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Physics 114A - Mechanics Lecture 10 (Walker: 5.1-4) Newton’s Laws January 28, 2013 John G. Cramer Professor Emeritus, Department of Physics Office: B451 PAB firstname.lastname@example.org Announcements Homework Assignment #3 and #4 are due at 11:59 PM on Thursday, January 31 and Thursday, February 7, respectively. As of today 210/213 clickers are registered. Exam 1 papers may be returned on Thursday. As soon as scores for the two parts of Exam 1 are available, they will be posted on WebAssign. For the multiple choice part of Exam 1, the average for 209 papers graded was 59.43±11.99 out of 75 points. The highest score was 75 and the lowest was 20. The Exam 1 solutions are available on the web from the “Exam 1” link on the Physics 114A Lecture Schedule. January 28, 2013 Physics 114A - Lecture 10 2/29 Lecture Schedule (Part 2) 28-Jan-13 10 Newton's Laws 14 29 5-1 to 5-4 29-Jan-13 11 Common Forces 11 26 5-5 to 5-7 4 31-Jan-13 12 Free Body Diagrams - 24 - HW3 1-D Dynamics 1-Feb-13 13 Friction 9 27 6-1 We are here. 4-Feb-13 14 Strings & Springs 12 29 6-2 to 6-4 5-Feb-13 15 Circular Motion 5 30 6-5 Newton's Laws 5 7-Feb-13 16 Work & Energy 11 23 7-1 to 7-2 HW4 Tension 8-Feb-13 17 Work & Power 7 25 7-3 to 7-4 11-Feb-13 18 Potential Energy 10 26 8-1 to 8-2 12-Feb-13 19 Energy Conservation I 16 18 8-3 to 8-5 6 14-Feb-13 R2 Review & Extension - 49 - HW5 Work-energy 15-Feb-13 E2 EXAM 2 - Chapters 5-8 18-Feb-13 H3 President's Day Holiday 19-Feb-13 20 Momentum & Impulse 8 23 9-1 to 9-3 7 21-Feb-13 21 Momentum Conservation 11 24 9-4 to 9-5 HW6 Mom. & Collisions 22-Feb-13 22 Collisions & CM 10 22 9-6 to 9-8 January 28, 2013 Physics 114A - Lecture 10 3/29 Force Kinematics vs. dynamics: what causes acceleration? Answer: force. Force: push or pull Force is a vector – it has magnitude and direction January 28, 2013 Physics 114A - Lecture 10 4/29 Mass Mass is the measure of how hard it is to change an object’s velocity. Mass can also be thought of as a measure of the quantity of matter in an object or the quantity of inertia possessed by the object. One liter of water has a mass of 1 kg. January 28, 2013 Physics 114A - Lecture 10 5/29 The Law of Inertia You push on an object and it moves. If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest. This is Newton’s 1st Law, and it is also known as the Law of Inertia. January 28, 2013 Physics 114A - Lecture 10 6/29 Motion and Inertial Frames In order to change the velocity of an object – in magnitude or in direction – a net force is required. An inertial reference frame is one in which the first law is true. Accelerating reference frames, e.g., a rotating frame, are not inertial. January 28, 2013 Physics 114A - Lecture 10 7/29 Inertia If no force acts on an object, an inertial reference frame is any frame in which there is no acceleration on an the object. In (a) the plane is flying horizontally at constant speed, and the tennis ball does not move horizontally. In (b) the pilot suddenly opens the throttle and the plane rapidly gains speed, so that the tennis ball accelerates toward the back of the plane. Inertia is the tendency of mass to resist acceleration, so that a force must be supplied to overcome inertia and produce acceleration. January 28, 2013 Physics 114A - Lecture 10 8/29 Newton’s First Law of Motion Newton’s 1st Law: In the absence of external forces, an object at rest remains at rest; an object in motion remains in motion. January 28, 2013 Physics 114A - Lecture 10 9/29 Calibrating Spring Force Two equal weights exert twice the force of one; this can be used for calibration of a spring: January 28, 2013 Physics 114A - Lecture 10 10/29 Acceleration vs. Force Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force: F1 a1 2 F1 2a1 January 28, 2013 Physics 114A - Lecture 10 11/29 Acceleration vs. Mass Acceleration is inversely proportional to mass: M a1 2M 1 a1 2 January 28, 2013 Physics 114A - Lecture 10 12/29 Newton’s Second Law of Motion Combining these two observations gives F F a , and choosing appropriate units we can make a m m Or, more familiarly, F ma or F ma This is the mathematical expression of Newton’s 