L 6 — Newton s Law of Motion Lecture

L 6 - Newton’s Law of Motion Lecture Outline 1. Forces and Interaction 2. Principle of Superposition 3. Newton’s First Law 4. Newton’s Second Law 5. Newton’s Third Law 6. Applications of Newton’s Laws 7. Free Body Diagrams (FBDs) 1

1. Forces and Interaction • A force is always exerted by something on something. • Force is a measure of an interaction between two objects. Forces always come in pairs • Dynamics is the relationship of motion to the forces that cause it. § Contact forces (e. g. push, pull, friction) § Long-range forces (e. g. electric, magnetic, gravitational) 2

Remember about Forces: • A force has a magnitude and a direction— force is a vector. • Drawing diagrams to show the forces acting on an object—free body diagrams (FBD)—we use arrows to show the relative size and direction. • Weight is the gravitational force acting on an object. Weight is measured in Newtons (N) • Need to find a single force—the resultant force through SUPERPOSITION of all forces 3 acting on an object

2. Principle of superposition § Resultant (net) force 4

Principle of Superposition Vector addition of forces 5

Example 1 A 10. 0 x 103 kg barge (longboat) is pulled by two smaller boats as shown. Find the acceleration of the barge. 6

3. Newton’s First Law (Law of Inertia) A object moves with a velocity that is constant in magnitude and direction, unless acted on by a non-zero net force. For a body in equilibrium, we have 7

4. Newton’s Second Law § The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass. § And Where the constant defines the inertial Mass m of an object 8

Mass and Force 9

Mass and Weight 10

5. Newton’s Third Law “Forces are always in Pairs” (Action – Reaction) § If a body A exerts a force on body B (an ‘action’), then body B exerts a force on body A (a ‘reaction’). These two forces have equal magnitude and opposite direction 11

Newton’s Third Law 12

Example - Using Newton’s Laws 13

6. Applications of Newton’s Laws Pulley • • Assumptions The pulley is frictionless The pulley has negligible mass The strings connecting pulleys are inextensible and have negligible masses 14

Atwood Machine (Fixed Pulley) 15

Movable Pulley 16

6. Applications of Newton’s Laws Terminal Speed Assumptions • Object is falling in gravity (force down = weight) • The object falls through a fluid (air or liquid) that resists the falling (resistance force is upward) • The Terminal speed is reached when the forces of resistance equals the weight, 17 and the Net Force = zero

Terminal Speed Force of Resistance from Fluid Force of Gravitation mg When an object falls through a fluid in gravitational field, The object feels two opposite forces. When those two forces are equal, it has a terminal speed since there is no net force on the object. 18

7. Free Body Diagram (FBD) To create a free body diagram: Step 1 – Identify only ONE object for each FBD. Step 2 – Draw simplified sketch Step 3 – Draw vectors to show all external forces acting on that ONE object. (weight of a uniform body is downward from center) Step 4 - If there is a net Force, show it as vector next to the object. What is the FBD of the system drawn above? 19

7. Free Body Diagram (FBD) Questions you need to answer about the object Is there… Then include the vector …gravity? Weight W or mg …a surface it sits on? Normal N …a reaction force? RA ond/or R 1 etc … friction? Ff … other external forces? FA ond/or F 1 etc. a net acceleration? touching) a (near but not 20

7. FBD - Examples On a flat surface with no external force On a sloping surface with friction force that opposes the object’s sliding motion 21

Example 2: pulling a box The person is pulling a box along a floor and the box is moving faster and faster. Construct a free body diagram for the box in this situation. Note. Often the object is reduced to a point or line from which all forces act. 22 This assumes there is no acceleration. What if there is acceleration?

Free body Diagram for Box pulled with constant acceleration F Normal Friction Net Force Applied Force Weight mg 23

Example 3: Draw a Free Body Diagram for the following case, assume that the person and the mass are accelerating to the left with a constant acceleration. 24

Example 4 Two boxes of 20. 0 kg and 30. 0 kg sit in contact on a frictionless surface. A force of 60. 0 N is applied to A as shown. Find: a) the acceleration of both boxes b) the force A exerts on B c) the force B exerts on A 25

Reading Essentials of College Physics, Serway § Chapter 4 Sections 4. 1 to 4. 6 Solved examples 4. 1, 4. 5 and 4. 6 Conceptual questions pp. 82 -83 (Solutions in A. 24) Problems pp. 83 -89 (Numerical answers in A. 24, A. 25) § Chapter 5 Section 5. 1 26

Answers to Examples 1: acceleration 1. 27 m. s-2 2: done with drawing FBD as per slide 3: Drawing must include two separate FBDs 4: (a) for both, a = 1. 20 m. s-2 , toward the right (b) FAB = +36 N (c) FBA = - 36 N 27