FORCES AND THE LAWS OF MOTION

1. FORCES AND THE LAWS OF MOTION CHAPTER 4

2. Changes in Motion TLWBAT: • Explain how force affects the motion of an object. • Distinguish between contact forces and field forces. • Interpret and construct free-body diagrams.

3. Force • What is it? Examples? • Typically we think of a push or a pull on an object! • Force is the interaction of an object with its environment. • Force: The cause of an acceleration, or the change in an object’s motion. • Causes an object to move. • Causes an object to stop moving. • Causes a moving object to change direction.

4. Force • The SI unit of force is the Newton. • Defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s2. • 1 N = 1 kg x 1 m/s2. • Weight of an object is a measure of the magnitude of the gravitational force exerted on the object.

5. Force • Forces can act through or at a distance. • Contact forces: result from physical contact between two objects. • Push or pulls. • Field forces: do not involve physical contact between two objects. • Exerts a force on the object, even when it is not in immediate contact with the object. • Examples.

6. Force • Theory of Fields: The presence of an object affects the space around it so that a force is exerted on any other object placed within that space. • The region of influence is called the field.

7. Force Diagrams • Effect of a force depends on : • Magnitude • Direction • Therefore, force is a vector quantity. • A force diagram displays the objects involved in a situation and the forces exerted on the objects. • Forces are shown as vectors. • Forces are assumed to all act at a single point.

8. Free-body Diagrams • Includes the forces exerted on the object, and disregards the forces exerted by the object on other objects. • Used to analyze the forces affecting the motion of an object. • Constructed and analyzed like other vector diagrams. • Used to find component and resultant forces. • Example.

9. Free-body DiagramsHelp to analyze a situation. • Draw a diagram to represent the isolated object under consideration. • Isolate and identify all the forces acting on the object. • Draw and label vector arrows representing all the external forces acting on the object. • Label the vectors with the size or a name that will distinguish it from the other forces acting on the object.

10. Free-body DiagramsHelp to analyze a situation. • The only forces included are the forces exerted on the object. • Now the diagram can be used to find the net external force acting on an object, using the roles for vector analysis. • Example.

11. Newton’s First Law TLWBAT: • Explain the relationship between the motion of an object and the net external force acting on it. • Determine the net external force on an object. • Calculate the force required to bring an object into equilibrium.

12. Newton’s First LawInertia • An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless it experiences a net external force. • Inertia: The tendency of an object to maintain its state of motion. • When the net external force on an object is zero, its acceleration (or change in motion) is zero. • Examples.

13. Newton’s First LawInertia • The net external force can be determined by a change in motion. • External forces vs. net external force (resultant force). • The vector sum of all the external forces acting on a body (find through vector resolution). • Equivalent to the one force that would produce the same effect on the object as all the external forces combined. • Example: a game of tug-a-war or a car.

14. Newton’s First LawInertia

15. Newton’s First LawInertia • Sample Problem: Carrissa left her physics book on top of a drafting table. The table is inclined at a 35o angle. Find the net external force acting on the book, and determine whether the book will remain at rest in this position. • Given: Fgb = 22 N, Ff = 11 N, and Ftb = 18 N.

16. Newton’s First LawInertia • Sample Problem: An agriculture student is designing a support to keep a tree upright. Two wires have been attached to the tree at right angles to each other. One wire exerts a force of 30.0 N on the tree: the other wire exerts a 40.0 N force. Determine the placement and force in the wire for a third wire so that the tree will have zero net force from the three wires.

17. Newton’s First LawInertia • Sample Problem: A flying, stationary kite is acted on by a force of 9.8 N downward. The wind exerts a force of 45 N at an angle of 50.0o above the horizontal. Find the angle and force that the string exerts on the kite.

18. HOMEWORK HOMEWORK P 97 15-18

19. Newton’s First LawInertia • Mass is a measurement of inertia. • How does mass affect inertia? • The inertia of an object is directly proportional to its mass. • Inertia is the tendency of an object to maintain its state unless acted on by a net force.

20. QUIZ • What is the mass of a cat that weighs 30.0N? • An elevator with a mass of 1.10 x 103 kg accelerates upward at 0.45 m/s2. What is the force acting on the elevator’s support cable? • What is the acceleration of a 35kg mass that has a force of 270N applied to it horizontally? • A crate is pushed East across a frictionless surface with a force of 240N and pulled to the East by a rope with a force of 120 N. What is the net force on the crate?

21. QUIZ • You are pulling your little sister on her sled across an icy (frictionless) surface. When you exert a constant horizontal force of 110N, the sled has an acceleration of 2.5m/s2. If the sled has a mass of 7.0kg, what is the mass of your little sister? • A 92kg water skier floating in a lake is pulled form rest to a speed of 12m/s in a distance of 25m. What is the net force exerted on the skier, assuming acceleration is constant.

22. QUIZ • On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00kg, and on this particular planet its weight is 40.0N. If the astronaut exerts an upward force of 46.2N on the rock, what is its acceleration? • In a grocery store, you push a 12.5kg shopping cart with a force of 14.0N. If the cart starts at rest, how far does it move in 3.00s?

23. Newton’s First LawEquilibrium • Equilibrium: The state of a body in which there is no change in motion. • At rest or with constant velocity. • The net external force acting on a body in equilibrium must be equal to zero. • The force that brings an accelerating object into equilibrium must be equal and opposite to the force causing the object to accelerate. • ΣFx = 0 and ΣFy = 0.

