Lecture 3 Chapter 3 Linear Motion (Motion in a straight line, such as falling straight downward) Some material courtesy Prof. A. Garcia, SJSU Help sessions Announcements M 1600-1700 in TH116 (A. Kelly) M 1700-1900 in TH116 (D. Lim) T 1600-1700 in TH118 (Z. Hadley) W 1510-1600 in TH230 (J.M. Lockhart) Course web page www.physics.sfsu.edu/~lockhart/courses/phys101.html 1
Concepts you ll learn today Speed and Velocity Acceleration Relationships among distance, velocity, and acceleration. Falling motion. Reference Frames Every measurement must be made with respect to a reference frame. Usually, speed is relative to the Earth. 2
Average Speed The average speed (SI unit: m/s) is defined as the distance traveled divided by the time the trip took: Average speed = distance / elapsed time Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h? Could average speed ever be negative? Average Speed Other common speed units: miles/h; km/h For example, 30 miles per hour means object travels distance of 30 miles in an elapsed time of one hour. Write as, 30 miles per hour = 30 miles hour 3
Speed and Distance From definition of speed, (Distance traveled) = (Avg. Speed) (Time elapsed) Example: If average speed is 30 mi/h and time elapsed is 2 hours then distance traveled is (30 mi/h) (2h) = 60 miles. Match units: This time elapsed is also 120 minutes but it s not correct to compute distance traveled as (30mi/h) (120min) = 3600 miles {WRONG}. Check Yourself What is the average speed of a cheetah that sprints 100 meters in 4 seconds? How about if it sprints 50 meters in 2 seconds? A car has an average speed of 100 kilometers per hour. How far does it travel in 60 minutes? 4
Average versus Instantaneous Sometimes consider average speed, other times we speak of instantaneous speed. For example, say it takes you one hour to drive the 30 miles from home to campus. Average speed is 30 miles per hour. Instantaneous speed (given by your speedometer) varies due to traffic, stop lights, morons driving in front of you, etc. Check Yourself A car has an average speed of 60 miles per hour. Is it possible for the instantaneous speed to always be less than 60 miles per hour? 5
Velocity (v) Velocity v is speed and direction of object s motion. Examples: 30 miles per hour, Northward 25 meters per second, Downward 300 miles per hour, Coming towards you - 30 m/s 25 m/s, upward 25 m/s, downward Same speeds Different velocities Check Yourself The speedometer of a car moving east reads 100 km/h. It passes another car moving west at 100 km/h. Do they have same speed? Velocity? During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? Constant velocity? 6
Discussion Questions 1. A yellow car is heading East at 100 km/h and a red car is going North at 100 km/h. Do they have the same speed? Do they have the same velocity? 2. A 16-lb bowling ball in a bowling alley in Del Mar heads due north at 10 m/s. At the same time, a purple 8-lb ball heads due north at 10 m/s in an alley in La Jolla. Do they have the same velocity? Changes in Velocity Velocity changes if speed or direction of motion change. Velocity changes in both these cases. 10 m/s, downward 25 meters per second, 45 degrees upward 25 m/s, downward 25 meters per second, 45 degrees downward 7
(Average) Acceleration (a) Changing velocity means an acceleration a is present. There is acceleration if either the magnitude or the direction of the velocity changes. Average acceleration is the rate of change of the velocity r r r r v v f v i a average = = t t SI acceleration units: (m/s)/s = m/s 2 Average acceleration is a vector quantity (i.e. described by both magnitude and direction). In 1-Dim., can use + or - to indicate direction. Acceleration in 1-Dim Average acceleration (+ and - for direction): 8
Average & Instantaneous Acceleration Define average acceleration as, AVG. ACCELERATION = (Change in Velocity) (Time interval) Instantaneous acceleration is how fast velocity is changing at an instant in time Note: An object accelerates anytime its velocity changes. Examples include: Object speeds up. Object slows down (speed decreases). Object speed constant but direction changes (curved path) Conceptual Question 1. Velocity & acceleration are both vectors. Are the velocity and the acceleration always in the same direction? If the object is slowing down, the acceleration vector is in the opposite direction of the velocity vector! 9
