Section 3.7 Projectile Motion: Solving Problems © 2015 Pearson Education, Inc.

Example 3.11 Dock jumping In the sport of dock jumping, dogs run at full speed off the end of a dock that sits a few feet above a pool of water. The winning dog is the one that lands farthest from the end of the dock. If a dog runs at 8.5 m/s (a pretty typical speed for this event) straight off the end of a dock that is 0.61 m (2 ft, a standard height) above the water, how far will the dog go horizontally before splashing down? © 2015 Pearson Education, Inc.

Example 3.11 Dock jumping In the sport of dock jumping, dogs run at full speed off the end of a dock that sits a few feet above a pool of water. The winning dog is the one that lands farthest from the end of the dock. If a dog runs at 8.5 m/s (a pretty typical speed for this event) straight off the end of a dock that is 0.61 m (2 ft, a standard height) above the water, how far will the dog go horizontally before splashing down? © 2015 Pearson Education, Inc.

Example 3.11 Dock jumping (cont.) solve We’ll start by solving for the time interval Δt, the time the dog is in the air. This time is determined by the vertical motion, which is free fall with an initial velocity (vy)i = 0 m/s. We use the vertical position equation from Synthesis 3.1 to find the time interval: Rearranging terms to solve for Δt, we find that Δt = 0.35 s © 2015 Pearson Education, Inc.

Example 3.11 Dock jumping (cont.) This is how long it takes the dog’s vertical motion to reach the water. During this time interval, the dog’s horizontal motion is uniform motion at the initial velocity. We can use the horizontal- position equation with the initial speed and Δt = 0.35 s to find how far the dog travels. This is the distance we are looking for: The dog hits the water 3.0 m from the edge of the dock. assess 3.0 m is about 10 feet. This seems like a reasonable distance for a dog running at a very fast clip off the end of a 2- foot-high dock. Indeed, this is a typical distance for dogs in such competitions. © 2015 Pearson Education, Inc.

The Range of a Projectile The range of a projectile is the horizontal distance traveled (assuming that it is launched from ground level). For smaller objects air resistance is critical, and the maximum range comes at an angle less than 45°. © 2015 Pearson Education, Inc.

Instruction Check-in Given your reading of the text, and the lecture (up to this point) complete the following sentence. My understanding of projectile motion is extremely good – I basically understand everything. fairly good, but there is an aspect or two I still find confusing. not good – I understand some of it, but I have some serious confusions. poor – I only understood the very basics, and I am not really following what’s going on. worthless – what’s motion again? Answer: B © 2015 Pearson Education, Inc.

QuickCheck 3.18 Projectiles 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance. Projectile 1 hits first. Projectile 2 hits first. They hit at the same time. There’s not enough information to tell. Answer: B © 2015 Pearson Education, Inc.

QuickCheck 3.18 Projectiles 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance. Projectile 1 hits first. Projectile 2 hits first. They hit at the same time. There’s not enough information to tell. © 2015 Pearson Education, Inc.

Example Problem A grasshopper can jump a distance of 30. in (0.76 m) from a standing start. If the grasshopper takes off at the optimal angle for maximum distance of the jump, what is the initial speed of the jump? Answer: A: initial velocity is 2.7 m/s B: initial velocity is 3.2 m/s © 2015 Pearson Education, Inc.

Section 3.8 Motion in Two Dimensions: Circular Motion © 2015 Pearson Education, Inc.

Motion in Two Dimensions: Circular Motion For circular motion at a constant speed, the acceleration vector a points toward the center of the circle. An acceleration that always points directly toward the center of a circle is called a centripetal acceleration. Centripetal acceleration is just the name for a particular type of motion. It is not a new type of acceleration. © 2015 Pearson Education, Inc.

QuickCheck 3.19 A car is traveling around a curve at a constant speed of 45 mph. Is the car accelerating? Yes No Answer: A © 2015 Pearson Education, Inc.

QuickCheck 3.19 A car is traveling around a curve at a constant speed of 45 mph. Is the car accelerating? Yes No © 2015 Pearson Education, Inc.

QuickCheck 3.20 A car is traveling around a curve at a steady 45 mph. Which vector shows the direction of the car’s acceleration? Answer: B E. The acceleration is zero. © 2015 Pearson Education, Inc.

