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**PHYSICS UNIT 2: DYNAMICS (Explaining Motion)**

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**FORCES Force: a "push" or a "pull“**

unit: Newtons, N (1 N is about ¼ lb) vector - includes direction contact forces and field forces (act over a distance) net force: total effect of all forces acting on an object

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FORCES Typical Forces gravity, FG: object’s weight, always directed toward center of earth (FG=mg mass × acceleration due to gravity) normal force, FN: supporting force a surface exerts on an object, always directed upward perpendicular to the surface tension, FT: force transmitted by a rope or chain, directed along the rope, constant throughout the rope

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FORCES Free body diagrams: show just one object & the forces acting on the object (NOT forces the object is exerting on other things) example: car hitting a wall

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**Examples Apple on a table Rock under water Block on a hill Water skier**

Child pulled forward at an angle on a sled

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**NEWTON’S LAWS OF MOTION**

The Law of Inertia (1st Law): an object’s velocity stays constant unless acted upon by a net external force inertia: resistance to change in motion (mass is a measure of inertia, more mass = more inertia)

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**Example of Newton’s 1st Law**

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**NEWTON’S 2nd LAW OF MOTION**

The Law of Acceleration (2nd Law): a net force causes an acceleration proportional to the force, in the same direction, and inversely proportional to mass. Fnet = ma Fnet: sum of all forces or net force (N), m: mass (kg), a: acceleration (m/s2) 1 N = 1 kg·m/s2

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**NEWTON’S 2nd LAW OF MOTION**

Second The greater the force, the greater the acceleration The greater the mass, the greater the force needed for the same acceleration Calculated by: F = ma (F = force, m = mass, a = acceleration)

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**NEWTON’S 3rd LAW OF MOTION**

The Law of Interaction (3rd Law): for every action force from one object on another, there is an equal magnitude, opposite direction reaction force from the 2nd object back on the 1st action: hammer hits anvil reaction: anvil hits hammer

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**NEWTON’S 3rd LAW OF MOTION**

Law of Interaction (3rd Law) action & reaction forces do not balance each other - they are on different bodies (ex: car pulling a trailer) equal force does not mean equal acceleration - depends on mass (ex: person jumping off the ground)

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**Examples of Newton’s 3rd law**

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**FORCES Finding the Net Force (total of all forces on an object)**

draw a free body diagram identify & label x & y axes separate forces into x and y parts – Fx=Fcosq Fy=Fsinq add all x forces, add all y forces equilibrium: no net force – x forces add up to zero, y forces add up to zero

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Example

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LAB 2.3 – Elevator Scene 1

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LAB 2.3 – Elevator Scene 2

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LAB 2.3 – Elevator Scene 3

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LAB 2.3 – Elevator Frame 1

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LAB 2.3 – Elevator Frame 2

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LAB 2.3 – Elevator Frame 3

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LAB 2.3 – Elevator Frame 4

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LAB 2.3 – Elevator Frame 5

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LAB 2.3 – Elevator Frame 6

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LAB 2.3 – Elevator Frame 7

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QUIZ 2.1 Joe rolls a ball down a hill. The ball has a mass of kg. The force pulling the ball down the hill is 6.00 N. The hill is m long. (a) What is the ball’s acceleration? (b) How fast is the ball going at the bottom of the hill, if it started at rest at the top? (c) If the force on the ball doubled, what would happen to the ball’s acceleration? (d) If instead the mass of the ball doubled, what would happen to its acceleration? 12.0 m/s2 49.0 m/s doubles (24 m/s2) halves (6 m/s2)

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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**NEWTON’S LAWS OF MOTION**

Law of Inertia (1st Law) objects slow & stop, or require continued force to keep moving, due to friction

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FRICTION Friction Force, Ff: resistance to motion between objects in contact with each other acts parallel to contact surface, opposite to motion caused by uneven surfaces, molecular attraction

