and Ry by adding each vectors components. • Use RxandRy to find resultant and angle.

18. Practice Draw free-body diagrams and determine the Fnet for each of the following: • A 800. N weight is being pulled upward by Samantha using a force of 1200. N. • The same 800. N weight is dropped by Olivia. As the weight drops, it experiences 600.N of air resistance. • Jenine shoves a book across the table towards Parker with 200. N. The book experiences a frictional force of 20.N. • If Ellen, Tiana, Meredith, and Brittany each pull a rope to the left with 80. N, how much force would Tyler, Logan, and Deion have to exert in order to balance out the girls’ force?

19. More Practice • Draw free-body diagrams and determine the Fnet for each of the following: • Sara pulls a rope around a box with 25 N at 77°. Robert pulls a different rope around the same box with 35 N at 25°. What is the equilibrant force? • Sean pulls his bookbag full of chocolate with 15 N at 155°, while Morgan pulls with 18 N at 20.° and Christina pulls with 18 N at 280°. • Howard is pushing a desk to the left with 10.0 N while Robin pulls it with 20.0 N at 150°. What would be the equilibrant force needed to keep the desk from moving?

20. Prep for Force Table Lab • Complete the preparation questions. • If you do not finish in class, it will be homework.

21. 4.3 Newton’s Second Law • Second Law: Fnet=ma • F is the vector sum of all external forces (N) • m is the mass (kg) • a is acceleration (m/s2)

22. Relationships between Variables • Relationships between variables • a of an object is directly proportional toFnet • a of an object is inversely proportional to m • a is inversely proportional to inertia

23. Practice • Determine the accelerations that result when a 12-N net force is applied to a 3-kg object. Then to a 6-kg object. • A net force of 15 N is exerted on an encyclopedia to cause an acceleration of 5 m/s2. How much did the encyclopedia weigh? • Suppose a sled is accelerating at a rate of 2 m/s2. If the net force is tripled, what happens to the acceleration? If the mass is doubled, what happens to the acceleration?

24. Force is a VECTOR • KEEP X and Y separate and then combine them!! • Fnet =mais actually made up of: • Fx =max • Fy =may

25. Practice (pg. 86) An airboat with a mass of 350 kg has an engine that produces a net horizontal force of 770 N after accounting for forces of resistance. • Find the acceleration of the airboat. • Starting from rest, how long does it take the airboat to reach a speed of 12.0 m/s? • After reaching this speed, the pilot turns off the engine and drifts to a stop over a distance of 50.0 m. Find the resistance force, assuming it’s constant.

26. Practice (pg. 87) • Two horses are pulling a barge with mass 2.00 x 103 kg along a canal. The cable connected to the first horse makes an angle of 30.0° with respect to the direction of the canal, while the cable connected to the second horse makes an angle of 45.0°. • Find the initial acceleration of the barge, starting at rest, if each horse exerts a force of 6.00 x 102 N on the barge. Ignore factors of resistance on the barge.

27. Classwork • In pairs, work on the four problems provided. If you do not finish, you will be required to finish for homework. • Homework: BRING YOUR BOOK!!

28. Gravitational Force • The mutual force of attraction between any two objects in the Universe • Weakest of fundamental forces • Think about what happens when you rub a balloon to your head. Are gravitational forces or electric forces stronger?

29. Law of Universal Gravitation • Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them • The greater the mass, the greater the attraction. • Why do we not feel the attraction towards objects surrounding us? • Why does the moon not fall to the Earth? • The moon is moving forward and down at the same time, and Earth’s gravity provides a centripetal force to keep it close and in orbit.

30. Weight • Mass is the amount of matter in an object and does not vary based on location. • Weight is the force of gravity acting on an object. • Fg=mag • Since “ag” varies with mass or location, weight will also vary. • ag=-9.81 m/s2 on Earth • ag=-1.6 m/s2 on the Moon • ag= -274 m/s2 on the Sun

31. Free Fall Motion • The only force acting upon an object is gravity. • All falling objects near Earth have a=-9.8 m/s2. • Mass and Fg are directly proportional. • As an object falls, it usually experiences some degree of air resistance (Fair). • Speed and air Fair are directly proportional • Area of the object and Fair are directly proportional

32. Classwork • The following classwork will become homework: • Pg. 109 • #1, 2, 6, 7, 8, 11

33. 4.4 Newton’s Third Law • Forces exist in pairs (action-reaction) • When two objects interact with one another, they exert forces on each other. The forces exerted on each other are opposite in direction and equal in magnitude • A single isolated force CANNOT exist.