QuickCheck 3.20 A car is traveling around a curve at a steady 45 mph. Which vector shows the direction of the car’s acceleration? B. E. The acceleration is zero. © 2015 Pearson Education, Inc.

Motion in Two Dimensions: Circular Motion Take Home from Circular Motion – Another Equation which belongs on your cheat sheet © 2015 Pearson Education, Inc.

QuickCheck 3.21 A toy car moves around a circular track at constant speed. It suddenly doubles its speed — a change of a factor of 2. As a result, the centripetal acceleration changes by a factor of ¼ ½ No change since the radius doesn’t change. 2 4 Answer: E © 2015 Pearson Education, Inc. 18

QuickCheck 3.21 A toy car moves around a circular track at constant speed. It suddenly doubles its speed — a change of a factor of 2. As a result, the centripetal acceleration changes by a factor of ¼ ½ No change since the radius doesn’t change. 2 4 © 2015 Pearson Education, Inc. 19

Example 3.14 Acceleration in the turn World-class female short-track speed skaters can cover the 500. m of a race in 45 s. The most challenging elements of the race are the turns, which are very tight, with a radius of approximately 11 m. Estimate the magnitude of the skater’s centripetal acceleration in a turn. © 2015 Pearson Education, Inc.

Example 3.14 Acceleration in the turn (cont.) prepare The centripetal acceleration depends on two quantities: the radius of the turn (given as approximately 11 m) and the speed. The speed varies during the race, but we can make a good estimate of the speed by using the total distance and time: solve We can use these values to estimate the magnitude of the acceleration: assess This is a large acceleration—a bit more than g—but the photo shows the skaters leaning quite hard into the turn, so such a large acceleration seems quite reasonable. © 2015 Pearson Education, Inc.

© 2015 Pearson Education, Inc.

Chapter 4 Forces and Newton’s Laws of Motion Chapter Goal: To establish a connection between force and motion. © 2015 Pearson Education, Inc.

Chapter 4 Preview Looking Ahead: Forces A force is a push or a pull. It is an interaction between two objects, the agent (the woman) and the object (the car). In this chapter, you’ll learn how to identify different forces, and you’ll learn their properties. © 2015 Pearson Education, Inc.

Chapter 4 Preview Looking Ahead: Forces and Motion Acceleration is caused by forces. A forward acceleration of the sled requires a forward force. A larger acceleration requires a larger force. You’ll learn this connection between force and motion, part of Newton’s second law. © 2015 Pearson Education, Inc.

Chapter 4 Preview Looking Ahead: Reaction Forces The hammer exerts a downward force on the nail. Surprisingly, the nail exerts an equal force on the hammer, directed upward. You’ll learn how to identify and reason with action/reaction pairs of forces. © 2015 Pearson Education, Inc.

Chapter 4 Preview Looking Back: Acceleration You learned in Chapters 2 and 3 that acceleration is a vector pointing in the direction of the change in velocity. If the velocity is changing, there is an acceleration. And so, as you’ll learn in this chapter, there must be a net force. © 2015 Pearson Education, Inc.

Chapter 4 Preview Stop to Think A swan is landing on an icy lake, sliding across the ice and gradually coming to a stop. As the swan slides, the direction of the acceleration is To the left. To the right. Upward. Downward. Stop to Think Answer: B © 2015 Pearson Education, Inc.

Chapter 4 Preview Stop to Think A swan is landing on an icy lake, sliding across the ice and gradually coming to a stop. As the swan slides, the direction of the acceleration is To the left. To the right. Upward. Downward. Stop to Think Answer: B © 2015 Pearson Education, Inc.

Section 4.1 Motion and Forces © 2015 Pearson Education, Inc.

What Causes Motion? In the absence of friction, if the sled is moving, it will stay in motion. © 2015 Pearson Education, Inc.

What Causes Motion? NEWTON’S FIRST LAW The motion of an object with no forces acting upon it is always uniform. I.e. If it begins at rest it will remain at rest. If it begins with some non-zero velocity, it will continue to move in the same direction at the same speed it began at. © 2015 Pearson Education, Inc.

