Motion—Day 4 Vertical Acceleration Pick up the handout from the front table! Motion—Day 4 Vertical Acceleration Materials Needed: Writing Utensil Folder Notebook

Day 4 Bell Work: As the ball falls from the girl’s hand, how does the speed change? What happens to the speed as the ball returns to her hand? At what points does the ball have zero velocity? Agenda: Notes on vertical acceleration Practice solving acceleration story problems Prep for free fall lab

Q1: What rock is formed from cooling magma? igneous metamorphic sedimentary weathered SC8.4.2.f DOK 1

Q2: What is a property of a gas? A. has definite shape and definite volume B. has definite shape but no definite volume C. has definite volume but no definite shape D. has no definite volume and no definite shape SC8.2.1.d DOK 1

Mathematics Booster You won a spring break trip to Cancun with the hotel, food, and entertainment paid for! The only catch is that you will have to pay for your ticket. Decide which of the following is the best deal. Delta round trip ticked at $1000. Delta one way ticket is $450 to Cancun, the ticket to Omaha is $650. What is the percentage of money you will save?

Greek and Latin Day 4 Create an original picture for each of your example words. Greek/Latin Picture -at –ation curv- dis- mot- veloc-

Objectives Day 4 I will know the difference between horizontal and vertical acceleration. I will be able to solve vertical acceleration problems. I will be able to read and interpret data and graphs.

Bell work Day 4 -- answers As the ball falls from the girl’s hand, how does the speed change? Its speed increases. What happens to the speed as the ball returns to her hand? The speed decreases. At what points does the ball have zero velocity? When it touches the girls hand and while it touches the floor.

A1: What rock is formed from cooling magma? igneous metamorphic sedimentary weathered SC8.4.2.f DOK 1

A2: What is a property of a gas? A. has definite shape and definite volume This is a solid. B. has definite shape but no definite volume A state of matter cannot have a definite shape without having a definite volume. C. has definite volume but no definite shape This is a liquid. D. has no definite volume and no definite shape A gas will take on the shape and volume of any container. SC8.2.1.d DOK 1

Mathematics Booster Answer Decide which of the following is the best deal. Delta round trip ticked at $1000. Delta one way ticket is $450 to Cancun, the ticket to Omaha is $650. ($450+ $650 = $1100) The round trip ticket is the better deal. What is the percentage of money you will save? You will save $100 or 10% $1100- $1000 = $100, 100/1000= 0.1 or 10%

1. accelerating 2. acceleration 3.curve Greek and Latin Day 4 – possible answers 1. accelerating 2. acceleration 3.curve

4. displacement 5. motion 6. velocity

Vertical Acceleration Free fall is the movement of an object toward Earth solely because of gravity. The unit for velocity is meters per second. The unit for acceleration, then, is meters per second per second. This unit is typically written as meters per second squared (m/s2). Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2.

The change in the stone’s speed is What Is Acceleration? t = 0 s v = 0 m/s Each second an object is in free fall, its velocity increases downward by 9.8 meters per second. The change in the stone’s speed is 9.8 m/s2, the acceleration due to gravity. t = 1 s v = 9.8 m/s t = 2 s v = 19.6 m/s t = 3 s v = 29.4 m/s

Final Velocity Equation for a Dropped Object Equation: vf = vi + at a = acceleration (unit m/s2) vf = final velocity (unit m/s) vi = initial velocity (unit m/s) (vi will generally be zero unless you give it an initial velocity) t = time (unit s)

Calculating Acceleration – Modeled Practice A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water?

t vi = 0 vf g = 9.8 m/s2 Givens: 2 s = What is the initial velocity? Unknown = Any time you drop something, what variable can you use? g = 9.8 m/s2 Rearranged: vf = vi + at Equation = a = vf – vi t Plug it in = Walk the students through this step by step. Have them tell you what variable to use for each number. On the answer portion: explain how one of the s in s2 is canceled out by the s on the top vf = 0 + (9.8 m/s2)(2s) Answer = vf = 19.6 m/s

Turn to a partner practice Explain a situation in which you can accelerate even though your speed doesn’t change. Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds.

Turn to a partner practice -- answer Explain a situation in which you can accelerate even though your speed doesn’t change. 2. Find the final velocity of a book dropped from cliff at a time frame of 3.8 seconds. ANSWER: A car turn a corner. (Any situation where you are changing direction.) Givens: 3.8 s = t Know: g = 9.8 m/s2 vi = 0 m/s Unknown: vf Equation: vf = vi + gt Plug in numbers: vf = 0 m/s + (9.8 m/s2)(3.8 s) Answer: 37.24 m/s

Graphs of Accelerated Motion You can use a graph to calculate acceleration. Graph speed on the vertical axis and time on the horizontal axis. The slope is change in speed divided by change in time, which is equal to the acceleration.

Let’s Practice! Graphs of Accelerated Motion The skier’s acceleration is positive. Find the acceleration (slope).

