Chapter 1: The laws of motion, Part I First two chapters: Introduce the “language of physics”

1. Chapter 1: The laws of motion, Part I First two chapters: Introduce the “language of physics” Subsequent chapters: Explore objects and underlying physical concepts • Reading assignment for today: Chapter 1.2 • Also purchase book, lab manual and i-clicker (or REEF) • Homework 1.2: • due Thursday, Jan. 24 in class: • Exercises: 14, 15, 18, 19 • Problem: 3, 4, 5, 6, 7

2. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SUNDAY PHY110 TUTOR SESSIONS (Hours to come soon) The tutors: Daniel Vickers, Martin Gamer, Ray Clark, Dizhou Wu, Lucas Tommervik The tutor sessions in semesters past were successful and received high marks from many students. All students are encouraged to take advantage of this opportunity. Tutor sessions will last two hours. Time/room to be announced. Private tutors are also available: see Kittye McBride in department office (Olin 100)

3. Chapter 1.2 Falling balls: Concepts Demos and Objects Gravity Weight Everything falls at the same rate Symmetry of up and down motion Vector components Falling balls Two falling balls Throwing balls Shooting a falling apple (target)

4. i-clicker question-1: • Suppose that I throw a ball upward into the air*. After the ball leaves my hand, • there is a force pushing the ball upward. • there is a force pushing the ball downward. • there is no force acting on the ball. • it moves at constant velocity. * We are ignoring friction, drag, buoyant force

5. Observations About Falling Balls • A dropped ball: • Begins a rest, but soon acquires downward speed • Covers more and more distance each second • A tossed ball: • Rises to a certain height • Comes briefly to a stop • Begins to descend, much like a dropped ball  There is a _________ force acting on the ball!

6. i-clicker question-2: You are throwing a ball straight up in the air. At the highest point, the ball’s velocity and acceleration are zero. velocity is nonzero but its acceleration is zero. acceleration is nonzero, but its velocity is zero. velocity and acceleration are both nonzero.

7. Brief Aside: Gravity and Newton’s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force of: G… Gravitational constant G = 6.673·10-11 N·m2/kg2 m1, m2…masses of particles 1 and 2 r… distance separating these particles • On earths surface: • Gravity creates a downward force on any object. • Object attracted directly to towards the center of the earth. • Gravitational force is equal to the objects weight. Weight = F = m·g

8. Mass, weight and gravity from a physicists point of view • The mass of an object, m, does not change. It is measured in kilogram. • The weight of an object is given by W = m·g, • g: acceleration due to gravity • m: mass of the object • Weight is a force! • Gravity: attractive force between two objects. • (mainly between the earth and objects on earth) On earth: g = 9.8 m/s2 On the moon: g = 1.6 m/s2

9. A Falling Ball • Falling ball accelerates steadily downward • Its acceleration is constant and downward • Its velocity increases in the downward direction • Falling from rest (stationary): • Velocity starts at zero and increases downward • Altitude decreases at an ever faster rate

10. How can we quantitatively describe motion? Motion with constant acceleration 1. Velocity: Velocity = starting velocity + acceleration x time v = v0 + a • t 2. Position: Position: x = x0 + v0 t + 1/2 a • t2 x0… starting position v0… starting velocity

11. A dropping ball Quantitatively: 1. Acceleration is constant a = g = - 9.8 m/s2 2. Velocity increases v = v0 + g•t But v0 = 0 because ball released from rest so v = - 9.8m/s2 • t 3. Position changes rapidly x = x0 + v0t + 1/2 gt2 with x0 = 0 and v0 = 0 we have x = 0.5•(-9.8m/s2) •t2

12. Black board examples • If it takes you 1.4 s to reach the water from a 10 m platform, how fast will you go just before you enter the water? • How far will you fall during a 5-second free fall?

13. A Falling Ball, Part 2 • A falling ball can start by heading upward! • Velocity starts in the upward direction • Velocity becomes less and less upward • Altitude increases at an ever slower rate • At some point, velocity is momentarily zero • Velocity becomes more and more downward • Altitude decreases at ever faster rate

14. i-clicker question-3: You have the ability to throw a rock with a speed of 30 m/s (67 mi/h). In order to break the ice of a pond, do you throw the rock up or down?* a. Straight up b. Straight down c. Doesn’t matter * We are ignoring friction, drag, buoyant force, same release height

15. Throwing a ball upward Note that the up and down motions are symmetric!! It takes the same time to go up as it does to come back down.

16. Throwing a ball straight up and down Going down Going up

17. Throws and Arcs • Gravity only affects vertical motion • A ball can coast horizontally while falling vertically

18. Bouncing Balls: Same Time up as Down

19. Vertical and horizontal components of a vector (velocity, acceleration, force, …)

20. The vertical velocity gets smaller as the horizontal component gets larger

21. i-clicker question-4: i-clicker question-4: • An apple drops at the same time a shot is fired. Do we aim • At the target? • Above the target? • Below the target?

22. i-clicker question-5: Dropping balls • Which ball will hit the ground first? • Straight drop • Straight out • Both at the same time