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 1 2 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. 4.1 The Concepts of Force and Net Force This figure illustrates what happens in the presence of zero and nonzero net force. However, if the net force the vector sum of all forces acting on the object is not zero, the velocity will indeed change. 3 4 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. 5 6 1
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). 7 8 Question 4.1a Newton s First Law I A book is lying at rest on a table. The book will remain there at rest because: a) there is a net force but the book has too much inertia b) there are no forces acting on it at all c) it does move, but too slowly to be seen d) there is no net force on the book e) there is a net force, but the book is too heavy to move Question 4.1b Newton s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero 9 10 Question 4.1c Newton s First Law III You put your book on a) a net force acted on it the bus seat next to b) no net force acted on it you. When the bus c) it remained at rest stops suddenly, the book slides forward off d) it did not move, but only seemed to the seat. Why? e) gravity briefly stopped acting on it Question 4.1d Newton s First Law IV You kick a smooth flat stone out on a frozen pond. The stone slides, slows down, and eventually stops. You conclude that: a) the force pushing the stone forward finally stopped pushing on it b) no net force acted on the stone c) a net force acted on it all along d) the stone simply ran out of steam e) the stone has a natural tendency to be at rest 11 12 2
Experiments show that the acceleration of an object is proportional to the force exerted on it and inversely proportional to its mass. Force (newtons, N) The units of force are called newtons. 1 N = 1 kg. m/s 2. Acceleration (m/sec 2 ) Mass (kg) 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. 13 14 5.2 Newton's Second Law 5.2 Newton's Second Law If you apply more force to an object, it accelerates at a higher rate. 15 If an object has more mass it accelerates at a lower rate because mass has inertia. 16 An object s weight is the force exerted on it by gravity. 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! Here, g is the acceleration of gravity: g = 9.81 m/s 2 Weight therefore has the same units as force newtons. 17 18 3
4.3 Newton's Second Law Newton s second law applies separately to each component of the force. Three forms of the second law: 19 20 Question 4.2a Cart on Track I Question 4.2b Cart on Track II Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? a) slowly come to a stop b) continue with constant acceleration c) continue with decreasing acceleration d) continue with constant velocity e) immediately come to a stop We just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration? a) push the cart harder before release b) push the cart longer before release c) push the cart continuously d) change the mass of the cart e) it is impossible to do that 21 22 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. 23 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? 24 4
Question 4.9a Going Up I A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? a) N > mg b) N = mg c) N < mg (but not zero) d) N = 0 e) depends on the size of the elevator v m 25 26 A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? Question 4.9b Going Up II a) N > mg b) N = mg c) N < mg (but not zero) d) N = 0 e) depends on the size of the elevator Question 4.12 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? a) this slows your initial velocity, which is already upward b) you don t go up, you re too heavy c) you re not really pulling down it just seems that way d) the rope actually pulls you up e) you are pulling the ceiling down a m 27 28 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. 29 Equilibrium The condition of zero acceleration is called equilibrium. In equilibrium, all forces cancel out leaving zero net force. Objects that are standing still are in equilibrium because their acceleration is zero. Objects that are moving at constant speed and direction are also in equilibrium. A static problem usually means there is no motion. 30 5
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. 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. 31 32 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 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. 33 34 For kinetic 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. The constant μ k is called the coefficient of kinetic friction, and is usually smaller than μ s. 35 36 6
The coefficients of friction depend on both materials involved. 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. 37 38 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. This figure shows the velocity as a function of time for a falling object with air resistance. 39 40 Question 4.19 Friction A box sits in a pickup truck on a frictionless truck bed. When the truck accelerates forward, the box slides off the back of the truck because: a) the force from the rushing air pushed it off b) the force of friction pushed it off c) no net force acted on the box d) truck went into reverse by accident e) none of the above 41 7