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Chapter 4

Chapter 4. Newton’s Laws of Motion. Isaac Newton (1642-1727). His three laws of motion first appeared in his book called Principia. Newton’s First Law. a.k.a “Law of Inertia” A body remains at rest or moves in a straight line at a constant speed unless acted upon by a force.

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Chapter 4

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  1. Chapter 4 Newton’s Laws of Motion

  2. Isaac Newton (1642-1727) • His three laws of motion first appeared in his book called Principia.

  3. Newton’s First Law • a.k.a “Law of Inertia” • A body remains at rest or moves in a straight line at a constant speed unless acted upon by a force.

  4. Newton’s First Law Examples • Weight and string • Card, cup, and coin • Fixing a Hammer • Demo - Coins on elbow • Demo - Lead Brick and Hammer • Demo - Table setting Figure 4.1

  5. Mass • the quantity of matter in an object • the measurement of the inertia • measured in kilograms (kg)

  6. Weight • the force upon an object due to gravity • Weight = Mass  Acceleration of gravity W = mg • measured in Newtons (N) in the metric system or pounds (lb) in the British system

  7. The weight of a 10 kg brick is... • A) 98 N • B) 10 kg • C) 9.8 kg • D) 10 N • E) 98 kg

  8. Mass and Weight should not be confused with... • Volume • the quantity of space an object occupies • Density • the quantity mass per unit volume

  9. Mass and Weight • On the Moon the gravitational force is only 1/6 as strong as on the Earth. • In space you are “weightless” but not “massless”. • Your mass does not depend on where your are. • (e.g. Earth, Moon, or space).

  10. Location Mass Weight Earth 18.4 kg 180 N Moon 18.4 kg 30 N Space 18.4 kg 0 N

  11. Newtons’ Second Law • F = m a • The acceleration of an object is directly proportional to the net force acting on the object, and inversely proportional to the mass of the object.

  12. Example Questions * • How much acceleration does a 747 jumbo jet of mass 30,000kg experience in takeoff when the thrust of all of the engines is 120,000N? • The same net force is applied to two blocks. If the blue one has a smaller mass than the yellow one, which one will have the larger acceleration?

  13. m m m m m M M M m NEWTON'S 2nd LAW OF MOTION a F F a F a F a F a F a

  14. If the net force is parallel to the velocity, then the speed of the object increases. If the net force is anti-parallel to the velocity, then the speed of the object decreases.

  15. If the net force is perpendicular to the velocity, the direction of the velocity changes.

  16. Force and acceleration are vector quantities. • If v is parallel to F, speed increases. • If v is antiparallel to F, speed decreases. • If v perpendicular to F, direction of v changes. • See example questions page 60, 62 & 64.

  17. When Acceleration Is Zero - Equilibrium Scales pushing up Static Equilibrium Velocity is zero Examples: Normal up Weight down Computer setting on a table Weighing yourself on a set of scales Hanging from a tree Tree pulling up Weight down Car parked on an incline Normal Friction Weight down Weight down

  18. When Acceleration Is Zero... • …we say the object is in Mechanical Equilibrium. • …the net force is zero. • For Static Equilibrium the velocity is zero. • For Dynamic Equilibrium the velocity is constant.

  19. Dynamic Equilibrium Velocity is nonzero and constant Examples: Driving at constant velocity Normal up Friction Force from road Air resistance Weight down Terminal velocity in parachuting Weight down

  20. When the Acceleration is g... • …the object is in Free Fall. • Consider a 1kg rock and a 1gram feather. • Which object weighs more? • Answer: The rock • On which is the gravitation force stronger? • Answer: The rock • Which has a greater acceleration when dropped from rest? • Answer: Both have the same acceleration, g.

  21. When the Acceleration Is Less Than g... • …the object is not in Free Fall. • In this case there is a force other than gravity. • That force is air resistance. • Air resistance depends on size and speed.

  22. Example: A heavy parachutists will fall faster than a light one. • When the force of air resistance is equal to weight of the falling object, the object will reach a Terminal Velocity. • See Questions on page 66,67 and 69.

  23. * • After jumping from an airplane a skydiver will fall until the air resistance equals her weight. At that point... • A) she will fall with constant speed • B) she will fall no farther • C) she will fall faster • D) she opens her parachute • E) she will hit the ground

  24. correct lift drag thrust weight Lecture 5, Pre-Flight Questions 3&4 An airplane is flying from Hartsfield airport. Many forces act on the plane, including weight (gravity), drag (air resistance), the trust of the engine, and the lift of the wings. At some point during its trip the velocity of the plane is measured to be constant (which means its altitude is also constant). At this time, the total force on the plane: 1. is pointing upward2. is pointing downward3. is pointing forward4. is pointing backward5. is zero

  25. lift drag thrust weight Lecture 5, Pre-Flight Questions 3&4(great answers) When the velocity is constant the objects acceleration is equal to zero. The only time acceleration is equal to zero is when the sum of the net force is equal to zero. SF= ma = m0 = 0 An object traveling at a constant velocity along a straight line will continue to do so as long as there is no net force acting on it (Newton's First Law). The total force acting on the plane is zero, because its motion is constant in a straight line.

