UNIT Forces and Motion: 1 Dynamics 2 www.com OVERALL EXPECTATIONS UNIT CONTENTS ANALYZE, predict, and explain the motion of selected objects in vertical, horizontal, and inclined planes. CHAPTER 1 Fundamentals of Dynamics INVESTIGATE, represent, and analyze motion and CHAPTER 2 Dynamics in Two forces in linear, projectile, and circular motion. Dimensions RELATE your understanding of dynamics to the CHAPTER 3 Planetary and Satellite development and use of motion technologies. Dynamics S pectators are mesmerized by trapeze artists making perfectly timed releases, gliding through gracefu l arcs, and intersecting the paths of their partners.
An error in timing and a graceful arc could become a trajectory of panic. Trapeze artists know that tiny differences in height, velocity, and timing are critical. Swinging from a trapeze, the performer forces his body from its natural straight- line path. Gliding freely through the air, he is subject only to gravity.
Then, the outstretched hands of his partner make contact, and the performer is acutely aware of the forces that change his speed and direction. In this unit, you will explore the relationship between motion and the forces that cause it and investigate how different perspectives of the same motion are related. You will learn how to analyze forces and motion, not only in a straight line, but also in circular paths, in parabolic trajectories, and on inclined surfaces. You will discover how the motion of planets and satellites is caused, described, and analyzed.
UNIT PROJECT PREP Refer to pages 126–127 before beginning this unit. In the unit project, you will design and build a working catapult to launch small objects through the air. ■ What launching devices have you used, watched, or read about? How do they develop and control the force needed to propel an object? ■ What projectiles have you launched? How do you direct their flight so that they reach a maximum height or stay in the air for the longest possible time? 3 www.com C H A P T E R 1 Fundamentals of Dynamics CHAPTER CONTENTS Multi-Lab Thinking Physics 5 1.1 Inertia and Frames of Reference 6 Investigation 1-A Measuring Inertial Mass 8 1.3 Vertical Motion 27 Investigation 1-B Atwood’s Machine 34 1.4 Motion along an Incline 46 PREREQUISITE CONCEPTS AND SKILLS ■ Using the kinematic equations for uniformly accelerated motion. H ow many times have you heard the saying, “It all depends on your perspective”? The photographers who took the two pictures of the roller coaster shown here certainly had different perspectives.
When you are on a roller coaster, the world looks and feels very different than it does when you are observing the motion from a distance. Now imagine doing a physics experiment from these two perspectives, studying the motion of a pendulum, for example. Your results would definitely depend on your perspective or frame of reference. You can describe motion from any frame of reference, but some frames of reference simplify the process of describing the motion and the laws that determine that motion.
In previous courses, you learned techniques for measuring and describing motion, and you studied and applied the laws of motion. In this chapter, you will study in more detail how to choose and define frames of reference. Then, you will extend your knowledge of the dynamics of motion in a straight line. 4 MHR • Unit 1 Forces and Motion: Dynamics www.com TARGET SKILLS M U LT I Thinking Physics Predicting L A B Identifying variables Analyzing and interpreting Suspended Spring Analyze and Conclude Tape a plastic cup to one end of a short 1.
Describe the motion of the cup and the section of a large-diameter spring, such as lower end of the spring. Compare the a Slinky™. Hold the other end of the spring motion to your prediction and describe high enough so that the plastic cup is at least any differences. 1 m above the floor.
Is it possible for any unsupported object release the spring, predict the to be suspended in midair for any length exact motion of the cup of time? Create a detailed explanation to from the instant that it is account for the behaviour of the cup at the released until the moment moment at which you released the top of that it hits the floor. While the spring. your partner watches the 3. Athletes and dancers sometimes seem to cup closely from a kneel- be momentarily suspended in the air.
ing position, release the How might the motion of these athletes top of the spring. Observe be related to the spring’s movement in the motion of the cup. this lab? Thought Experiments 2. A golf pro drives a ball through the air.
Without discussing the following questions What force(s) is/are acting on the golf ball with anyone else, write down your answers. for the entirety of its flight? (a) force of gravity only 1. Student A and A B (b) force of gravity and the force of Student B sit in identical office the “hit” chairs facing (c) force of gravity and the force of air each other, as resistance illustrated. (d) force of gravity, the force of the “hit,” Student A, who and the force of air resistance is heavier than Student B, suddenly push- 3.
A photographer es with his feet, causing both chairs to accidentally drops move. Which of the following occurs? a camera out of a A B C D (a) Neither student applies a force to the small airplane as other. it flies horizontally. As seen from the (b) A exerts a force that is applied to B, ground, which path would the camera but A experiences no force.
most closely follow as it fell? (c) Each student applies a force to the other, but A exerts the larger force. Analyze and Conclude (d) The students exert the same amount Tally the class results. As a class, discuss the of force on each other. answers to the questions.