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**FRICTION static friction: resistance to starting motion (at rest)**

kinetic friction < static friction static friction: resistance to starting motion (at rest) beneficial (walking, building, eating, wheels rolling) kinetic friction: resistance to continued motion (sliding) undesirable (machines, moving furniture, wheels skidding)

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FRICTION coefficient of friction, m: constant that depends on type of surfaces in contact ms: coefficient of static friction mk: coefficient of kinetic friction Ff = mFN (friction force = m × normal force)

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FRICTION

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**FRICTION FN Ff mg on horizontal surface: FN = mg**

(normal force = body weight) so Ff = mmg

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**FN Ff mg mgcosq q FRICTION on tilted surface: FN = mgcosq**

so f = mmgcosq

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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QUIZ 2.2 A 1200 kg car sits on a horizontal road. (a) How much force does Joe need to push the car at a constant speed if the coefficient of kinetic friction is 0.600? (b) How much will the car accelerate if Joe uses a force of 10,000 N? a) 7060 N b) 2.45 m/s2

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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**PROJECTILE MOTION Projectile motion: parabolic trajectory (path)**

Two dimensions of motion: horizontal (x), vertical (y) vy q v vy = vsinq vx vx = vcosq

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**PROJECTILE MOTION Vertical Motion**

if a bullet was fired horizontally, and another bullet was dropped from the same height at the same time, which would hit the ground first? constant vertical acceleration due to gravity (2nd Law)

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PROJECTILE MOTION A monkey hangs from a tree branch. A hunter aims his tranquilizer gun barrel straight at the monkey. When the hunter fires his gun, should the monkey keep holding on to the branch, or let go?

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**PROJECTILE MOTION Vertical Motion position: y = h + visinqit – ½gt2**

a. for ground launch, h=0, y = visinqit – ½gt2 b. for horizontal cliff launch, q0=0, y = h – ½gt2 speed: vy = visinqi – gt flight time, T: t when y=0 ground: cliff:

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**PROJECTILE MOTION Horizontal Motion**

A tank moving at constant speed fires a shell straight up into the air. Where will the shell come back down? constant horizontal speed due to no horizontal force (1st Law)

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PROJECTILE MOTION A snowmobile fires a flare, then slows down. Where does the flare land? If the snowmobile speeds up instead, where does the flare land?

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**PROJECTILE MOTION Horizontal Motion position: x = vicosqit**

for horizontal cliff launch, qi=0, x = vit speed: vx = vicosqi range, R: x when t = T ground: cliff:

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PROJECTILE MOTION Example: A projectile is launched from ground level with a velocity of 50 m/s at an angle of 30 degrees. What is its position and velocity 2 seconds later? What is its flight time? What is its range?

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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**RELATIVE MOTION Reference Frames: A plane moving at constant speed**

drops a flare. Describe the path of the flare. Reference Frames: projectile motion in one reference frame can be vertical free fall in another reference frame (and vice versa)

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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**QUIZ 2.3 Circle your answers! Watch sig. fig's & units!**

1. Joe throws a ball from ground level at an angle of 41º and a speed of 19 m/s. (a) Find the ball's vertical position after 1.5 seconds. (b) Find the ball's horizontal speed after 1.5 seconds. 2. Jane throws a ball off a 95-m tall building horizontally at 19 m/s. (a) Find the ball's flight time. (b) Find the ball's range. y = h + visinqit – ½gt vy = visinqi – gt x = vicosqit vx = vicosqi 7.67 m 14.3 m/s 4.40 s 83.6 m

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**UNIT 2: DYNAMICS (Explaining Motion)**

PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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**UNIT 2 REVIEW Newton's Laws (Memorize!):**

1st Law: velocity stays constant unless acted upon by a net force 2nd Law: net force = mass x acceleration 3rd Law: for every action force, there is an equal and opposite reaction force

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**UNIT 2 REVIEW SF = ma FG = mg Ff = mFN vf = vi + at Dx= vit + ½at2**

vf2=vi2 + 2aDx y = h + visinqit – ½gt2 x = vicosqit vy = visinqi – gt vx = vicosqi

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