Chapter 4: Forces Goals of Period 4 Section 4.1: To discuss the effect of net forces acting on objects Section 4.2: To examine the acceleration of falling objects Section 4.3: To describe the frictional force 4.1 Net Force and Acceleration In Period 3 we discussed Newton s second law of motion, F = M a, which indicates that the amount of acceleration of an object is proportional to the net force acting on it. F M a (Equation 4.1) where F = net force (in newtons) M = mass (in kilograms) a = acceleration (in meters/second 2 ) From this equation, we might expect that giving an object a push with a force F would cause it to accelerate forever, since Newton s Law does not specify the duration of the acceleration. However, our everyday experience tells us that a giving an object a push causes it to slide and then come to a stop. How can we explain our experience in terms of Newton s Law? Newton s Law requires that we consider all of the forces acting on an object. In equation 4.1, F is the net force acting. A net force is the sum of the forces acting in the same direction or the difference of forces acting in opposite directions. Figures 4.1 and 4.2 show the net force acting on a box, which is sitting on a horizontal surface such as a level floor. Forces acting on an object in the same direction add together. For example, it is easier to move a stalled car with two people pushing in the same direction because their forces add. Fig. 4.1 Two Forces Acting on a Box in the Same Direction Force 1 Force 2 Net Force Net Force = Force 1 + Force 2 27
When forces act on an object in opposite directions, the net force is the difference between the forces. Equal forces acting in opposite directions cancel each other. For example, if you hold a box in your hands, the force of gravity pushing down on the box is balanced by the force of your hands pushing up on the box. Since the box does not move, the net force acting on it is zero. Fig. 4.2 Forces Acting in Opposite Directions Net Force Force 1 Force 2 Net force = Force 1 - Force 2 In the case of a sliding box, the force of friction acts in the direction opposite to the motion of the box and slows its acceleration. Figure 4.3 illustrates an applied force greater than the force of friction. The net force on the box is the difference between the applied force and the force of friction. In this case, the net force accelerates the box in the direction of the applied force. Fig 4.3 An Applied Force Larger than the Force of Friction Applied Force The object accelerates. Force of Friction If the applied force is greater than the force of friction, the box accelerates across a level floor in the direction of the applied force. Next we consider an applied force equal to or less than the force of friction. If an object is at rest, an applied force greater than the force of friction is necessary to start the object in motion. Therefore, an object at rest remains at rest when a force equal to or less than the force of friction is applied. To an object in motion we can continuously apply an amount of force on the object equal to the force of friction so that the object moves at a constant velocity. In the case of constant velocity, the applied force equals the force of friction between the object and the surface it is sliding across. Figure 4.4 illustrates a box moving at a constant velocity. Since the applied force is equal to and in the opposite direction of the force of friction, the net force on the box is zero. 28
Fig 4.4 An Applied Force Equal to the Force of Friction Applied Force The object moves at a constant velocity. Force of Friction If the applied force is equal to the force of friction, the box moves with constant velocity across a level floor in the direction of the applied force. If a force less than the force of friction is applied to a moving object, the object slows down (decelerates) and will eventually comes to rest. Figure 4.5 illustrates this situation. Fig 4.5 An Applied Force Less than the Force of Friction Applied Force The object slows down (decelerates). Force of Friction If the box is in motion and the applied force is less than the force of friction, the box slows down (decelerates). When an object accelerates in air, water, or other medium, it must push the molecules of the medium out of its way. As the object s velocity increases, it must push aside increasing amounts of the medium per unit time. The greater the amount of the medium it must push aside, the greater the resistance to its motion. This resistance is a frictional force between the surface of the object and the medium it moves through. The amount of the frictional force increases as the velocity of the object increases. Eventually the object reaches a velocity at which the frictional force is equal to the applied force. The two equal forces acting in opposite directions cancel, and the object moves at constant velocity. 29