2nd Law of Motion. Units: Mass has SI units of kg, and acceleration has SI units of m/s2. We define the SI unit of force as: 1 newton = 1 N 1 kg m/s2. January 28, 2013 Physics 114A - Lecture 10 13/29 Example: Accelerated Mass m1 A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of unknown mass. What is the mass of the object? F (3.0 N) m1 = 2 1.5 kg a1 (2.0 m/s ) January 28, 2013 Physics 114A - Lecture 10 14/29 Newton’s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: (5-1) January 28, 2013 Physics 114A - Lecture 10 15/29 Combining Forces Forces add vectorially. n Fnet F1 F2 Fi i 1 January 28, 2013 Physics 114A - Lecture 10 16/29 Clicker Question 1 Two forces are exerted on an object. Which third force would make the net force point to the left? (a) (b) (c) (d) January 28, 2013 Physics 114A - Lecture 10 17/29 Newton’s Second Law of Motion Newton’s 2nd Law: An object of a given mass m subjected to forces F1, F2, F3, … will undergo an acceleration a given by: a = Fnet /m where Fnet = F1 + F2 + F3 + … The mass m must be positive so that force and acceleration are in the same direction. January 28, 2013 Physics 114A - Lecture 10 18/29 Typical Forces January 28, 2013 Physics 114A - Lecture 10 19/29 Newton’s Second Law of Motion Free-body diagrams: A free-body diagram shows every force acting on an object. To draw a free-body diagram: Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components Apply Newton’s second law to each coordinate direction January 28, 2013 Physics 114A - Lecture 10 20/29 2nd Law and Free-Body Diagrams Example of a free-body diagram: January 28, 2013 Physics 114A - Lecture 10 21/29 Example: A Sliding Ice-Cream Carton A force exerted by a stretched rubber band produces an acceleration of 5.0 m/s2 on an ice cream carton of mass 1.0 kg. When a force exerted by an identical rubber band stretched the same amount is applied to a carton of ice cream of mass m2, it produces an acceleration of 11.0 m/s2. (a) What is the mass of the second carton? (5.0 m/s 2 ) F m1a1 m2 a2 so m2 (1 kg) 2 0.45 kg (11.0 m/s ) (b) What is the magnitude of the force applied by the rubber band? F m1a1 =(1 kg)(5.0 m/s 2 ) 5.0 N January 28, 2013 Physics 114A - Lecture 10 22/29 Example: A Space Walk You are stranded in space, away from your spaceship. Fortunately, you have a propulsion unit that provides a constant net force F for 3.0 s. You turn it on, and after 3.0 s you have moved 2.25 m. If your mass is 68 kg, find F. x v0t 1 at 2 1 at 2 2 2 2x 2(2.25 m) a 2 0.50 m/s 2 t (3.0 s) 2 ˆ a axi 0.50 m/s2i ˆ ˆ ˆ F ma (68 kg)(0.50 m/s 2 )i 34 Ni January 28, 2013 Physics 114A - Lecture 10 23/29 Clicker Question 2 January 28, 2013 Physics 114A - Lecture 10 24/29 Example: Three Forces Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force parallel to the dock. (a) What is the acceleration of the boat if they all push in the same direction? (b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown? F1 FM FL FC 3(80.5 N) 241.5 N a1 F1 / m (241.5 N) / (752 kg) 0.321 N/kg 0.321 m/s 2 F2 FM FL FC 80.5 N a2 F2 / m (80.5 N) / (752 kg) 0.107 m/s 2 January 28, 2013 Physics 114A - Lecture 10 25/29 Newton’s Third Law of Motion Forces always come in pairs, acting on different objects: If Object 1 exerts a force F on Object 2, then Object 2 exerts a force –F on Object 1. These forces are called action-reaction pairs. January 28, 2013 Physics 114A - Lecture 10 26/29 Newton’s Third Law of Motion Some action-reaction pairs: January 28, 2013 Physics 114A - Lecture 10 27/29 Newton’s Third Law of Motion Although the forces are the same, the accelerations will not be unless the objects have the same mass. Contact forces: The force exerted by one box on the other is different depending on which one you push. January 28, 2013 Physics 114A - Lecture 10 28/29 End of Lecture 10 Before the next lecture on Tuesday, read Walker, Chapter 5.5-5.7. Homework Assignments #3 and #4 should be submitted using the WebAssign system by 11:59 PM on Thursday, January 31 and February 7, respectively. Exam 1 Solutions are available on the web from the “Exam 1” link on the Physics 114A Course Schedule.
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