24. HOMEWORK PG. 135 1-3.

25. Newton’s Second and Third Laws TLWBAT: • Describe the acceleration of an object in terms of its mass and the net external force acting on it. • Predict the direction and magnitude of the acceleration caused by a known net external force. • Identify action-reaction pairs. • Explain why action-reaction pairs do not result in equilibrium.

26. Newton’s Second Law • Relates force, mass, and acceleration. • The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the mass of the object. • Examples. • Net External Force = mass x acceleration • ΣF = ma

27. Newton’s Second LawSample Problem A 5.5 kg watermelon is pushed across the table. If the acceleration of the watermelon is 4.2 m/s2 to the right, find the net external force exerted on the watermelon.

28. Newton’s Second LawSample Problem A 7.5 kg bowling ball initially at rest is dropped from the top of an 11 m building. It hits the ground 1.5 s later. Find the net external force on the falling ball.

29. Newton’s Second LawSample Problem Space shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude?

30. Newton’s Second Law In solving problems, it may be necessary to break the Newton’s law equation into its components.

31. Newton’s Second LawHomework Pg. 138 1 - 5.

32. Newton’s Third LawForces always exist in pairs. • If two bodies interact, the magnitude of the force exerted on object #1 by object #2 is equal to the magnitude of the force simultaneously exerted on object #2 by object #1, and these two forces are opposite in direction. • OR, for every action there is an equal and opposite reaction.

33. Newton’s Third LawForces always exist in pairs. • Action-Reaction Pair: a pair of simultaneous equal but opposite forces resulting from the interaction of two objects. • Action-reaction forces act on different objects. • If a nail exerts a force on the hammer equal to the hammer on the nail, why doesn’t the nail remain at rest? • Draw a free-body diagram!

34. Newton’s Third LawHomework Pg. 140 1 – 4.

35. Quiz 1) Two lifeguards pull on ropes attached to a raft. If they pull in the same direction, the raft experiences a net external force of 334 N to the right. If they pull in opposite directions, the raft experiences a net external force of 105 N to the left. Find the force exerted by each lifeguard on the raft (disregard any other forces acting on the raft).

36. Quiz 2) A dog pulls on a pillow with a force of 5 N at an angle of 37o above the horizontal. Find the x and y components of this force.

37. Quiz • What net external force is required to give a 25 kg suitcase an acceleration of 2.2 m/s2 to the right? • What acceleration will you give to a 24.3 kg box if you push it with a force of 85.5 N?

38. Quiz 5) A 5.0 kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, find the force exerted by the rope on the bucket of water.

39. Everyday Forces TLWBAT: • Explain the difference between mass and weight. • Find the direction and magnitude of the normal force. • Describe air resistance as a form of friction. • Use coefficients of friction to calculate frictional force.

40. Everyday ForcesWeight • The magnitude of the force of gravity on that object. • A scalar quantity. • Dependent on location…moon or high altitude? • Weight , unlike mass, is not an inherent property of an object. • Fg = mg

41. Everyday ForcesNormal Force • A contact force exerted by one object on another in a direction perpendicular to the surface of the contact. • Examples. • The normal force is always perpendicular to the contact surface, but it is not always opposite in direction to the force of gravity acting on an object. • Examples.

42. Everyday ForcesThe Force of Friction • Friction opposes the applied force. • Example: Object on table. • At rest: Only force of gravity and normal force. • Small push: A small horizontal force and a force in the opposite direction called friction. The net external force is zero and remains in equilibrium. • The frictional force that keeps the object from moving is static friction (Fs).

43. Everyday ForcesThe Force of Friction • Until the applied force is large enough to move the object, Fs = -F. • When the applied force is as great as it can be without moving the object, the static friction has reached its maximum, Fs,max. • When the applied force exceeds Fs,max the object will begin to accelerate in the direction of the applied force. • The net external force acting on the object is equal to the difference between the applied force and the maximum force of static friction (F - Fs,max).

44. Everyday ForcesThe Force of Friction • When the object begins to move, the retarding frictional force becomes less than Fs,max. • The retarding force of an object in motion is called the force of kinetic friction (Fk). • Fk is the force exerted on a moving object and is less than static friction. • The net external force becomes F – Fk. • Surface adhesion (cold-welded).

45. Everyday ForcesThe Force of Friction • Friction depends on the surfaces in contact. • Examples. • Ffriction is proportional to Fn. • Ffriction also depends on the composition and qualities of the surfaces in contact.

46. Everyday ForcesThe Force of Friction • Coefficient of Friction: The ratio of the force of friction to the normal force acting between two objects. • μs = Fs,max Fn • μk = Fk Fn

47. Everyday ForcesThe Force of Friction • The value for the coefficient of kinetic friction is always lower than the value for static friction. • How does the coefficient of friction relate to the force necessary to move an object? • Air resistance is a form of friction. • What is terminal speed?

48. Everyday ForcesCoefficients of Friction A 24 kg crate initially at rest on a horizontal surface requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.

49. Everyday ForcesCoefficients of Friction A 91 kg refrigerator is placed on a ramp. The refrigerator begins to slide when the ramp is raised to an angle of 34o. What is the coefficient of static friction.

50. Everyday ForcesCoefficients of Friction A 91 kg refrigerator slides down a 27o ramp at constant speed. What is the coefficient of kinetic friction?