Concept Check 4.1 a) You apply a horizontal force to the side of a box to push it across a level floor. What must be the net force on a 5 kilogram box for it to move with an acceleration of 2 meters/second each second (2 meters/second 2 )? b) Once this box is moving, you must apply a force of 6 N to keep it moving at a constant velocity in a straight, horizontal line. How great is the force of friction between the bottom of the box and the surface it slides across? 4.2 The Acceleration of Falling Objects So far, we have considered a net force accelerating an object in a horizontal direction. Next, we discuss the acceleration caused by the force of gravity. The force of gravity causes unsupported objects near the Earth to accelerate toward the Earth s center. We will learn more about how the gravitational force operates in Period 6. In this period, we examine the relationship between the acceleration of falling objects and the net force acting on them. We have seen that an object moving horizontally through air or fluid reaches a constant velocity when the force accelerating it equals the force needed to push aside the air or fluid, that is when the net force acing on the object is zero. Similarly, a falling object must push air molecules out of its way as it falls. The object reaches a constant velocity when the force of the friction of air molecules pushing up equals the force of gravity pulling down the net force is zero. The greater the surface area of the falling object, the greater the upward force of air resistance. A parachutist drifts to earth at a safe constant velocity because the large surface area of the parachute creates enough friction as it pushes aside air molecules to equal the force of gravity pulling the parachutist down, which results in zero net force. 4.3 The Frictional Force What Determines the Amount of Frictional Force? The amount of friction between surfaces depends upon the type of materials in contact, the smoothness of their surfaces, and the amount of force pressing them together. A block of wood sliding across rough sandpaper experiences more friction than the same block sliding across a smooth surface. The rough sandpaper surface provides more opportunity for collisions between atoms of the two surfaces, resulting in greater friction. However, surface smoothness is not the only predictor of frictional force the type of surface material is also a factor. In class we will compare the frictional force between different surfaces by calculating their coefficient of friction the ratio of the frictional force to the weight of the object. 30
The greater the amount of force pressing surfaces together, the more friction between the surfaces. With more force pushing objects together, the atoms in their surfaces interlock to a greater extent, increasing the frictional force. You can feel this increased friction when you rub your hand gently and then with firm pressure against a surface. The force of gravity presses objects against surfaces. Thus, the amount of frictional force is related to the fundamental gravitational force as well as the electromagnetic force. Because increased force increases friction, drivers sometimes put sandbags in their cars in winter to add weight. The increased gravitational force of the bags pressing the car onto the road increases the friction between the car's tires and the pavement and decreases the chance of sliding on a slippery road. Types of Friction If you try to move a heavy table by pushing on it, you may find that a great deal of force is needed to start it moving. Before an object will move, we must exert a force to overcome static friction, the frictional force between two surfaces that are not moving relative to one another. Once the table begins to move, it experiences sliding friction as the rough surface on the bottom of the table legs slides over the floor. As our class activities will illustrate, static friction is greater than sliding friction. Is Friction Good or Bad? Sometimes friction is very undesirable. The pistons of a car engine should move freely, with very little friction between the pistons and cylinder walls. We reduce friction in a car s engine by keeping a layer of oil between the pistons and their cylinders. Running a car s engine without sufficient oil can overheat the pistons and cylinder walls, causing the piston to freeze in the cylinder and ruin the engine. As a car moves, it experiences a frictional force from the air. You can feel this force by putting your hand out of a moving car s window. The frictional force of air resistance results in a substantial energy cost because the car's engine must move the car as well as the air molecules around the car. In order to reduce air resistance, car designers shape vehicles aerodynamically to move through the air with less friction. In other cases friction is very desirable. Friction between our feet and the ground allows us to walk without slipping. Walking with too little friction, such as on an icy sidewalk, is difficult! Friction also keeps objects in place. When we put dishes on a table, we can assume they will stay there. Without friction, the dishes would slowly slide off the table, unless the table was exactly level. You may have seen a similar effect as a puck slides around an air hockey table. Friction also makes it possible for us to stop or turn a car. When we press on the brake pedal of a car, a brake pad presses against the brake disc or drum on the car wheels. The resulting frictional force slows the car. The brakes convert the mechanical energy of motion of the car into thermal energy. To turn a car, the tires must press against the road so that the road will press back against the tire and force the car in the direction of the turn. If the tires do not make good contact with an icy or slick road, there may be too little friction to turn the car. 31