Chapter 1 Fundamentals of Dynamics • MHR 5 www.com Inertia and Frames 1.1 of Reference SECTION Imagine watching a bowling ball sitting still in the rack. Nothing E X P E C TAT I O N S moves; the ball remains totally at rest until someone picks it up • Describe and distinguish and hurls it down the alley. Galileo Galilei (1564–1642) and later between inertial and non- Sir Isaac Newton (1642–1727) attributed this behaviour to the inertial frames of reference. property of matter now called inertia, meaning resistance to changes in motion.
Stationary objects such as the bowling ball • Define and describe the concept and units of mass. remain motionless due to their inertia. Now picture a bowling ball rumbling down the alley. • Investigate and analyze Experience tells you that the ball might change direction and, if linear motion, using vectors, the alley was long enough, it would slow down and eventually graphs, and free-body stop.
Galileo realized that these changes in motion were due to diagrams. factors that interfere with the ball’s “natural” motion. Hundreds of years of experiments and observations clearly show that Galileo KEY was correct. Moving objects continue moving in the same direc- TERMS tion, at the same speed, due to their inertia, unless some external • inertia force interferes with their motion.
• inertial mass • gravitational mass • coordinate system • frame of reference • inertial frame of reference • non-inertial frame of reference • fictitious force Figure 1.1 You assume that an inanimate object such as a bowling ball will remain stationary until someone exerts a force on it. Galileo and Newton realized that this “lack of motion” is a very important property of matter. Analyzing Forces Newton refined and extended Galileo’s ideas about inertia and straight-line motion at constant speed — now called “uniform motion.” NEWTON’S FIRST LAW: THE LAW OF INERTIA An object at rest or in uniform motion will remain at rest or in uniform motion unless acted on by an external force. 6 MHR • Unit 1 Forces and Motion: Dynamics www.com Newton’s first law states that a force is required to change an LANGUAGE LINK object’s uniform motion or velocity.
Newton’s second law then permits you to determine how great a force is needed in order to The Latin root of inertia means change an object’s velocity by a given amount. Recalling that “sluggish” or “inactive.” An inertial acceleration is defined as the change in velocity, you can state guidance system relies on a gyro- scope, a “sluggish” mechanical device Newton’s second law by saying, “The net force ( F ) required to accelerate an object of mass m by an amount ( a ) is the product that resists a change in the direction of the mass and acceleration. What does this suggest about the chemical properties of an inert gas? NEWTON’S SECOND LAW The word equation for Newton’s second law is: Net force is the product of mass and acceleration. F = m a QuantitySymbol SI unit force F N (newtons) mass m kg (kilograms) acceleration a m (metres per second s2 squared) Unit analysis metres m kg · m (mass)(acceleration) = (kilogram) kg 2 = =N second2 s s2 Note: The force ( F ) in Newton’s second law refers to the vector sum of all of the forces acting on the object.
Inertial Mass When you compare the two laws of motion, you discover that the first law identifies inertia as the property of matter that resists a change in its motion; that is, it resists acceleration. The second law gives a quantitative method of finding acceleration, but it does not seem to mention inertia. Instead, the second law indicates that the property that relates force and acceleration is mass. Actually, the mass (m) used in the second law is correctly described as the inertial mass of the object, the property that resists a change in motion.
As you know, matter has another prop- erty — it experiences a gravitational attractive force. Physicists refer to this property of matter as its gravitational mass. Physicists never assume that two seemingly different properties are related without thoroughly studying them. In the next investigation, you will examine the relationship between inertial mass and gravita- tional mass.
Chapter 1 Fundamentals of Dynamics • MHR 7 www.com I N V E S T I G AT I O N 1-A TARGET SKILLS Hypothesizing Measuring Inertial Mass Performing and recording Analyzing and interpreting Problem 4. Add unit masses one at a time and measure Is there a direct relationship between an object’s the acceleration several times after each inertial mass and its gravitational mass? addition. Average your results. Graph the acceleration versus the number of Hypothesis unit inertial masses on the cart.
Formulate an hypothesis about the relationship between inertial mass and its gravitational mass. Remove the unit masses from the cart and replace them with the unknown mass, then Equipment measure the acceleration of the cart. Use the graph to find the inertial mass of the ■ pulley and string unknown mass (in unit inertial masses). Find the gravitational mass of one unit of ■ standard mass (about 500 g) inertial mass, using a laboratory balance.
■ metre stick and stopwatch or motion sensor 9. Add a second scale to the horizontal axis of ■ unit masses (six identical objects, such as small your graph, using standard gravitational mass C-clamps) units (kilograms). Use the second scale on the graph to predict the gravitational mass of the unknown mass. Verify your prediction: Find the unknown’s 1.
Arrange the pulley, string, standard mass, gravitational mass on a laboratory balance. and dynamics cart on a table, as illustrated. Analyze and Conclude 1. Based on your data, are inertial and dynamics cart gravitational masses equal, proportional, pulley or independent? 2.
Does your graph fit a linear, inverse, expo- nential, or radical relationship? Write the relationship as a proportion (a ∝ ?). Write Newton’s second law. Solve the standard expression for acceleration.