Quick Review Equations of Kinematics

Free Fall Quick Review Drop a stone from top of 50 m building How long to hit the ground? Uniform acceleration g = -9.8 /s2 Distance y = -50 m y = vot + ½ gt2 -50 m = 0 + ½ (-9.8 m/s2)t2 t2 = t = 3.19 s

Quick Review An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. At which point of the trajectory is the arrow’s acceleration the greatest? The least? Ignore air resistance; the only force acting is gravity. A B C D E All the same Answer: Same at all points.

2 Falling Balls Time spent in air depends on vertical motion! Which will hit the ground first? https://www.youtube.com/watch?v=zMF4CD7i3hg around 1 minute in

Train Demo A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A) Forward of the center of the car B) At the center of the car C) Backward of the center of the car https://www.youtube.com/watch?v=nAifrGXkE2k correct Do x(t) for cart and ball. Show they are the same. vtrain car Ball and car start with same x position and x velocity, Since ax = 0 they always have same x position. 5

vtrain car 6

Projectile Motion & Frames of Reference Time spent in air depends on vertical motion! 7

Projectile Motion Horizontal Vertical Boring = Nothing going on 8

Field Goal Example A field goal kicker can kick the ball at 26 m/s horizontally and 15 m/s vertically. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y x 3 m D y-direction voy = 15 m/s y = yo + voyt + ½ at 2 3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2 t = 2.8 s or t = 0.22 s. x-direction vox = 26 m/s D = xo + vox t + ½ at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2 = 72.8 m http://www.chicagomag.com/Chicago-Magazine/November-2006/How-to-Kick-a-Field-Goal-Robbie-Gould-Style/ 74-90 mph is initial velocity Bob Thomas, now a justice on the Illinois Supreme Court, shares the team record for the longest field goal. He nailed a 55-yarder against the L.A. Rams in 1975. 10 feet high http://www.youtube.com/watch?v=VvT9wvWHFM8 70 yard practice 9

A destroyer simultaneously fires two shells with the same initial speed at two different enemy ships. The shells follow the trajectories shown. Which ship gets hit first. Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time correct 10

1.7 The Components of a Vector

SOH CAH TOA

Kinematics Descriptions of motion Relationships between position & time Equations only; no causes

Causes and Rules for Motion Laws of Motion Causes and Rules for Motion

Laws of Motion Aristotle Galileo Newton

Aristotle Celestial & terrestrial motion different Falling & horizontal motion different Objects had “natural” motion Celestial: circles Terrestrial: at rest

Aristotle Horizontal motion Speed result of balance between Propulsion Resistance Movement requires a Mover (all motion)

Aristotle Falling motion Arranged by weight (as shown) Elements Fire Air Water Earth

Galileo Starts ball rolling (literally) to modern view of motion Was a premier experimentalist 1st experimental physicist Used models that simplified problem

Galileo Horizontal motion Inclined plane to study motion Inertia Smaller angle of plane --> further ball rolls Angle zero --> ball rolls forever? Rolling ball rolls unless something affects rolling Inertia Moving object keeps moving unless disturbed “natural state” is no change in motion

Galileo Falling motion Used inclined plane to slow down falling During equal time periods falling body increases speed by equal amounts Acceleration Falling bodies accelerate

Galileo Falling motion Couldn’t create vacuum Increased density of medium Compared rates of fall of heavy/light object Greater density --> different rates Medium w/o resistance (vacuum) All bodies fall with same acceleration

Galileo Same laws falling & horizontal motion Unification Acceleration key to falling motion Same rate for all bodies w/o resistance Inertia Motion doesn’t change w/o influence No natural motion Superposition

Newton’s Laws of Motion A body at rest tends to remain at rest, and a body in motion tends to remain in motion at a constant velocity, unless acted on by an outside force Defines inertia: resistance to change What happens when net force is zero Mass is measure of inertia (kilogram)

Newton’s Laws of Motion The time rate of change of momentum of a body is proportional to the outside force acting on the body, and is in the direction of the outside force Defines Force F = ma F is resultant force F = 0 equilibrium a  F a  1/m Unit is Newton (N)

Newton’s Laws of Motion For every action there is an equal and opposite reaction Forces always exist in pairs Single force can’t exist Action-reaction pairs work on different objects Momentum conserved