Graphs of Accelerated Motion -- answer The skier’s acceleration is positive. Find the acceleration (slope). a = vf – vi t a = 16 m/s – 0 m/s 4 s – 0 s Remind students that the acceleration equation is just like the slope of a line equation y2 – y1 over x2 – x1! a = 4 m/s2

Graphs of Accelerated Motion Speed-Time Graphs Constant acceleration is represented on a speed–time graph by a straight line. The graph is an example of a linear graph, in which the displayed data form straight-line parts.

Graphs of Accelerated Motion Constant negative acceleration decreases speed. On a speed-time graph of a bicycle slowing to a stop, a line sloping downward represents the bicycle decelerating. The change in speed is negative, so the slope of the line is negative.

Graphs of Accelerated Motion – Turn to a partner The biker moves at a constant speed and then slows to a stop. What is the biker’s constant speed? What is the biker’s deceleration?

Graphs of Accelerated Motion – Turn to a partner Answers The biker moves at a constant speed and then slows to a stop. What is the biker’s constant speed? 5 m/s What is the biker’s deceleration? 0 m/s – 5 m/s = -0.5 m/s2 20 s – 10 s

Assessment Question #1 What is acceleration? the rate at which speed increases the time an object’s velocity increases the rate at which displacement changes the rate at which velocity changes

Assessment Question #1 answer What is acceleration? the rate at which speed increases the time an object’s velocity increases the rate at which displacement changes the rate at which velocity changes ANS: D

Assessment Question #2 A sports car can accelerate from 0 m/s to 28 m/s in four seconds. What is the acceleration of the car? 24 s 7 m/s 27 m/s 32 m/s

Assessment Question #2 -- answer A sports car can accelerate from 0 m/s to 28 m/s in four seconds. What is the acceleration of the car? 24 s 7 m/s 27 m/s 32 m/s ANS: B

3. Which of the following is an example of negative acceleration? Assessment Question #3 3. Which of the following is an example of negative acceleration? Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h. Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h. Mike sits on his bike at the top of the hill and rests. Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h.

Assessment Question #3 -- answer 3. Which of the following is an example of negative acceleration? Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h. Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h. Mike sits on his bike at the top of the hill and rests. Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h. ANS: B

Assessment Question #4 4. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration. A. True B. False

Assessment Question #4 -- answer 4. If an object experiences a steady velocity change in a straight line, it is undergoing constant acceleration. A. True B. False ANS: True

Pre-Lab What are variables? A variable is any factor, trait, or condition that can exist in differing amounts or types. Most experiments have three different types of variables: independent, dependent and controlled Independent variable: the one changed by the scientist Dependent variable: the one that changes in response to the independent variable The independent variable is the one that is changed by the scientist. To insure a fair test, a good experiment has only one independent variable. As the scientist changes the independent variable, he or she observes what happens. The scientist focuses his or her observations on the dependent variable to see how it responds to the change made to the independent variable. The new value of the dependent variable is caused by and depends on the value of the independent variable. For example, if you open a faucet (the independent variable), the quantity of water flowing (dependent variable) changes in response--you observe that the water flow increases. The number of dependent variables in an experiment varies, but there is often more than one. Experiments also have controlled variables. Controlled variables are quantities that a scientist wants to remain constant, and he must observe them as carefully as the dependent variables. For example, if we want to measure how much water flow increases when we open a faucet, it is important to make sure that the water pressure (the controlled variable) is held constant. That's because both the water pressure and the opening of a faucet have an impact on how much water flows. If we change both of them at the same time, we can't be sure how much of the change in water flow is because of the faucet opening and how much because of the water pressure. In other words, it would not be a fair test. Most experiments have more than one controlled variable. Some people refer to controlled variables as "constant variables.“ CHECKLIST FOR GOOD VARIABLES: Is the independent variable measurable? Can you change the dependent variable during the experiment? Are all dependent variables measurable? Have you identified all controlled variables? Can all controlled variables be held steady during the experiment? If the answer is yes to all, you have pretty good variables http://www.sciencebuddies.org/science-fair-projects/project_variables.shtml Controlled variable: the ones that are the same in all tests (do not change)

Pre-Lab questions

Homework Write a paragraph on terminal velocity. (You must define it and explain how it relates to a sport.) From Wikipedia: A free-falling object achieves its terminal velocity when the downward force of gravity (FG) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero. Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e.:face down) free-fall position is about 195 km/h (122 mph or 54 m/s).[2] This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on. Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s),[2] which is almost the terminal velocity of the Peregrine Falcon diving down on its prey.[3] The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to earth having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study.[4] Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 614 mph (988 km/h) by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.[2]

Exit Slip As your exit ticket, describe what is happening in the following graph and provide an example of a real life situation: an object starting from rest, accelerating up to a speed, maintaining that speed, the slowing to a stop. This could be a car speeding up, remaining constant, and slowing down. This could be an airplane during take off, flight, and landing.