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Chapter 4 Force and Motion

Units of Chapter 4 The Concepts of Force and Net Force Inertia and Newton’s First Law of Motion Newton’s Second Law of Motion Newton’s Third Law of Motion More on Newton’s Laws: Free-Body Diagrams and Translational Equilibrium Friction

4.1 The Concepts of Force and Net Force A force is something that is capable of changing an object’s state of motion, that is, changing its velocity. Any particular force may not actually change an object’s state of motion, as there may be other forces that prevent it from doing so. However, if the net force—the vector sum of all forces acting on the object—is not zero, the velocity will indeed change.

4.1 The Concepts of Force and Net Force This figure illustrates what happens in the presence of zero and nonzero net force.

4.1 The Concepts of Force and Net Force We distinguish two types of forces: 1. A contact force, such as a push or pull, friction, tension from a rope or string, and so on. 2. A force that acts at a distance, such as gravity, the magnetic force, or the electric force.

4.2 Inertia and Newton’s First Law of Motion 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 experiments 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.

4.2 Inertia and Newton’s First Law of Motion 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 (constant velocity). Later, Newton realized that mass is a measure of inertia.

4.2 Inertia and Newton’s First Law of Motion Newton’s first law is sometimes called the law of inertia: In the absence of an unbalanced applied force (F net = 0), a body at rest remains at rest, and a body already in motion remains in motion with a constant velocity (constant speed and direction).

4.3 Newton’s Second Law of Motion Experiments show that the acceleration of an object is proportional to the force exerted on it and inversely proportional to its mass. 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.

4.3 Newton’s Second Law of Motion The units of force are called newtons. 1 N = 1 kg. m/s 2.

4.3 Newton’s Second Law of Motion An object’s weight is the force exerted on it by gravity. Here, g is the acceleration of gravity: g = 9.81 m/s 2 Weight therefore has the same units as force—newtons.

4.3 Newton’s Second Law of Motion Newton’s second law may be applied to a system as a whole, or to any part of a system. It is important to be clear about what system or part you are considering!

4.3 Newton’s Second Law of Motion Newton’s second law applies separately to each component of the force.

4.4 Newton’s Third Law of Motion For every force (action), there is an equal and opposite force (reaction). Note that the action and reaction forces act on different objects. This image shows how a block exerts a downward force on a table; the table exerts an equal and opposite force on the block, called the normal force N.

4.4 Newton’s Third Law of Motion This figure illustrates the action–reaction forces for a person carrying a briefcase. Is there a reaction force in (b)? If so, what is it?

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 given point. You should draw such a diagram whenever you are solving second-law problems.

4.5 More on Newton’s Laws: Free- Body Diagrams and Translational Equilibrium If an object is to be in translational equilibrium, there must be no net force on it. This translates into three separate requirements—that there be no force in the x -direction, the y -direction, or the z -direction.

4.6 Friction The force of friction always opposes the direction of motion (or of the direction the motion would be in the absence of friction). Depending on the circumstances, friction may be desirable or undesirable.

4.6 Friction Types of friction: Static friction: when the frictional force is large enough to prevent motion Kinetic friction: when two surfaces are sliding along each other Rolling friction: when an object is rolling without slipping

4.6 Friction We observe that the frictional force is proportional to the normal force. For static friction: The constant μ s is called the coefficient of static friction. The static frictional force may not have its maximum value; its value is such that the object does not move, and depends on the physical circumstances.

4.6 Friction For kinetic friction: The constant μ k is called the coefficient of kinetic friction, and is usually smaller than μ s.

4.6 Friction This figure illustrates what happens as the applied force increases: first, the static frictional force increases; then the kinetic frictional force takes over as the object begins to move.

4.6 Friction The coefficients of friction depend on both materials involved.

4.6 Friction This form for the frictional force is an approximation; the actual phenomenon is very complicated. The coefficient of friction may vary somewhat with speed; there may be some dependence on the surface area of the objects. Also, remember that these equations are for the magnitude of the frictional force—it is always perpendicular to the normal force. (Why?)

4.6 Friction Air resistance is another form of friction. It depends on an object’s shape and size, as well as its speed. For an object in free fall, as the force of air resistance increases with speed, it eventually equals the downward force of gravity. At that point, there is no net force on the object and it falls with a constant velocity called the terminal velocity.

4.6 Friction This figure shows the velocity as a function of time for a falling object with air resistance.

Review of Chapter 4 A force is capable of changing an object’s state of motion; that state of motion will change if and only if there is a net force on the object. Newton’s first law: In the absence of unbalanced external forces, an object’s velocity will not change. Newton’s second law:

Review of Chapter 4 Weight is the force exerted on an object by gravity: Newton’s second law holds separately for each component of the force and acceleration.

Review of Chapter 4 Newton’s third law: For every force, there is an equal and opposite force (reaction force) acting on the other object. Translational equilibrium: an object having no net force on it in any direction. Its velocity is constant or zero.

Review of Chapter 4 Friction is the resistance to motion that occurs when different surfaces are in contact. Static friction: Kinetic friction: An object falling in air experiences air resistance; this resistance increases until the object reaches its terminal velocity.