Chapter 4 Dynamics: Newton's Laws of Motion PDF

Chapter 4 Dynamics: Newton’s Laws of Motion © 2014 Pearson Education, Inc.  4-1 Force A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force...

Chapter 4 Dynamics: Newton’s Laws of Motion © 2014 Pearson Education, Inc.  4-1 Force A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The magnitude of a force can be measured using a spring scale. © 2014 Pearson Education, Inc.  4-2 Newton’s First Law of Motion Newton’s first law is often called the law of inertia. Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. © 2014 Pearson Education, Inc.  4-2 Newton’s First Law of Motion Inertial reference frames: An inertial reference frame is one in which Newton’s first law is valid. This excludes rotating and accelerating frames. © 2014 Pearson Education, Inc.  4-3 Mass Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms. Mass is not weight: Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same. © 2014 Pearson Education, Inc.  4-4 Newton’s Second Law of Motion Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. (4-1) © 2014 Pearson Education, Inc.  4-4 Newton’s Second Law of Motion Force is a vector, so ΣF = ma is true along each coordinate axis. The unit of force in the SI system is the newton (N). Note that the pound is a unit of force, not of mass, and can therefore be equated to newtons but not to kilograms. © 2014 Pearson Education, Inc.  4-5 Newton’s Third Law of Motion Any time a force is exerted on an object, that force is caused by another object. Newton’s third law: Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. © 2014 Pearson Education, Inc.  4-5 Newton’s Third Law of Motion A key to the correct application of the third law is that the forces are exerted on different objects. Make sure you don’t use them as if they were acting on the same object. © 2014 Pearson Education, Inc.  4-5 Newton’s Third Law of Motion Rocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket. Note that the rocket does not need anything to “push” against. © 2014 Pearson Education, Inc.  4-5 Newton’s Third Law of Motion Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source. (4-2) © 2014 Pearson Education, Inc. Second vs Third Law: What’s the Difference? Second Law considers forces which are applied all to ONE object. Third Newton’s described action-reaction forces, they are applied to TWO different objects. Action: object 1 acts on object 2 Reaction: object 2 acts on object 1.  4-6 Weight—the Force of Gravity; and the Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is: (4-3) © 2014 Pearson Education, Inc. Direction of Force of Gravity A person of mass m is riding an elevator standing on the bathroom scale (people are doing strange things). Elevator starts from the ground floor accelerating up with acceleration a. What is the reading of bathroom scale?  4-6 Weight—the Force of Gravity; and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? The force exerted perpendicular to a surface is called the normal force. It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!) © 2014 Pearson Education, Inc.  Normal Force, or Force of Reaction of Supports Important: Normal force is not always equal in magnitude to force of gravity! And not always opposite in direction! These two are two independent forces! Normal Force is always perpendicular to the area of support:  4-7 Solving Problems with Newton’s Laws— Free-Body Diagrams 1. Draw a sketch. 2. For one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each. © 2014 Pearson Education, Inc.  4-7 Solving Problems with Newton’s Laws— Free-Body Diagrams 3. Resolve vectors into components. 4. Apply Newton’s second law to each component. 5. Solve. © 2014 Pearson Education, Inc.  4-7 Solving Problems with Newton’s Laws— Free-Body Diagrams When a cord or rope pulls on an object, it is said to be under tension, and the force it exerts is called a tension force. © 2014 Pearson Education, Inc.  4-8 Problems Involving Friction, Inclines On a microscopic scale, most surfaces are rough. The exact details are not yet known, but the force can be modeled in a simple way. For kinetic—sliding—friction, we write: μk is the coefficient of kinetic friction, and is different for every pair of surfaces. © 2014 Pearson Education, Inc.  4-8 Problems Involving Friction, Inclines This table lists the measured values of some coefficients of friction. Note that the coefficient depends on both surfaces. © 2014 Pearson Education, Inc.  4-8 Problems Involving Friction, Inclines Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied. © 2014 Pearson Education, Inc.  4-8 Problems Involving Friction, Inclines The static frictional force increases as the applied force increases, until it reaches its maximum. Then the object starts to move, and the kinetic frictional force takes over. Sliding friction is called kinetic friction. Approximation of the frictional force: Ffr = μkFN. © 2014 Pearson Education, Inc.  4-8 Problems Involving Friction, Inclines An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force. The normal force is always perpendicular to the surface. The friction force is parallel to it. The gravitational force points down. If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero. © 2014 Pearson Education, Inc. An object of mass m is dragged along horizontal floor by the force directed θ above the horizontal, so that acceleration of this object is a. Coefficient of kinetic friction between floor and object is μ. Find the magnitude of force F in terms of given variables. Objects A and B are connected through a pulley and cord of zero mass, as it is shown in the figure. Masses of objects, as well as coefficient of kinetic friction μ and angle of incline θ are given. Object B is accelerating down. Find acceleration and force of tension in the cord.