Chapter 4 Force and Motion September 4 Newton’s first law of motion

1. Chapter 4 Force and Motion September 4 Newton’s first law of motion 4.1 The Concepts of Force and Net Force Force: A force is something that is capable of changing the velocity of an object, that is, producing an acceleration. In everyday life, force is a push or a pull. It is a vector.Any particular force may not actually change an object’s velocity, as there may be other forces that prevent it from doing so. However, if the force acts alone on the object, the object will indeed change its velocity. Here changing velocity means to change either or both of its speed and direction, that is, to produce an acceleration.

2. Net force: The net force is the vector sum of all the forces acting on an object. An unbalanced, or non-zero net force always produce an acceleration. Types of forces:Forces can be divided into two types: A contact force arises because of physical contact between objects, such as a push or pull, friction, tension from a rope or string, and so on. An action-at-a-distance force arises even though when the objects are not in contact, such as gravity, the magnetic force, and the electric force. More about of forces:Force is the most elusive physical quantity in our study. Although it is the cause of the change of the state of the motion of an object, in many cases the magnitude and direction of a force are not known at first hand. They have to be derived from the motion state of the object. Throughout your study you will meet many kinds of forces, each having its own specific characters. They make the physics world.

3. 4.2 Inertia and Newton’s First Law of Motion • Galileo’s experiment: • According to Aristotle, the natural state of objects was to be at rest, and if you got them moving, eventually they would come to rest again. • Galileo did the experiments of rolling balls down and up inclined planes, and realized that in the absence of some kind of force, an object would keep moving forever once it got started. Galileo called this inertia. Inertia is the natural tendency of an object to maintain a state of rest or to remain in uniform motion in a straight line. Newton realized that mass is a quantitative measure of inertia. A massive object has more inertia, or more resistance to a change its motion.

4. Newton’s first law of motion;sometimes called the law of inertia: In the absence of an unbalanced applied force, a body at rest remains at rest, and a body in motion remains in motion with a constant velocity. • Why is Newton’s first law of motion not so apparent to us in our everyday life? • Real-world complications mask simple physics • Solution: minimize or overwhelm complications • To demonstrate inertia: • Work on level ground (minimize gravity influence) • Use wheels, ice, or air support (minimize friction) • Work fast (overwhelm friction) • Use vacuum (remove air resistance) Demo: Tablecloth Isaac Newton (1642-1727)

5. Read: Ch4: 1-2 Homework: Ch4: E7,9 Due: September 13

6. September 6 Newton’s second law of motion 4.3 Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the applied net force. The unit of force is newton (N), 1 N = 1 kg . m/s2. Newton’s second law of motion allows the quantitative analysis of force and motion. If the net force acting on an object is zero, the object’s acceleration is zero, and it remains at rest or in uniform motion, which is Newton’s first law of motion. Demo: Hammer, blocks, and hand Mass and weight: Weight of an object is the gravitational force of attraction that a celestial body exerts on the object. For us, this is mainly due to the Earth. Near the surface of the earth, the weight of an object is Here, g is the acceleration of gravity. One kg of mass has a weight of 9.8 N. This equation also explains why all objects in free fall have the same acceleration g.

7. A system: A system consists of one or more objects that you are studying. Virtually any one object, or any group of objects can form a system, if you are interested in analyzing their motions. Once a system is defined, all existing forces can be distinguished as either external force or internal force. Internal forces cancel each other when applying Newton’s second law of motion. Newton’s second law may be applied to the whole system, or to any part of a system (which actually forms their own system). Example 4.1: Newton’s Second Law: Finding Acceleration Example4.3: Newton’s Second Law: All or Part of the System? (When a string is stretched taut, it is said to be under tension. For a light string, the forces at the two ends of the string has the same magnitude, which is also due to Newton’s second law.)

8. Newton’s second law in component form: Newton’s second law applies to each component of the acceleration: Example 4.4: Newton’s Second Law: Components of Force

9. Read: Ch4: 3 Homework: Ch4: E14,23,28 Due: September 13

10. September 9 Newton’s third law of motion 4.4 Newton’s Third Law of Motion For every force (action) that one object exerts on a second object, there is an equal but oppositely directed force (reaction) that the second object exerts on the first object. • Additional notes on Newton’s third law: • Which force is considered the action or the reaction is arbitrary. The two forces exist at the same time. • Newton’s third law is universal, it works whether the object is stationary or moving. • The two forces are exerted on two different objects. They do not cancel directly.(cf. Two forces exerted on the same object may cancel each other.) • The two forces are always in opposite directions. In mechanics they are also along one line. • Demo: Two persons pull each other with two different spring scales. • Example 4.5: Where Are the Newton’s Third Law Force Pairs?

11. Normal force: A normal force is the force a surface exerts on an object and is always perpendicularto the surface between the objects. Nature can adjust the strength and direction of the normal forces. 4.5 More on Newton’s Laws: Free-Body Diagrams and Translational Equilibrium A free-body diagram draws the forces on an object as though they all act at a common point. This diagram is used to discuss the motion of the object with the help of Newton’s second-law. • Draw Cartesian axes with the origin at a point where the forces act, and with one axe in the direction of the acceleration of the body. • Draw all force vectors from the origin of the axes. • Resolve any force that is not along the x- or y-axis into its x- and y-components. • Use force components to analyze the motion of the object using Newton’s second law of motion.

12. Example 4.6: Up or Down? Motion on a Frictionless Inclined Plane Example4.7: Components of Force and Free-Body Diagrams Translational equilibrium: An object either at rest or moving at a constant velocity is said to be in translational equilibrium. According to Newton’s laws, the condition for translational equilibrium is S Fi=0, or Example4.8: Keep It Straight: In Static Equilibrium

13. Read: Ch4: 4-5 Homework: Ch4: E32,36,40,55 Due: September 20

14. September 10 Friction 4.5 Friction Friction refers to the resistance to motion that occurs whenever two objects are in contact with each other. Frictional force is parallel to the contact surface between the objects. • More on frictional force: • It is resulted from the complicated electromagnetic forces between the microscopic structures of the contacting surfaces. • It adjusts itself in response to the situation. • Friction is ubiquitous. It can help us. It can bother us. Static and kinetic frictions: Static friction refers to the cases in which the frictional force is sufficient to prevent relative motion between two surfaces. It acts to prevent objects from starting to slide.Example: You push a desk but it does not move. There exists a static friction between the legs of the desk and the floor. Kinetic friction (sliding) occurs when there is relative motion between the surfaces of the two objects.Example: You push the desk harder and it is now moving. There is still a resistance between the legs of the desk and the floor, which tries to stop the motion of the desk.

15. Coefficients of friction: Frictional force ( f ) is approximately proportional to the normal force (N). Static friction prevents the relative motion between the surfaces. Its magnitude depends on the circumstances, and is in the range of Here ms is the coefficient of static friction. The maximum static fraction is

16. Once the object is sliding, the friction changes to kinetic friction, which opposes the motion of the object, and has a magnitude of Here mkis the coefficient of kinetic friction. Generally, the coefficient of kinetic friction is less than the coefficient of static friction, mk<ms, which means that the force of kinetic friction is less than the force of maximum static friction.

17. Example4.10: Pulling a Crate: Static and Kinetic Forces of Friction Example4.11: Pulling at an Angle: A Closer Look at the Normal Force

18. Read: Ch4: 6 Homework: Ch4: 63,64,66 Due: September 20

19. “Everything is a lost horse.”