Physics 114A - Mechanics Lecture 12 (Walker: Ch.5) Free Body Diagrams January 27, 2012 John G. Cramer Professor Emeritus, Department of Physics Office: B451 PAB

Announcements Homework Assignment #3 is now due at 11:59 PM on January 24 (tonight). Homework Assignment #4 is due at 11:59 PM on Thursday, February 2. There was an answer-key typo on Exam 1 Question 6 (D, not B). This has been corrected, and your WebAssign Exam1-MC score may have changed from yesterday. 145 students gained 5 points and 6 students lost 5 points. The Exam 1 solutions are available on the web from the “Exam 1” link on the Physics 114A Lecture Schedule. Compare your answers with the solutions before asking any questions about the grading. If you have a question or complaint about the grading of Exam 1, attach a blank sheet of paper to the exam page at issue, write your complaint/question on the blank page, and turn it in to Susan Miller by Monday. January 27, 20122/23Physics 114A - Lecture 12

January 26, 2012Physics 114A - Lecture 113/31 Exam 1 Statistics (Revised) Average = 73.5 Std Dev = High = 100 Median = 76 Low = 25

Physics 114A - Introduction to Mechanics - Winter-2012 Lecture: Professor John G. Cramer Textbook: Physics, Vol. 1 (UW Edition), James S. Walker WeekDateL#Lecture TopicPagesSlidesReadingHW DueLab 4 23-Jan-12E1 EXAM 1 - Chapters D Dynamics 24-Jan-1210Newton's Laws to Jan-1211Common Forces to Jan-1212Free Body Diagrams-24- HW Jan-1213Friction Newton's Laws Tension 31-Jan-1214Strings & Springs to Feb-1215Circular Motion5306-5HW4 3-Feb-1216Work & Energy to Feb-1217Work & Power to 7-4 Work-energy 7-Feb-1218Potential Energy to Feb-1219Energy Conservation I to 8-5HW5 10-Feb-12E2EXAM 2 - Chapters 5-8 Lecture Schedule (Part 2) We are here. January 27, 20124/23Physics 114A - Lecture 12

A horizontal force F acts on a block that is connected to another block by a string. Consider the constraints and the forces. The Massless String Approximation Isolate the string and consider the forces on it: (F net ) x = T A on S –T B on S = m S a, so T A on S = T B on S + m S a  T B on S Massless String Approximation: Assume that m S  0 so that T A on S = T B on S January 27, 20125/23Physics 114A - Lecture 12

Example: Comparing Tensions Blocks A and B are connected by massless String 2 and pulled across a frictionless surface by massless String 1. The mass of B is larger than the mass of A. Is the tension in String 2 smaller, equal, or larger than the tension in String 1? The blocks must be accelerating to the right, because there is a net force in that direction. We use the massless string approximation to directly relate the string tensions on A and B due to String 2: T A on B =T B on A (F A net ) x =T 1 -T B on A = T 1 -T 2 = m A a Ax so T 1 = T 2 + m A a Ax Therefore, T 1 > T 2. January 27, 20126/23Physics 114A - Lecture 12

Pulleys Strings and ropes often pass over pulleys that change the direction of the tension. In principle, the friction and inertia in the pulley could modify the transmitted tension. Therefore, it is conventional to assume that such pulleys are massless and frictionless. Massless String Approximation Massless and Frictionless Pulley Approximation January 27, 20127/23Physics 114A - Lecture 12

Clicker Question 1 a. T 1 >T 2 b. T 1 =T 2 c. T 1 <T 2 January 27, 20128/23Physics 114A - Lecture 12

Free-Body Diagrams January 27, 20129/23Physics 114A - Lecture 12

Drawing a Free-Body Diagram Identify all forces acting on the object. Draw a coordinate system. Use the axes defined in your pictorial representation. If those axes are tilted, for motion along an incline, then the axes of the free-body diagram should be similarly tilted. Represent the object as a dot at the origin of the coordinate axes. This is the particle model. Draw vectors representing each of the identified forces. Be sure to label each force vector. Draw and label the net force vector. Draw this vector beside the diagram, not on the particle. Or, if appropriate, write. Then check that points in the same direction as the acceleration vector on your motion diagram. January 27, /23Physics 114A - Lecture 12