Example Deceleration Deceleration : A word meaning slowing down. We try to avoid using it in physics. Instead (in one dimen.) talk about positive & negative acceleration. This is because (for one dimen. motion) deceleration does not necessarily mean the acceleration is negative! a 10
Conceptual Question 2. Velocity & acceleration are vectors. Is it possible for an object to have a zero acceleration and a non-zero velocity? If the object is moving at a constant velocity, the acceleration vector is zero! Conceptual Question 3. Velocity & acceleration are vectors. Is it possible for an object to have a zero velocity and a non-zero acceleration? If the object is instantaneously at rest (v = 0) but is either on the verge of starting to move or is turning around & changing direction, the velocity is zero, but the acceleration is not! 11
Acceleration is a Vector Direction of acceleration = direction in which velocity changes Accel. in same direction as velocity speed increases Accel. in direction opposite to velocity speed decreases Accel. at right angles to velocity direction changes Example: An unexpected shove from the side as you run straight down a hallway might send you careening into the wall. Can you feel if you re moving with a constant velocity? Can you feel being accelerated? Why? Free Fall Objects moving under the influence of only the force of Earth gravity are said to be in free fall For free fall, air resistance (air drag) must be small enough to be ignored -- gravity must be the only force acting on the object Objects with more mass have greater weight, but also greater inertia. These two effects cancel out, so all objects in free fall have the same constant acceleration. 12
Acceleration Due to Gravity All objects in free fall near the earth s surface fall downward with a constant acceleration of size g = 9.80 m/s 2 10 m/s 2 (called the acceleration due to gravity) g is always directed downward toward the center of the earth At San Francisco g = 9.80 m/s 2. If upward is designated as the positive direction, then a = -g. (Note that g is always a positive number, but a may have either sign.) Falling Objects in Air Falling Objects in Air An object falling in air is subject to air resistance (and thus is not freely falling). Amount of air resistance depends on shape & size. 13
Velocity in Free Fall (Down) How fast do objects go when they fall? Acceleration due to gravity is 9.8 10 meters per second per second. With each second of fall, speed increases by 10 meters/second Release 1 second 2 s 3 s 4 s Zero m/s. 10 m/s 20 m/s 30 m/s. 40 m/s Velocity in Free Fall (Up & Down) Moving upward, with each second the speed decreases by 10 meters/second. Going back down the motion exactly reverses itself. See Fig. 3.8 (pg. 43) Zero m/s 10 m/s 20 m/s 30 m/s 40 m/s 14
Position in Free Fall How far do objects go when they fall? More complicated because speed is increasing. There s a pattern & Galileo figured it out. But it wasn t easy. Release 1 s 2 s 3 s 5 m 20 m 45 m 4 s 80 m Position in Free Fall (cont.) Galileo realized that: Distance Fallen = [½ (Acceleration)(Time)](Time) Gravity acceleration is 10 meters per second per second, so at a time of 3 seconds, Distance Fallen = ½ (10m/s 2 )(3s)(3s) = 45 m Release 1 second 2 seconds 3 s 5 meters 20 meters 45 m 4 seconds 80 meters 15
Demo: Dropping the Ball How long does it take a ball to fall 3 meters? Using the formula, Distance Fallen = d = ½ at 2 t 2 = 2d/a = 2(3m)/(10 m/s 2 ) = 0.6s 2 t = 0.6s 2 = 0.77 s Beauty of science: Predict, then verify by dropping balls! Demo: Catch a Buck Put thumb and index fingers near Washington s head. Can you react fast enough to catch the money? 16
Demo: Reaction Time Distance (inch) Time (s) 1 0.07 2 0.10 3 0.12 4 0.14 5 0.16 6 0.17 7 0.19 8 0.20 10 0.23 12 0.25 14 0.27 16 0.29 18 0.30 Catch Release Key Points of Lecture 3 v r avg Average Speed ( v avg ) & Velocity ( ) Instantaneous Speed ( v ) and Velocity ( v r ) Changes in velocity Definition of Acceleration ( a ) Average and Instantaneous Acceleration Free Fall acceleration (g) Velocity changes in free fall Before the next lecture, read Hewitt through first half of Chap. 4 Homework Assignment #1 (first graded assignment) is due before 11:00 PM on Thursday, Sept. 2. 17