34. Real-life Examples The action force is equal and opposite in direction to the reaction force. • Examples: • Weight: Earth’s pull on us vs. our pull on Earth • Walking: our foot’s frictional force vs. the ground against our foot. • A fish uses its fins to push water backwards, which accelerates the water. The water pushes the fish forwards.

35. Normal Force on Flat Surface • Fn = vector perpendicular to the surface of the object and in the opposite direction of Fg • Fn=mag because Fg=-mag (opposite and equal) on a FLAT Surface

36. Identifying Pairs • Explain the opposite force for: • A baseball pushing a glove backwards. • A bowling ball knocking over a pin • Air particles in a balloon push outwards against the wall of the balloon.

37. 4. 5 Applications of Newton’s Laws • Only pay attention to the forces acting ON THE OBJECT. • Identify ALL forces acting on the object. • Draw a free-body diagram.

38. Applications of Newton’s Laws, continued • Choose an appropriate coordinate system • Determine the x and y components • Determine the appropriate kinematic equations

39. Practice • Assume the box has a mass of 5.0 kg. What is the acceleration?

40. Practice (pg. 96) The combined weight of the crate and dolly is 300. N. If the man pulls on the rope with a constant force of 20.0 N, what is the acceleration of the system, and how far will it move in 2.00 s. Assume that the system starts at rest and there is no friction.

41. Practice (pg. 98) A man weighs a fish with a spring scale attached to the ceiling of an elevator. While the elevator is at rest, he measures a weight of 40.0 N. • What weight does the scale read if the elevator accelerates upward at 2.00 m/s2? • What does the scale read if the elevator accelerates downward at 2.00 m/s2? • If the elevator cable breaks, what does the scale read?

42. Homework • Elevator Worksheet

43. 4.6 Forces of Friction • Friction: the resistance encountered by an object moving on a surface or through a viscous medium, such as air or water • The nature of the two surfaces is the cause of friction.

44. Static Friction (Fs)-not moving • Force that resists the initiation of sliding motion between 2 surfaces that are in contact and at rest. • If an object does not move, Fs=-Fapplied • Fs,max is reached when Fapplied is as great as can be WITHOUT making the object move • When Fappliedexceeds Fs,max, the object accelerates

45. Kinetic Friction (Fk)- moving • Sometimes called sliding friction • Force that opposes the movement of 2 surfaces in contact and sliding over each other • Fnet =Fapplied– Fk • If Fapplied= Fk, then a=0 and velocity is constant.

46. Properties Affecting Friction • Friction is proportional to Fn of an object • Fn is proportional to mass • Fnis in the opposite direction of the Fs or Fk • Friction depends on composition and quality and area of the surface coefficient of friction () • Static Friction Equations: Fs sFn and= • Kinetic Friction Equations: Fk=kFnand = • ks

47. Coefficients of Friction

48. Practice (pg. 103) The hockey puck struck by a hockey stick is given an initial speed of 20.0 m/s on a frozen pond. The puck remains on the ice and slides 120. m, slowing down steadily until it comes to rest. Determine the coefficient of kinetic friction between the puck and the ice.

49. Friction Lab HORIZONTAL FORCES WITH FRICTION • Horizontal forces • Find weight of block plus 1.0 to 2.0kg Fg = • Find Normal force FN= • Pull with spring scale until the block just starts to move. • Find Fsand then find coefficient of static friction. • Draw a free body diagram showing all forces, equation, and all work. Repeat above experiment except pull with spring scale while moving at a constant velocity. Find Fk and then find coefficient of kinetic friction. • Draw a free body diagram showing all forces, equation, and all work. • A. Which is higher, static or kinetic? Is this what you expected? Why? • B. If you added more mass to the block would mu change? Prove it.

50. Homework • Complete the provided worksheet.