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Chapter 2

Chapter 2. Motion, Forces and Newton ’ s Laws. Mechanics. Mechanics is one area of physics It is concerned with the motion of objects 2 questions need to be answered to understand mechanics What causes motion? Given a particular situation, how will an object move?

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Chapter 2

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  1. Chapter 2 Motion, Forces and Newton’s Laws

  2. Mechanics • Mechanics is one area of physics • It is concerned with the motion of objects • 2 questions need to be answered to understand mechanics • What causes motion? • Given a particular situation, how will an object move? Newton’s Laws are a cornerstone of physics • They are the basis for nearly everything discussed in the first part of the text • They are based on ideas developed in centuries before Newton.

  3. Aristotle’s Mechanics is Wrong!! • Types of motion identified by Aristotle • Celestial motion • The motion of things like the planets, the Moon, and the stars • Terrestrial motion • The motion of “everyday” objects • Objects move when acted on by forces • Motions of celestial objects and terrestrial objects look very different • Mainly because terrestrial objects seem to come to a stop and celestial objects do not • The natural state of terrestrial objects was at rest

  4. More About Aristotle’s Terrestrial Motion • Motion is caused by forces • Terrestrial objects move only when acted upon by another object • In modern terminology, this would say that an object moves only when acted on by a force • Forces are produced by contact with other objects

  5. Forces • A force is a push or a pull on an object • Force is a vector quantity • The magnitude of the force is the strength of the push or pull • The direction of the force is the direction of the push or pull • Denoted by

  6. Motion • One way to think about motion is in terms of velocity • Velocity is a vector quantity • The magnitude is the distance traveled in one second • The direction is the direction of motion

  7. Aristotle’s Law of Motion is WRONG! • Aristotle thought the velocity of the object was proportional to the force acting on it and inversely proportional to the resistance to the motion • This was incorrect! • But does seem to explain many everyday motions • Failures of Aristotle’s Mechanics • Doesn’t work in all situations • Examples: baseball, falling objects • Lack of direct contact • Force and velocity are not always in the same direction • Newton’s Laws overcome the difficulties of Aristotle’s Mechanics

  8. Example of Failure of Aristotle’s Laws • Falling object • Aristotle’s prediction • A heavy object will fall faster than a light one when both are dropped in the same medium • Galileo’s Experiment • Light objects fall at the same rate as heavy objects

  9. What Is Motion? Section 2.2 • Defined in terms of various concepts • Look at motion in terms of • Position • Velocity • Acceleration

  10. Definition of Motion • Start by considering one-dimensional motion • Can be shown by a motion diagram • Could be a multiple exposure • Sometimes is a sketch • Shows the location of an object at regularly spaced time intervals Section 2.2

  11. Representations of Motion • A shows a motion diagram • Multiple images of a hockey puck traveling across an icy surface • B shows a position – time graph of the motion • The dots correspond to the images of the puck • C shows a velocity-time graph of the motion Section 2.2

  12. Velocity and Speed Section 2.2 • The magnitude of the velocity is called the speed • This is the distance traveled per unit of time • Speed is a scalar quantity • The direction of the velocity gives the direction of the motion • SI unit is meters / second (m/s) • Remember that speed and velocity are not the same

  13. Velocity and Speed, cont. Section 2.2 • One-dimensional motion • Direction of velocity will be parallel to the x-axis • Will have only one component • One-, two- or three-dimensional motion • Velocity may be positive, negative, or zero • Speed is equal to the magnitude of the velocity • Speed cannot be negative

  14. Displacement and Velocity Section 2.2 • An object’s change in position is its displacement • Displacement: Δx = xfinal - xinitial • Average velocity is the displacement per unit time:

  15. Velocity and Position • In general, the average velocity is the slope of the line segment that connects the positions at the beginning and end of the time interval Section 2.2

  16. Velocity Example • A shows a multiple exposure sketch of a rocket powered car • B shows the position-time graph • C shows the velocity-time graph • In this case, the speed of the car increases with time Section 2.2

  17. Instantaneous Velocity • Average velocity doesn’t tell us anything about details during the time interval • To look at some of the details, smaller time intervals are needed • The slope of the curve at the time of interest will give the instantaneous velocity at that time • Will be referred to as velocity in the text Section 2.2

  18. Velocity of a Bicycle (Example 2.1) • Need average velocity from 2.0 to 3.0 seconds • Draw a picture • Find displacement, Δx • Find average velocity, vave = Δx / Δt • Solve Section 2.2

  19. Graphical Analysis of Velocity (Example 2.3) • To find the velocity graphically • Find the slope of the line tangent to the x-t graph at the appropriate times • For the average velocity for a time interval, find the slope of the line connecting the two times Section 2.2

  20. Average Acceleration Section 2.2 Acceleration is related to how velocity changes in time Acceleration is defined as the rate at which the velocity is changing: SI unit is m/s²

  21. Instantaneous Acceleration • The instantaneous acceleration can also be defined: • The instantaneous acceleration is the slope of the velocity-time graph at a particular instant in time • In this case, the average acceleration equals the instantaneous acceleration Section 2.2

  22. Finding Acceleration from a Graph (Example 2.4) • The acceleration is the slope of the velocity-time graph • The slopes of the tangent lines at various locations on the graph will give the acceleration Section 2.2

  23. Velocity and Acceleration Section 2.2 • Acceleration and velocity do not necessarily reach a maximum value at the same time • Acceleration is the slope of the velocity-time curve • It is the rate of change of the velocity with respect to time

  24. Motion: Summary Section 2.2 • Graphical • Velocity is the slope of the position-time graph • Acceleration is the slope of the velocity-time graph • Position, displacement, velocity and acceleration are all that are needed to formulate a complete theory of motion • Newton’s Laws of Motion explain why these relationships are valid