Two Forces Applied to a Box superposition of forces January 27, /22Physics 114A - Lecture 12

Examples of Force Vectors Pull (contact force) Push (contact force) Gravity (long-range force) January 27, /23Physics 114A - Lecture 12

Clicker Question 2 A.2000 N B.500 N C.1000 N D.0 N E.2000 kg A pair of tug-of-war teams are pulling on the ends of a rope, each team with a force of 1000 N. If the rope does not move, the tension in the rope is: January 27, /23Physics 114A - Lecture 12

Identifying Forces Identify “the system” and “the environment.” The system is the object whose motion you wish to study; the environment is everything else. Draw a picture of the situation. Show the object—the system—and everything in the environment that touches the system. Ropes, springs, and surfaces are all parts of the environment. Draw a closed curve around the system. Only the object is inside the curve; everything else is outside. Locate every point on the boundary of this curve where the environment touches the system. These are the points where the environment exerts contact forces on the object. Name and label each contact force acting on the object. There is at least one force at each point of contact; there may be more than one. When necessary, use subscripts to distinguish forces of the same type. Name and label each long-range force acting on the object. For now, the only long-range force is weight. January 27, /23Physics 114A - Lecture 12

The Forces on a Bungee Jumper T w January 27, /23Physics 114A - Lecture 12

n fkfk The Forces on a Skier T w January 27, /23Physics 114A - Lecture 12

The Forces on a Rocket F thrust wD January 27, /23Physics 114A - Lecture 12

Using Free-Body Diagrams The vector sum of the forces of a free-body diagram is equal to ma. January 27, /23Physics 114A - Lecture 12

Example: A Dogsled Race During your winter break, you enter a dogsled race in which students replace the dogs. Wearing cleats for traction, you begin the race by pulling on a rope attached to the sled with a force of 150 N at 25° above the horizontal. The mass of the sled-passenger-rope system is 80 kg, and there is negligible friction between the sled runners and the ice. (a) Find the acceleration of the sled (b) Find the magnitude of the normal force exerted on the surface by the sled. January 27, /23Physics 114A - Lecture 12

Example: Unloading A Truck You are working for a big delivery company, and you must unload a large, fragile package from your truck, using a 1 m high frictionless delivery ramp. If the downward component of velocity of the package is greater than 2.50 m/s when it reaches the bottom of the ramp, the package will break. What is the greatest angle  at which you can safely unload? xx January 27, /23Physics 114A - Lecture 12

Example: Picture Hanging A picture weighing 8.0 N is supported by two wires with tensions T 2 and T 2. Find each tension. January 27, /23Physics 114A - Lecture 12

Example: An Accelerating Jet Plane As your jet plane speeds along the runway on takeoff, you decide to determine its acceleration, so you take out your yo-yo and note that when you suspend it, the string makes an angle of 22° with the vertical. (a) What is the acceleration of the airplane? (b) If the mass of the yo-yo is 40.0 g, what is the tension in the string? January 27, /23Physics 114A - Lecture 12

Example: Weighing Yourself in an Elevator Suppose that your mass is 80 kg, and you are standing on a scale fastened to the floor of an elevator. The scale measures force and is calibrated in newtons. (a)What does the scale read when the elevator is rising with acceleration a? (b)When it is descending with acceleration a’? (c)When it is rising at 20.0 m/s and its speed is decreasing at 8.0 m/s 2 ? January 27, /23Physics 114A - Lecture 12

Before Monday, read Walker Chapter 6.1 Homework Assignment #3 is now due at 11:59 PM on January 27 (tonight). Homework Assignment #4 is due at 11:59 PM on Thursday, February 2. As of today, 196/205 clickers are registered. I have sent an reminder to the nine students without clicker registrations. End of Lecture 12