What Is a Force? A force is a push or a pull - it is anything that can potentially cause an object to accelerate. A force acts on an object. Every force has an agent, something that acts or pushes or pulls. © 2015 Pearson Education, Inc.

What Is a Force? A force is represented mathematically as a vector. The general symbol for a force is the vector symbol . The size or strength of such a force is its magnitude F. Contact forces are forces that act on an object by touching it at a point of contact. Long-range forces are forces that act on an object without physical contact. © 2015 Pearson Education, Inc.

Force Vectors Text: p. 100 © 2015 Pearson Education, Inc.

Force Vectors © 2015 Pearson Education, Inc.

Combining Forces Experiments show that when several forces are exerted on an object, the combine to form a net force that is the vector sum of all the forces: The net force is sometimes called the resultant force. It is not a new force. Instead, we should think of the original forces being replaced by . COMP: Symbols with overarrows are MathType © 2015 Pearson Education, Inc.

QuickCheck 4.1 The net force on an object points directly to the left. Two of three forces are shown. Which is the missing third force? Answer: C A. B. C. D. © 2015 Pearson Education, Inc.

QuickCheck 4.1 The net force on an object points directly to the left. Two of three forces are shown. Which is the missing third force? A. B. C. D. Vertical components cancel © 2015 Pearson Education, Inc.

Section 4.2 A Short Catalog of Forces © 2015 Pearson Education, Inc.

Weight The gravitational pull of the earth on an object on or near the surface of the earth is called weight. The agent for the weight forces is the entire earth pulling on an object. An object’s weight vector always points vertically downward, no matter how the object is moving. © 2015 Pearson Education, Inc.

Spring Force Springs come in in many forms. When deflected, they push or pull with a spring force. © 2015 Pearson Education, Inc.

Tension Force When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force. The direction of the tension force is always in the direction of the string or rope. © 2015 Pearson Education, Inc.

Normal Force The force exerted on an object that is pressing against a surface is in a direction perpendicular to the surface. The normal force is the force exerted by a surface (the agent) against an object that is pressing against the surface. © 2015 Pearson Education, Inc.

Normal Force The normal force is responsible for the “solidness” of solids. The symbol for the normal force is . COMP: n[overarrow] is MathType. © 2015 Pearson Education, Inc.

Friction Friction, like the normal force, is exerted by a surface. The frictional force is always parallel to the surface. Kinetic friction, denoted by , acts as an object slides across a surface. Kinetic friction is a force that always “opposes the motion.” Static friction, denoted by , is the force that keeps an object “stuck” on a surface and prevents its motion relative to the surface. Static friction points in the direction necessary to prevent motion. © 2015 Pearson Education, Inc.

Friction © 2015 Pearson Education, Inc.

Quick Check A box is at rest on a perfectly horizontal table, which is not frictionless. Which of the following statements concerning the force of friction is true? The force of friction on the box points upwards. The force of friction on the box points downwards. The force of friction points to the right. The force of friction points to the left. The force of friction is zero. Stop to Think Answer: B © 2015 Pearson Education, Inc.

Quick Check A box is at rest on a perfectly horizontal table, which is not frictionless. Which of the following statements concerning the force of friction is true? The force of friction on the box points upwards. The force of friction on the box points downwards. The force of friction points to the right. The force of friction points to the left. The force of friction is zero. Stop to Think Answer: B © 2015 Pearson Education, Inc.

Drag The force of a fluid (like air or water) on a moving object is called drag. Like kinetic friction, drag points opposite the direction of motion. You can neglect air resistance in all problems unless a problem explicitly asks you to include it. © 2015 Pearson Education, Inc.

Thrust Thrust is a force that occurs when a jet or rocket engine expels gas molecules at high speed. Thrust is a force opposite the direction in which the exhaust gas is expelled. © 2015 Pearson Education, Inc.

Electric and Magnetic Forces Electricity and magnetism, like gravity, exert long-range forces. The forces of electricity and magnetism act on charged particles. These forces—and the forces inside the nucleus—won’t be important for the dynamics problems we consider in the next several chapters. You will have a chance to get intimately acquainted with electricity and magnetism next semester in Physics 107 & 108. © 2015 Pearson Education, Inc.