Concept Check 4.2 a) What determines the amount of friction between two objects? b) As you push a box from rest across a floor, what types of friction exist between the floor and the box? How Physics Helps You Stay Alive: Stopping a Car Before antilock brakes became available on cars, drivers learned to "pump" their brakes when trying to stop on a slippery road to prevent their wheels from locking and sliding. However, in cars equipped with antilock brakes, you should NOT pump the brakes when stopping. Antilock brakes automatically pump for you. When you apply antilock brakes on a slippery road, you may hear a pulsating or vibrating sound as the brakes engage and disengage rapidly. Every time a wheel begins to lock up and slide, the brakes on that wheel are momentarily eased to keep the tire rolling and to prevent a skid. Why is locking brakes dangerous? Brakes use friction between the brake drum and the wheel to convert the car s energy of motion into thermal energy. When wheels lock, the site of friction moves from the brake drum to the surface between the road and the wheel. If the wheels lock, the usual static friction between rolling car wheels and the road becomes sliding friction. The coefficient of sliding friction is less than the coefficient of static friction between rolling wheels and the road and much less than the coefficient of friction inside the brake drum, making a car with locked wheels much more difficult to stop. Throughout the World of Energy, we will use equations to do calculations involving physics concepts. To help you use equations, the next Skills and Strategies box examines the connection between equations and the concepts they represent. 32
Skills and Strategies #6: Turning Words into Equations When we say that the area of a circle is equal to times its radius squared, we have used a sentence to express a mathematical relationship. Equations are a shorthand way to express mathematical relationships. In an equation, we represent the nouns in the sentence with alphabet letters, such as A for area or r for radius. We represent the verb forms in the sentence with operating signs: is equal to with an equal sign ( = ), squared by a 2 above the letter and times by a x or by placing letters side by side. Our shorthand sentence gives the equation 2 A r In equations we encounter two types of nouns variables, whose values change depending on the situation, and constants, whose values never change. In this example, r is an independent variable because we can choose any value for the radius. A is a dependent variable the area of the circle can change, but its value depends on the radius we choose. is a constant no matter which radius we choose, always equals 3.14159. In this text, we will indicate dependent and independent variables in boldface italics to distinguish them from constants and the units of each quantity. Units indicate the way we have measured each quantity. We could specify the radius of the circle in units of feet (ft), meters (m), miles (mi), or any other unit of length. When we square the radius, we square its units as well as its value. (4 ft) 2 = 4 ft x 4 ft = 16 ft 2 The units of area might be in feet squared (ft 2 ), meters squared (m 2 ) or miles squared (mi 2 ) depending on how we have measured the radius. The constant has no units 2 A r 2 2 2 x (4 3.14159... (Although a calculator gives the answer as 50.26548, we round to 50.) ft) x 16 ft 50 ft Concept Check 4.3 Turn the sentences into equations. a) The circumference of a circle is equal to 2 times times its radius. b) The volume of a sphere is equal to 4/3 times times its radius cubed. 33
Period 4 Summary 4.1 The net force of all forces acting in the same direction is the sum of the forces. The net force of forces acting in opposite directions is the difference of the forces. The net force on an object that is not accelerating is zero. When a moving object is not accelerating, its velocity is constant. An object reaches a constant velocity when the sum of the forces acting on it cancel. (The net force equals zero.) 4.2: The force of gravity accelerates a falling object. A falling object reaches a Constant velocity when the force of the friction of air molecules pushing up equals the force of gravity pulling down the net force is zero. 4.3: The amount of friction between surfaces depends on (1) the type of materials in contact, (2) the smoothness of their surfaces, and (3) the amount of force pressing them together. Stationary objects experience static friction and moving objects experience friction. Static friction is greater than sliding friction. The coefficient of friction between an object and the surface over which it moves is the ratio of the frictional force divided by the weight of the object. 34