Announcements :Announcements Homework for tomorrow… (Ch. 2, Problems 27 & 43) Office hours… MTWRF 11-noon


More Trig… :More Trig… Pythagorean Theorem To find an angle, you need the inverse trig function i.e. x = y = 1 What is r? ?


Chapter 2 :Chapter 2 Motion in 1D


Dynamics & Kinematics :Dynamics & Kinematics Dynamics is the study of motion and of physical concepts (i.e. relationship between force and mass) Kinematics is a part of dynamics description of motion Not concerned with the cause of the motion


Quantities in Motion :Quantities in Motion Any motion involves three concepts Displacement Velocity Acceleration These concepts can be used to study objects in motion


Section 2.1:Displacement :Defined as the change in position f stands for final i stands for initial SI units are meters (m) Section 2.1:Displacement


Displacement vs. Distance :Displacement vs. Distance Displacement is NOT the same as Distance i.e. Throw a ball straight up and then catch it at the same point you released it The distance is twice the height The displacement is zero


Vector & Scalar Quantities :Vector & Scalar Quantities Vector has magnitude & direction i.e. - instantaneous velocity - instantaneous acceleration Scalar has magnitude only


Section 2.2:Velocity :Section 2.2:Velocity Speed the total distance traveled divided by the total time elapsed Speed is a scalar quantity Average speed completely ignores any variations in the object’s actual motion


Average Velocity… :Average Velocity… the displacement divided by Units?


Speed vs. Velocity :Speed vs. Velocity Cars on both paths have the same average velocity… Why? … they have the same displacement (in the same time interval). The car on the blue path will have a greater average speed…Why? … the distance it travels is larger (in the same time interval)!


Graphical Interpretation of Velocity :Graphical Interpretation of Velocity Average velocity equals the slope of the line joining the initial and final positions (vs. time)


Position vs. Time Graphs :Position vs. Time Graphs What will the position vs. time graph look like for the following: Stand still Slow steady walk Fast steady walk How should I move to reproduce the graph on the previous slide?


Serway: Prob 2.3 :Serway: Prob 2.3 Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip wins. Which boat wins and by how much? (Or is it a tie)? What is the average velocity of the winning boat?


Section 2.3:Acceleration :Section 2.3:Acceleration the change in velocity divided by Units?


Graphical Interpretation of Average Acceleration :Graphical Interpretation of Average Acceleration Average acceleration equals the slope of the line joining the initial and final velocities (vs. time)


Quick Quiz… :Quick Quiz… Match each velocity vs. time graph to its corresponding acceleration vs. time graph.


Section 2.4: Motion Diagrams (Relationship between a and v) :Section 2.4: Motion Diagrams (Relationship between a and v) Uniform velocity What is the acceleration? a = 0


Relationship Between a and v :Relationship Between a and v v and a are in the same direction a is constant v is increasing


Relationship Between a and v :Relationship Between a and v v and a are in opposite directions a is constant v is decreasing


Section 2.5: 1D Motion w/Constant Acceleration :Section 2.5: 1D Motion w/Constant Acceleration Valid for uniform (constant) acceleration


Serway 2.36 :Serway 2.36 A car accelerates uniformly from rest to a speed of 40.0 mi/hr in 12.0 s. Find … the distance the car travels the constant acceleration of the car


Section 2.6: Freely Falling Objects :Section 2.6: Freely Falling Objects Galileo Galilei – Italian Physicist 1564 – 1642 Galileo formulated the laws that govern the motion of objects in free fall.


Demo :Demo If I drop my book and a feather, at the same time, which object will hit the ground first? Why?


Free Fall :Free Fall A freely falling object is any object moving freely under the influence of gravity alone, regardless of it’s motion Free fall does not depend on v0 !


Free Fall :Free Fall All objects fall with a constant acceleration a = -g if… … they are near the Earth’s surface. … they are affected only by gravity. (i.e. air resistance is negligible)


Acceleration due to Gravity :Acceleration due to Gravity g = 9.8 m/s2 … … is always directed towards the center of the Earth. … is a constant!


Free Fall Equations :Free Fall Equations Valid for constant gravitational acceleration


Quiz Question 1 :Quiz Question 1 A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration increase decrease increase and then decrease decrease and then increase remain constant


Quiz Question 2 :Quiz Question 2 As the tennis ball of the previous problem travels through the air, its speed increases decreases decreases and then increases increases and then decreases remains the same.


Demo :Demo Drop the rocks..


Problem 1:Peak Altitude :Problem 1:Peak Altitude An object is thrown vertically upwards with a velocity of v0. What is the maximum height reached?


Problem 2:Time of Flight :Problem 2:Time of Flight An object is thrown vertically upwards with a velocity of v0. What is the object’s velocity right before it hits the ground? What is the object’s ‘time of flight’ ?


Quiz Question 3 :Quiz Question 3 A ball is thrown vertically upwards. What is true at the top of its trajectory? It has a nonzero velocity and zero acceleration It has zero velocity and zero acceleration It has zero velocity and nonzero acceleration It has nonzero velocity and nonzero acceleration None of the above


Quiz Question 4 :Quiz Question 4 If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s2. If instead you throw it downward, its downward acceleration after release is less than 9.8 m/s2 9.8 m/s2 more than 9.8 m/s2


Serway: Prob 50 :Serway: Prob 50 A parachutist with a camera descends at a constant speed of 10 m/s. The parachutist releases the camera at an altitude of 50 m. How long does it take the camera to reach the ground? What is the velocity of the camera just before it hits the ground?