  26. M=10 kg F1=200 N Find a F1 M F1 M F2 M=10 kg F1=200 N F2 = 100 N Find a Examples a = Fnet/M = 200N/10kg = 20 m/s2 a = Fnet/M = (200N-100N)/10kg = 10 m/s2

  27. m1 m2 F a1 F a2 = 2a1 Example • A force F acting on a mass m1 results in an acceleration a1.The same force acting on a different mass m2 results in an acceleration a2= 2a1. What is the mass m2? (a)2m1(b)m1(c)1/2m1 • F=ma • F= m1a1 = m2a2 = m2(2a1) • Therefore, m2 = m1/2 • Or in words…twice the acceleration means half the mass

  28. Newton’s Third Law • Action-Reaction • Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.

  29. Ffingerbox Fboxfinger Newton’s Third Law • For every action, there is an equal and opposite reaction. • Finger pushes on box • Ffingerbox = force exerted on box by finger • Box pushes on finger • Fboxfinger = force exerted on finger by box • Third Law: • Fboxfinger = -Ffingerbox

  30. Fw,m Fm,w Fm,f Ff,m Newton's Third Law... • FA ,B = - FB ,A. is true for all types of forces

  31. Example of Bad Thinking • Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ? Fb,m Fm,b a ?? ice

  32. Fan cart • 2 skateboards Example of Good Thinking • Consider only the box! • Fon box= mabox=Fm,b • Free Body Diagram (more on this next time) What about forces on man? Fb,m Fm,b abox ice

  33. * • You push on an box sitting on the floor horizontally with a force of 15 Newtons and the box does not move. The force of friction on the box is • A) 0 Newtons • B) 15 Newtons in the direction of your push • C) 15 Newtons opposite to your push • D) less that 15 Newtons.

  34. Questions from Page 72 and 75 * • We know that the Earth pulls on the moon. Does this mean that the moon also pulls on the Earth? • A high speed bus and a bug have a head-on collision. • The force of impact splatters the bug. • Is the corresponding force that the bug exerts against the windshield greater, less, or the same? • Is the resulting deceleration of the buss greater than, less than, or the same as the that of the bug? *

  35. Question * • An archer shoots an arrow. Consider the action force to be the bowstring against the arrow. The reaction force is the… • (a) weight of the arrow. • (b) air resistance against the bow. • (c) friction of the ground against the archer’s feet • (d) grip of the archer’s had on the bow • (e) arrow’s push against the bowstring.

  36. Question * • A skydiver falls toward the earth. The attraction of the earth on the diver pulls the diver down. What is the reaction to this force? • (a) air resistance the diver encounters while falling • (b) water resistance that will soon act upward on the diver. • (c) the attraction to the planets, stars, and every particle in the universe • (d) the attraction

  37. End of Chapter 4 • Your Mission: • Print out the study guide and define each term. • Work out the example online exam. • Read all of the “blue questions” and answers in Chapters 2, 3, and 4. • Make sure that you have read these chapters.

  38. You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s What will be the rotational speed of your friend who sit at the outer edge? Answer: 4 m/s What will be his rotational speed? Answer: 20 RPM • See this question on page 50. *

  39. End of Chapter 4

  40. The prince learned of this and was determined to rescue the one he loved, so he started out for the tower where the unhappy princess sat imprisoned. When he arrived at the base of the tower the prince looked up and noticed that there was a wooden beam protruding from the top of the structure. He immediately contrived a method to use this to reach his princess.

  41. He attached a sturdy basket to one end of a very long rope and to the other end he tied a stone. Then with a mighty heave he threw the stone across the top of the beam so that the rope was looped across the beam. The prince had thus constructed a simple pulley. He then stepped into the basket, and since the pulley had a mechanical advantage of two, he proceeded to hoist himself up.

  42. In due time the prince reached the top and was rewarded with a long embrace by the King’s daughter. The prince could not return the embrace, nor could he begin his work to release the princess, since letting go of the rope would cause the basket to fall. So he began searching for a way to fix the rope to the tower wall.

  43. Luck seemed to be smiling on the young man because close by he discovered a metal hook imbedded in the stone wall. The prince tugged on the hook with one hand (the other hand holding the rope tightly), and finding it secure, he proceeded to tie the rope to the hook.

  44. But the instant he did that, the supporting beam broke and the basket, together with the poor prince, came crashing to the ground. What had happened was this. The King, who was very wicked, also happened to have had Physics 101 (no connection between the two), and he had originally designed the beam to support the weight of the prince and the weight of the basket, but no more.

  45. During the time the unsuspecting prince was hoisting himself up, the total load on the beam was simply his weight plus the weight of the basket. But as soon as one end of the rope was hooked onto the tower, the situation changed drastically. Now the weight of the prince plus the weight of the basket all exerted a force on one end of the rope while the tower, via the hook, pulled down on the other end with an equal and opposite force. The total force on the beam was now twice the original weight. The beam broke. Why?

  46. Terminal Velocity Net Force Acceleration = g Velocity = 0 but motion is about to begin mg F Acceleration < g v increasing downward mg F Acceleration << g v still increasing downward just not as rapidly as before mg F Acceleration = 0 Terminal velocity mg

  47. Example: Mouse in a mine shaft • Light and heavy parachutists

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