Warm Up The graph below is a plot of position versus time. For which labeled region is the velocity positive and the acceleration negative? (A) A (B) B (C) C (D) D (E) E AP PhysicsMonday 13.09.30Standards: 1)a. Students should understand the general relationships between position velocity & acceleration for a particle along a straight line. Objective: SWBAT understand where the equations of motion come from and WBAT employ them to solve problems involving falling objects. Agenda • Warm Up • Galileo Video • 3 equations of motion applied to falling objects Notes • Falling Objects Problems Homework Make up Quiz Today After School Falling Objects HW p.15 1-5,8
AP PhysicsTuesday 13.10.01Standards: Use the three equations of motion for 1D constant accelerationObjective: SWBAT verify the acceleration due to gravity and the properties of gravity using the equations of motion. Warm Up Relate to two particles that start at x = 0 at t = 0 and move in one dimension independently of one another. Graphs, of the velocity of each particle versus time are shown below. Agenda • Warm Up • Correct & Turn in HW Wednesday • Falling Objects Stations B A #1. Which particle is farthest from the origin at t = 2 seconds. A (B) B (C) they are in the same location at t = 2 seconds (D) They are the same distance from the origin, but in opposite directions (E) It is not possible to determine #2. Which particle moves with constant non-zero acceleration? A (B) B (C) both A and B (D) neither A nor B (E) It is not possible to determine #3. Which particle is in its initial position at t = 2 seconds? (A) A (B) B (C) both A and B (D) neither A nor B (E) It is not possible to determine Homework Finish Monday’s HW 1-5,8 Finish Lab Write Up
I will be gone right after school today. Retakes Extended 1 Week AP PhysicsWednesday 13.10.02Standards: 2. Motion in 2D, including projectiles: a,b vectorsObjective: SWBAT resolve displacement and velocity vectors. Warm Up An object is dropped from rest from the top of a 400 m cliff on Earth. If air resistance is negligible, what is the distance the object travels during the first 6s of its fall? a) 30 m b) 60 m c) 120 m d) 180 m e) 360m Agenda • Warm Up • Correct HW 1-5,8 • Stations #2 15 min • Stations #3 15 min Homework Finish Data and Conclusions for Station 1,2, and 3
Warm Up Linearization Graph done on the board AP PhysicsThursday 13.10.03Standards: 2. Motion in 2D, including projectiles: a,bvectorsObjective: SWBAT be able to find resultant vectors of displacement, velocity, & acceleration and break them into components. Agenda • Warm Up • AP Problems Homework Finish AP Problems
Warm Up At a certain time, an object in free fall has a velocity of 4.0 m/s in the upward direction. What is the approximate velocity of the object one second later? a) 14m/s up b) 10 m/s up c) 4.0 m/s up d) 6.0m/s down e) 10 m/s down AP PhysicsFriday 13.10.04Standards: Standards: Use the three equations of motion for 1D constant accelerationObjective: Agenda • Warm Up • Review AP Questions • Work on 2 more AP questions Homework Finish Today’s Classwork
3 equations of Motion There are three equations of motion that we use. I will derive 1&3 1 is created by combining a=Δv/Δt & Δv=v-v0 1. No Δx 2 can be found by graphing the motion of an accelerating object on a v vs t graph and finding its area. It can be derived using calculus. 2. No v 3. 3 is created by substituting equation 1 into equation 2 No t Though you will not need to derive these, these illustrate a very important practice we undertake in Physics. There are situations where we can combine multiple equations in order solve problems that don’t seem to have a solution.
How to Use the 3 equations of motion 1. The # 1 rule is to use the givens to decide which equation to use. This equation can’t find an x, so don’t use it if you are given displacement or it is an unknown This equation can’t find v, so don’t use it if you are given final velocity or it is an unknown. This equation can’t find t, so don’t use it if you are given t or it is an unknown. We will call this equation of motion #1 We will call this equation of motion #2 We will call this equation of motion #3
How to use the equations of motion day 2? 2. The # 2 rule is avoid quadratics! If one of your givens is a v0and your unknown is t then equation 2 is going to be messy. 2a.Right now try to solve for t using: Δx=10m,Vo=20m/s,a=-9.8m/s2 2b.You can avoid this process by using equation 3 then equation 1. Now try solving the same problem using equation 1 & 3. 3. Remember what they are useful for. These equations work within the context of uniformly accelerated motion or constant acceleration. This includes no acceleration
Falling Objects & Equations of Motion • When objects fall they accelerate. There are only slight differences between the motion of falling objects and the motion of objects on the ground that speed up and slow down. • If we assume that gravity is the only force acting on an object then our acceleration becomes a given and a constant called g. g=9.8m/s2 • In general when an object is falling towards the ground acceleration in the motion equations is written a=-g. • Also the displacement is no longer horizontal x but vertical y. • From there we have the option of rewriting the equations of motion to apply specifically to falling objects.
Falling Objects Example #6 p.15 – The Westin Stanford Hotel in Detroit is 228 m tall. If a worker on the roof drops a sandwich, how long does it take the sandwich to hit the ground, assuming there is no air resistance? How would air resistance affect the answer?
Falling Objects Lab Stations Be sure to collect all data in class. You may analyze the data and calculate at home if necessary. Justify all of your conclusions with actual data. Station 1: A falling Marble. You will first make the appropriate calculation to predict the time it will take for the marble to fall. Then you will actually time it and find the % error between your calculation and your measurement. Station 2: What is gravity? By measuring the the time it takes for a golf ball to fall at different heights make a linear graph and find the slope of the graph for an accurate value of g. Find the % error. g=9.807m/s2 use significant figures Station 3:How does gravity work? Directions: Drop the following objects and time how long it takes them to fall to the ground. Does shape matter? Does size matter? Use what you know about gravity to make sense of what you observe. Once you have collected data write a paragraph explaining the physics of falling objects to the best of your ability. a. How does gravity affect a marble and a golf ball? b. How does gravity affect a piece of paper vs. a book? Can you find a way to make paper and a book fall at the same rate? c. Compare a large cylinder and a small cylinder. Does the orientation of the cylinder affect your result?
Kinematic Vector Practice Classwork 3: Resultant Vectors 1. 2. 3. 4. 5.
Breaking Vectors into Components • x component = horizontal component (left to right) • y component = vertical component (up and down) • If you have a vector, you have a quantity that has a magnitude (size) and a direction. s is a general way to right length or displacement. • In order to solve problems involving vectors, we benefit greatly by breaking them into components. • In 2 dimensional physics the components are x and y • In 3 dimensional physics the components are x, y, and z. • We will use 2 dimensions x and y. s=4m θ=30°
Breaking vectors into Components When you break vectors into components they are written using the following form: and are called unit vector. They have a magnitude of 1 and their sole purpose is to denote direction. means the vector component is in the horizontal direction means the vector component is in the vertical direction. s=4m y θ=30° x cos30=x/4m x=cos30(4m)Î x=3.46mÎ sin30=y/4m y=sin30(4m)Ĵ y=2mĴ