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Chapter 4

Chapter 4. Force; Newton’s Laws of Motion. Classical Mechanics. Describes the relationship between the motion of objects in our everyday world and the forces acting on them Conditions when Classical Mechanics does not apply very tiny objects (< atomic sizes)

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Chapter 4

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  1. Chapter 4 Force; Newton’s Laws of Motion

  2. Classical Mechanics • Describes the relationship between the motion of objects in our everyday world and the forces acting on them • Conditions when Classical Mechanics does not apply • very tiny objects (< atomic sizes) • objects moving near the speed of light

  3. Forces • Usually think of a force as a push or pull • Vector quantity • May be a contact force or a field force • Contact forces result from physical contact between two objects: pushing, pulling • Field forces act between disconnected objects • Also called “action at a distance” • Gravitational force: weight of object

  4. Contact and Field Forces

  5. Force as vector • Magnitude + Direction • Components Fx, Fy • Units: Newton (N), pound(lb) • 1lb=4.45N y q x

  6. Addition of Forces • Tail-to tip method • Parallelogram method • Components method

  7. Examples • Parallel forces • F1=150N, F2=100N and 53° to F1

  8. Newton’s First Law • An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force • The net force is defined as the vector sum of all the external forces exerted on the object

  9. External and Internal Forces • External force • Any force that results from the interaction between the object and its environment • Internal forces • Forces that originate within the object itself • They cannot change the object’s velocity

  10. Inertia • Is the tendency of an object to continue in its original motion

  11. Mass • A measure of the resistance of an object to changes in its motion due to a force • Scalar quantity • SI units are kg

  12. Condition for Equilibrium • Net force vanishes • No motion

  13. Newton’s Second Law • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. • F and a are both vectors

  14. Units of Force • SI unit of force is a Newton (N) • US Customary unit of force is a pound (lb) • 1 N = 0.225 lb

  15. Sir Isaac Newton • 1642 – 1727 • Formulated basic concepts and laws of mechanics • Universal Gravitation • Calculus • Light and optics

  16. Weight • Falling object • Weight w=mg • Object on a table?

  17. Weight • The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object • w = m g is a special case of Newton’s Second Law • g is the acceleration due to gravity • g can also be found from the Law of Universal Gravitation

  18. More about weight • Weight is not an inherent property of an object • mass is an inherent property • Weight depends upon location

  19. Newton’s Third Law • If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. • Equivalent to saying a single isolated force cannot exist

  20. Newton’s Third Law cont. • F12 may be called the action force and F21 the reaction force • Actually, either force can be the action or the reaction force • The action and reaction forces act on different objects

  21. Example: Force Table Three forces in equilibrium! Find tension in each cable supporting the 600N sign

  22. Examples • Calculate the acceleration of the box • A 50 kg box is pulled across a 16m driveway

  23. Projectile Motion(Ch. 5) • Example of motion in 2-dim • An object may move in both the x and y directions simultaneously • It moves in two dimensions • The form of two dimensional motion we will deal with is called projectile motion • vo and o

  24. Assumptions of Projectile Motion • We may ignore air friction • We may ignore the rotation of the earth • With these assumptions, an object in projectile motion will follow a parabolic path

  25. Rules of Projectile Motion • The horizontal motion (x) and vertical of motion (y) are completely independent of each other • The x-direction is uniform motion • ax = 0 • The y-direction is free fall • ay = -g • The initial velocity can be broken down into its x- and y-components

  26. Projectile Motion

  27. Projectile Motion at Various Initial Angles • Complementary values of the initial angle result in the same range • The heights will be different • The maximum range occurs at a projection angle of 45o

  28. Some Details About the Rules • Horizontal motion • vx =vxo =vo coso • x = xo+vxot • This is the only operative equation in the x-direction since there is uniform velocity in that direction

  29. More Details About the Rules • Vertical motion-- free fall problem • vy=vosino-gt • y=yo+ (vosino)t-(1/2)gt2 • the positive direction as upward • uniformly accelerated motion, so the motion equations all hold

  30. Velocity of the Projectile • The velocity of the projectile at any point of its motion is the vector sum of its x and y components at that point • Remember to be careful about the angle’s quadrant

  31. Example • Superman hits a home run with vo=15m/s and o=60°

  32. Some useful results • Trajectory • Maximum Height • Range

  33. Example A daredevil jumps a canyon 15m wide by driving a motorcycle up an incline sloped at an angle of 37° with the horizontal. What minimum speed must she have in order to clear the canyon? How long will she be in the air?

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