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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 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) • objects moving near the speed of light
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
Force as vector • Magnitude + Direction • Components Fx, Fy • Units: Newton (N), pound(lb) • 1lb=4.45N y q x
Addition of Forces • Tail-to tip method • Parallelogram method • Components method
Examples • Parallel forces • F1=150N, F2=100N and 53° to F1
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
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
Inertia • Is the tendency of an object to continue in its original motion
Mass • A measure of the resistance of an object to changes in its motion due to a force • Scalar quantity • SI units are kg
Condition for Equilibrium • Net force vanishes • No motion
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
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
Sir Isaac Newton • 1642 – 1727 • Formulated basic concepts and laws of mechanics • Universal Gravitation • Calculus • Light and optics
Weight • Falling object • Weight w=mg • Object on a table?
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
More about weight • Weight is not an inherent property of an object • mass is an inherent property • Weight depends upon location
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
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
Example: Force Table Three forces in equilibrium! Find tension in each cable supporting the 600N sign
Examples • Calculate the acceleration of the box • A 50 kg box is pulled across a 16m driveway
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
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
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
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
Some Details About the Rules • Horizontal motion • vx =vxo =vo coso • x = xo+vxot • This is the only operative equation in the x-direction since there is uniform velocity in that direction
More Details About the Rules • Vertical motion-- free fall problem • vy=vosino-gt • y=yo+ (vosino)t-(1/2)gt2 • the positive direction as upward • uniformly accelerated motion, so the motion equations all hold
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
Example • Superman hits a home run with vo=15m/s and o=60°
Some useful results • Trajectory • Maximum Height • Range
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?