College Physics, 7th Edition Lecture Outline Chapter 4 College Physics, 7th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

Chapter 4 Force and Motion © 2010 Pearson Education, Inc.

Units of Chapter 4 Concept of Force and Net Force Newton’s First Law of Motion - Inertia Newton’s Second Law of Motion – F=ma Newton’s Third Law of Motion – Action/Reaction Free-Body Diagrams (FBD) and Translational Equilibrium Friction – 2 Kinds © 2010 Pearson Education, Inc.

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. A force is defined as a push or a pull. A force may not actually change an object’s state of motion, as there may be other forces that prevent it from doing so. Resistant force – friction. If the net force—the vector sum of all forces acting on the object—is not zero, the velocity will indeed change. © 2010 Pearson Education, Inc.

4.1 The Concepts of Force and Net Force This figure illustrates what happens in the presence of zero and nonzero net force. © 2010 Pearson Education, Inc.

4.1 The Concepts of Force and Net Force We distinguish two types of forces: A contact force, such as a push or pull, friction, and tension from a rope or string. A force that acts at a distance (not touching), such as gravity, the magnetic force, or the electric force. These are called field forces. They are invisible and were not discovered/understood until “modern” times – late 1800’s. © 2010 Pearson Education, Inc.

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. © 2010 Pearson Education, Inc.

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. Inertia is Italian for lazy. Inertia is the lazy force. © 2010 Pearson Education, Inc.

4.2 Inertia and Newton’s First Law of Motion Newton’s first law is called the law of inertia: In the absence of an unbalanced applied force (Fnet = 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). The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out). © 2010 Pearson Education, Inc.

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. Double the force -> double the acceleration. Double the mass -> half the acceleration. And so on… © 2010 Pearson Education, Inc.

4.3 Newton’s Second Law of Motion The units of force are called Newtons after Isaac Newton. 1 N = 1 kg . m/s2. © 2010 Pearson Education, Inc.

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/s2 Weight therefore has the same units as force in the SI system—Newtons. © 2010 Pearson Education, Inc.

4.3 Newton’s Second Law of Motion NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes. When an object moves to a different planet – weight changes. What is the weight of an 85.3-kg person - On Earth? On Mars (ag= 3.2 m/s2)? © 2010 Pearson Education, Inc.

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! © 2010 Pearson Education, Inc.

4.3 Newton’s Second Law of Motion Newton’s second law applies separately to each component (x’s separate from the y’s) of the force. Must find the Cartesian components. © 2010 Pearson Education, Inc.

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. © 2010 Pearson Education, Inc.

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? © 2010 Pearson Education, Inc.

4.4 Newton’s Third Law of Motion “For every action there is an EQUAL and OPPOSITE reaction. This law focuses on action/reaction pairs (forces) They NEVER cancel out All you do is SWITCH the wording! PERSON on WALL WALL on PERSON © 2010 Pearson Education, Inc.

4.4 Newton’s Third Law of Motion Action: HAMMER HITS NAIL Reaction: NAIL HITS HAMMER Action: Earth pulls on YOU Reaction: YOU pull on the earth All you do is SWITCH the wording! © 2010 Pearson Education, Inc.

4.4 Newton’s Third Law of Motion This figure shows the force during a collision between a truck and a train. You can clearly see the forces are EQUAL and OPPOSITE. To help you understand the law better, look at this situation from the point of view of Newton’s Second Law. There is a balance between the mass and acceleration. One object usually has a LARGE MASS and a SMALL ACCELERATION, while the other has a SMALL MASS (comparatively) and a LARGE ACCELERATION. © 2010 Pearson Education, Inc.

4.5 More on Newton’s Laws: Free-Body Diagrams and Translational Equilibrium A free-body diagram (FBD) draws the forces on an object as though they all act at a given point. You should always draw such a diagram whenever you are solving Force problems. © 2010 Pearson Education, Inc.

4.5 More on Newton’s Laws: Free-Body Diagrams and Translational Equilibrium If an object is to be in translational (means motion) 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. © 2010 Pearson Education, Inc.

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. Image life without friction… © 2010 Pearson Education, Inc.

