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Unit 1, Chapter 4. CPO Science Foundations of Physics. Chapter 9. Unit 1: Measurement and Motion. Chapter 4: Acceleration in a Straight Line. 4.1 Acceleration 4.2 A Model for Accelerated Motion 4.3 Free Fall and the Acceleration due to Gravity. Chapter 4 Objectives.
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Unit 1, Chapter 4 CPO Science Foundations of Physics Chapter 9
Unit 1: Measurement and Motion Chapter 4: Acceleration in a Straight Line • 4.1 Acceleration • 4.2 A Model for Accelerated Motion • 4.3 Free Fall and the Acceleration due to Gravity
Chapter 4 Objectives • Calculate acceleration from the change is speed and the change in time. • Give an example of motion with constant acceleration. • Determine acceleration from the slope of the speed versus time graph. • Calculate time, distance, acceleration or speed when given three of the four variables. • Solve two-step accelerated motion problems. • Calculate height, speed, or time of flight in free fall problems. • Explain how air resistance makes objects of different masses fall with different accelerations.
Chapter 4 Vocabulary Terms • initial speed • free fall • acceleration due to gravity (g) • time of flight • friction • air resistance • terminal speed • acceleration • m/sec2 • delta D • constant acceleration • uniform acceleration • slope • term
Key Question: How is the speed of the ball changing? 4.1 Acceleration *Students read Section 4.1 AFTER Investigation 4.1
4.1 Acceleration of a car Acceleration is the rate of change in the speed of an object.
4.1 Acceleration vs. Speed • Positive acceleration and positive speed
4.1 Acceleration vs. Speed • Negative acceleration and positive speed
4.1 Acceleration Change in speed (m/sec) a = Dv Dt Acceleration (m/sec2) Change in time (sec)
A student conducts an acceleration experiment by coasting a bicycle down a steep hill. The student records the speed of the bicycle every second for five seconds. Calculate the acceleration of the bicycle. 4.1 Calculate Acceleration
4.1 Acceleration and Speed • Constant acceleration is different from constant speed. • Motion with zero acceleration appears as a straight horizontal line on a speed versus time graph. zero acceleration constant speed
4.1 Acceleration and Speed • Constant acceleration is sometimes called uniform acceleration. • A ball rolling down a straight ramp has constant acceleration. constant acceleration increasing speed
4.1 Acceleration and Speed • An object can have acceleration, but no speed. • Consider a ball rolling up a ramp. • As the ball slows down, eventually its speed becomes zero. constant negative acceleration decreasing speed
4.1 Slope and Acceleration • Use slope to recognize when there is acceleration in speed vs. time graphs. • Level sections (A) on the graph show an acceleration of zero. • The highest acceleration (B) is the steepest slope on the graph. • Sections that slope down (C) show negative acceleration (slowing down).
Key Question: How do we describe and predict accelerated motion? 4.2 A Model for Accelerated Motion *Students read Section 4.2 AFTER Investigation 4.2
The slope of a graph is equal to the ratio of rise to run. On the speed versus time graph, the rise and run have special meanings, as they did for the distance versus time graph. The riseis the amount the speed changes. The runis the amount the time changes. 4.2 Slope of a graph
Acceleration is the change in speed over the change in time. The slope of the speed versus time graph is the acceleration. 4.2 Acceleration and slope
The following graph shows the speed of a bicyclist going over a hill. Calculate the maximum acceleration of the cyclist and say when in the trip it occurred. 4.2 Calculate acceleration
A ball rolls at 2 m/sec onto a ramp. The angle of the ramp creates an acceleration of 0.75 m/sec2. Calculate the speed of the ball 10 seconds after it reaches the ramp. 4.2 Calculate speed
4.2 Solving Motion Problems initial position distance if at constant speed distance to add or subtract, depending on acceleration
4.2 Calculate position • A ball traveling at 2 m/sec rolls onto a ramp that tilts upward. • The angle of the ramp creates an acceleration of -0.5 m/sec2. • How far up the ramp does the ball get at its highest point? • (HINT: The ball keeps rolling upward until its speed is zero.)
4.2 Calculate time • A car at rest accelerates at 6 m/sec2. • How long does it take to travel 440 meters (about a quarter-mile) and how fast is the car going at the end?
A ball starts to roll down a ramp with zero initial speed. After one second, the speed of the ball is 2 m/sec. How long does the ramp need to be so that the ball can roll for 3 seconds before reaching the end? 4.2 Calculate position
A stone is dropped down a well and it takes 1.6 seconds to reach the bottom. How deep is the well? You may assume the initial speed of the stone is zero. 4.3 Calculate height
4.3 Air Resistance and Mass • The acceleration due to gravity does not depend on the mass of the object which is falling. • Air creates friction that resists the motion of objects moving through it. • All of the formulas and examples discussed in this section are exact only in a vacuum (no air).
4.3 Terminal Speed • You may safely assume that a = g = 9.8 m/sec2 for speeds up to several meters per second. • The resistance from air friction increases as a falling object’s speed increases. • Eventually, the rate of acceleration is reduced to zero and the object falls with constant speed. • The maximum speed at which an object falls when limited by air friction is called the terminal speed.
Key Question: How do you measure the acceleration of a falling object? 4.3 Free Fall and Acceleration due to Gravity *Students read Section 4.3 BEFORE Investigation 4.3
