Part One: Mechanics

Part One: Mechanics Hikers check their position using signals from GPS satellites, which are 20,000 km up & moving > 10,000 km/hr. Mechanics = Study of Motion Newtonian Mechanics = Classical Mechanics Restrictions: Size >> atom, else Quantum mechanics Speed << c, else Relativity

Chapters in Part One: Mechanics Motion in a Straight Line Motion in 2- & 3- Dimensions Force & Motion Using Newton’s Laws Work, Energy, & Power Conservation of Energy Gravity Systems of Particle Rotational Motion Rotational Vectors & Angular Momentum Static Equilibrium

2. Motion in 1-D 2.1. Average Motion 2.2. Instantaneous Velocity 2.3. Acceleration 2.4. Constant Acceleration 2.5. The Acceleration of Gravity

2.1. Average Motion Kinematics = Study of motion without regard to its cause. Pizza Trip: 15 min to Pizza Hut 10 km away & back. Average speed Displacement Average velocity

Directions & Coordinate Systems Displacement x has both magnitude & direction. ( x is a vector ) Coordinate system: origin, directions, magnitudes. One dimensional (1-D) coordinate system: origin : x = 0 directions : x > 0, x < 0 magnitudes : |x|

From 台北 to 台中 : 148  308 = 160 km Normally, trip takes 1 hr  Avg vel = 160 km / h From 左營 to 台中 : 148  ( 31) = 179 km Normally, trip takes 1 hr  Avg vel = 179 km / h A man took the train from 台北 to 台中. He fell asleep and didn’t wake up till the train reached 左營. He took the next available train ½ hr later back to 台中. What’s his average velocity and average speed for the entire trip?  Avg vel  Avg speed

2.2. Instantaneous Velocity Determining velocity of lava flow xi = 2.5

Average velocity Instantaneous velocity = Velocity  = tangent of x(t)

See Appendix A (page A-5) for a list of common derivatives.

Which object is moving with constant speed? Which reverses direction? Which starts slowly & then speeds up?

Example 2.2. Space Shuttle Ascends Altitude of space shuttle for 1st half-minute: Find the velocity v(t) and from it, v at t = 20s. Find the average velocity ( x = 0, t = 0 at lift-off ) For accelerating object,

2.3. Acceleration v changes  object under acceleration Average acceleration = Instantaneous acceleration = Speeds up Slows down Mixed units: A car goes from 0 to 100 km/h in 10s :

Position, Velocity, & Acceleration a v x t t = 2.6 v = 0, x = max t = 1.2 a = 0, v= max

Conceptual Example 2.1. Acceleration Without Velocity ? Can an object be accelerating even though it’s not moving? v = 0 at top of flight Motion of a projectile constant a

2.4. Constant Acceleration Constant acceleration:  Average velocity:  

Using the Equations of Motion Example 2.3. Landing a Jetliner A jetliner touches down at 270 km / h, then decelerates at 4.5 m / s2. What’s the minimum runway length on which it can land ? Minimum runway length

Example 2.4. Speed Trap • Speeding motorist passes stationary police car at 75 km / h in a 50 km / h zone. • Police car accelerates at 2.5 m / s2 in pursuit. • When the officer catches up the speeder, • How far down the road are they? • How fast is the police car going? Speeder: Police: Catch up pos. (v in m / s) :  vp = vs (mean value theorem) Police car velocity at catch up:

2.5. The Acceleration of Gravity Free fall = motion under gravity alone. Near Earth’s surface, acceleration of gravity g 9.8 m / s2 ( Galileo 1600, Leaning tower of Pisa ). Strobe photo of falling ball.

Example 2.5. Cliff Diving A diver drops from 10-m- high cliff. 1. At what speed does he enter water? 2. How long is he in the air?

Example 2.6. Tossing a Ball • Toss ball up at 7.3 m / s. • Leaves hand at 1.5 m above floor. • When does ball hit floor? • Maximum height of ball. • Its speed passing hand on way down.

Application: Keeping Time Atomic fountain clock: Super-cold free-falling Ce atoms, tossed up by laser. (see Prob 66) NIST-F1 clock

Part One: Mechanics