4.6 Friction Types of friction: Static friction: when the frictional force is large enough to prevent motion. Static – not moving. Kinetic friction: when two surfaces are sliding along each other. Kinetic – motion. Rolling friction: when an object is rolling without slipping. A ball rolling down a hill. Without rolling friction the ball would only translate down the hill – slide. © 2010 Pearson Education, Inc.

4.6 Friction We observe that the frictional force is proportional to the normal force. For static friction: The constant μs 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. © 2010 Pearson Education, Inc.

4.6 Friction For kinetic friction: The constant μk is called the coefficient of kinetic friction, and is usually smaller than μs. © 2010 Pearson Education, Inc.

Friction Force = x FN

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. © 2010 Pearson Education, Inc.

4.6 Friction The coefficients of friction depend on both materials involved. © 2010 Pearson Education, Inc.

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?) Note: Friction ONLY depends on the MATERIALS sliding against each other, NOT on surface area. © 2010 Pearson Education, Inc.

4.6 Friction Air resistance is another form of friction. It depends on an object’s shape and size, as well as its speed. VERY complex relationship = calculus. 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. © 2010 Pearson Education, Inc.

4.6 Friction This figure shows the velocity as a function of time for a falling object with air resistance. © 2010 Pearson Education, Inc.

Free-Body Diagrams A pictorial representation of forces complete with labels. FN Weight(mg) – Always drawn from the center, straight down Force Normal(FN) – A surface force always drawn perpendicular to a surface. Tension(T or FT) – force in ropes and always drawn AWAY from object. Friction(Ff)- Always drawn opposing the motion. T Ff T W1,Fg1 or m1g m2g © 2010 Pearson Education, Inc.

FBD - Inclines q q q Ff q FN q mg q Tips for inclines: Rotate Axis Break weight into components

Free-Body Diagrams TIPS for solving problems Draw a FBD – ALWAYS! Resolve anything into COMPONENTS Write equations of equilibrium (NSL) Solve for unknowns © 2010 Pearson Education, Inc.

Example 1 A 10-kg box is being pulled across the table to the right at a constant speed with a force of 50N. Calculate the Force of Friction Calculate the Force Normal FN Fa Ff mg

Example 2 FN Fa Fay Ff Fax mg Suppose the same box is now pulled at an angle of 30 degrees above the horizontal (10-kg box, 50 N force). Calculate the Force of Friction Calculate the Force Normal FN Fa Fay Ff 30 Fax mg

Example 3 A 10-kg box is being pulled across the table to the right by a rope with an applied force of 50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it. FN In which direction, is this object accelerating? The X direction! So N.S.L. is worked out using the forces in the “x” direction only Fa Ff mg

Example 4 A mass, m1 = 3.00 kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable. FN T T m1g m2g

Example 4

Example 5 A 1500 N crate is being pushed across a level floor at a constant speed by a force F of 600 N at an angle of 20° below the horizontal as shown in the figure. a) What is the coefficient of kinetic friction between the crate and the floor? Fa Fay FN 20 Fax Ff mg

Example 6 Fa If the 600 N force is instead pulling the block at an angle of 20° above the horizontal as shown in the figure, what will be the acceleration of the crate. Assume that the coefficient of friction is the same as found in (a) FN Fay 20 Fax Ff mg

Example 7 Masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a frictionless pulley. As shown in the diagram, m1 is held at rest on the floor and m2 rests on a fixed incline of angle 40 degrees. The masses are released from rest, and m2 slides 1.00 m down the incline in 4 seconds. Determine (a) The acceleration of each mass (b) The coefficient of kinetic friction and (c) the tension in the string. T FN m2 m2gcos40 Ff 40 T m2g m1 40 m2gsin40 m1g

Example 7

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: © 2010 Pearson Education, Inc.

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. © 2010 Pearson Education, Inc.

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. NFL – Inertia NSL – F=ma NTL – Action/reaction Translational equilibrium: an object having no net force on it in any direction. Its velocity is constant or zero. © 2010 Pearson Education, Inc.

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. © 2010 Pearson Education, Inc.