  25. The Principle of Inertia Section 2.3 Newton’s work was based largely on Galileo’s Galileo experimented on the motion of terrestrial objects The experiments showed an object can move even with zero force acting on it Galileo did not arrive at the correct laws of motion Galileo did discover the principle of inertia Newton’s Laws incorporated the principle of inertia

  26. Galileo’s Motion Experiments • Experimented with balls on an incline • When the ball was released from rest at the top of the incline, its velocity varied with time • The acceleration was constant and positive • The slope of the line in b is the value of the acceleration shown in c Section 2.3

  27. Galileo’s Motion Experiments, cont. • Repeated the experiment by rolling the ball up the incline • Give the ball an initial velocity • The slope of the velocity-time graph is negative • The slope of the v-t graph was always constant and depended upon the angle of the incline Section 2.3

  28. Galileo’s Motion Experiments, final Section 2.3 The acceleration when a ball rolled up a particular incline was always equal in magnitude, but opposite in sign, when compared with the acceleration when the ball rolled down the same incline Reasoned that if the tilt of the incline was exactly zero, the ball would move with a constant velocity Proposed that on a perfectly horizontal ramp, the ball would roll forever

  29. Inertia Section 2.3 • The Principle of Inertia • An object will maintain its state of motion unless it is acted upon by a force • The velocity is its state of motion • Demonstrated by Galileo’s experiments • Showed that one can have motion without a force • Broke Aristotle’s link between force and velocity • Still did not explain exactly how the force is linked to the motion • Newton’s Laws provide this link

  30. Newton’s Laws of Motion Section 2.4 The laws are three separate statements about how things move Newton’s First Law is a statement about inertia Newton’s Second Law gives the link between motion and forces Newton’s Third Law explains where forces come from

  31. Newton’s First Law Section 2.4 • If the total force acting on an object is zero, the object will maintain its velocity forever • If the total force is zero, the object will move with a constant velocity • Constant velocity means the same speed and in the same direction • Remember velocity is a vector

  32. Inertia and Mass Section 2.4 • Inertia is a measure of an object’s resistance to changes in its motion • This resistance to change depends on the object’s mass • The mass of an object is a measure of the amount of matter it contains • SI unit of mass is kg • Mass is an intrinsic property of an object • It is independent of the object’s location • It is independent of the object’s velocity or acceleration

  33. Newton’s Second Law Section 2.4 • In many situations, several different forces act on an object simultaneously • The total force on the object is the sum of these individual forces, • The acceleration of an object with mass m is then given by: • Newton’s Second Law is the link between force and motion • It tells us how an object will move when acted upon by a force or a collection of forces

  34. Newton’s Second Law, cont. • The acceleration of an object is directly proportional to the total force that acts on it. • Alternative statement • Remember forces are vectors so you need vector addition techniques • The direction of the acceleration is parallel to the sum of the forces Section 2.4

  35. Force Units Section 2.4 The SI unit of force is the newton (N) Deriving the newton unit: Newton’s Second Law has many applications

  36. Falling Object (Example 2.8) • The velocity graph is found from the position-time graph • Slopes at various points to define velocity points • The acceleration graph is found from the velocity-time graph • The acceleration is constant and negative • The force is negative and is proportional to the acceleration Section 2.4

  37. Directions • The direction of the acceleration is always parallel to the direction of the total force • The velocity and the total force do not need to be in the same direction • Example • Initial velocity is upward • The total force is downward • The acceleration is downward

  38. Newton’s Third Law • When one object exerts a force on a second object, the second object exerts a force of the same magnitude and opposite direction on the first object • Often called the action-reaction principle • Example • Force on ball • Force on bat Section 2.4

  39. Newton’s Third Law Consequences • Forces come in pairs • The two forces are always equal in magnitude and opposite in direction • The forces act on different objects • Person exerts a force on the refrigerator • The refrigerator exerts a force on the person Section 2.4

  40. Using Newton’s Laws Section 2.4 • Newton’s Second Law • Tells about an object’s acceleration • Looks at forces acting on one object • Accounts for all the forces acting on the object • Newton’s Third Law • Forces always come in pairs • For a force acting on one object, there must be a corresponding reaction force acting on another object

  41. Using Newton’s Laws, Example • Multiple forces act on the cell • The force the cell exerts on the water is equal and opposite to the force the water exerts on the cell • For Newton’s Second Law, you need to find the total force acting on the cell Section 2.5

  42. Laws of Nature Section 2.6 Ideas and theories can eventually lead to the discovery of a “law” of physics The process by which Newton’s Law came to be used to illustrate this

  43. Before Newton Section 2.6 • Aristotle’s Laws of Motion • For a long time, were the “Laws of Physics” • Didn’t explain some important observations • Galileo’s work on motion and ideas of inertia • Trying to explain the discrepancies in Aristotle’s Laws

  44. Newton Section 2.6 Likely tested his ideas (hypotheses) by comparing their predictions with experiments by Galileo and others Reworked ideas until they described motion of everything studied up to his time Laws applied to celestial motion as well as terrestrial motion Others used the Laws to make predictions that could be tested

  45. After Newton Section 2.6 • Newton’s Laws do not cover all areas involved with matter and energy • Found Newton’s Laws work in the classical regime • Wide range of phenomena • Break down in the quantum regime • The area of electrons, protons and neutrons • Newton’s Laws don’t tell us anything about energy

  46. Laws of Nature, Final All the presently known laws of physics are known to fail or to be inadequate in some regime or another A law of physics must correctly describe all behavior in a particular regime of nature Newton’s Laws provide an accurate description of all motion in the regime of classical physics

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