Conceptual Physics Chapter Six Notes: Newton’s Second Law of Motion – Force And Acceleration

6.1 Force Causes Acceleration Unbalanced forces acting on an object causes the object to accelerate. acceleration ~ net force ~ stands for “is directly proportional to” 6.2 Mass Resists Acceleration For a constant force, an increase in the mass will result in a decrease in the acceleration. acceleration ~ 1/mass Inversely – means that the two values change in opposite directions.

acceleration ~ net force 6.3 Newton’s Second Law Newton’s second law states that the acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object. acceleration ~ net force mass a = F m

6.4 Friction The force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together. The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. The friction force opposes the motion of the object. For example, if a book moves across the surface of a desk, the desk exerts a friction force in the direction opposite to the motion of the book.

where µ = coefficient of friction Friction results when two surfaces are pressed together closely, causing attractive intermolecular forces between the molecules of the two different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. The friction force can be calculated using the equation: Ffriction = µ x Fnorm where µ = coefficient of friction Friction is not restricted to solids sliding on one another. Friction also occurs in liquids and gases. They are both called fluids, because they flow. Ea: Try running through waist deep water. Air resistance is friction through air.

Drawing Free-Body Diagrams A diagram showing all the forces acting on an object is called a free-body diagram. Drawing Free-Body Diagrams Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams discussed in Chapter 2; these diagrams will be used throughout your study of physics.

The size of the arrow in a free-body diagram is reflective of the magnitude of the force. The direction of the arrow reveals the direction in which the force acts. Each force arrow in the diagram is labeled to indicate the type of force. It is customary in a free-body diagram to represent the object by a box and to draw the force arrow from the center of the box outward in the direction in which the force is acting. One example of a free- body diagram is shown right.

The free-body diagram above depicts four forces acting upon the object The free-body diagram above depicts four forces acting upon the object. Objects do not always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation. Thus, to construct free-body diagrams, it is extremely important to know the types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction; label each force arrow according to its type. If necessary, refer to the "Net Force Help Sheet" for descriptions of the force types and their symbols. (Next three slides.)

Contact Forces Action-at-a-Distance Forces Types of Forces A force is a push or pull acting upon an object as a result of its interaction with another object. Forces may be placed into two broad categories, based on whether the force resulted from the contact or non-contact of the two interacting objects. Contact Forces Action-at-a-Distance Forces Frictional Force Gravitational Force Tensional Force Electrical Force Normal Force Magnetic Force Air Resistance Force Applied Force Spring Force These types of forces will now be discussed in detail. To read about each force listed above, continue scrolling through the table on the next three pages.

Type of Force and its Symbol Description of Force Applied Force Fapp An applied force is a force which is applied to an object by another object or by a person. If a person is pushing a desk across the room, then there is an applied force acting upon the desk. The applied force is the force exerted on the desk by the person. Gravity Force (also known as Weight) Fgrav The force of gravity is the force with which the earth, moon, or other massive body attracts an object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity which is directed "downward" towards the center of the earth. The force of gravity on an object on earth is always equal to the weight of the object as given by the equation: Fgrav = m * g where: g = acceleration of gravity = 9.8 m/s2 (on Earth) m = mass (in kg) (Caution: do not confuse weight with mass. See slide 13.)

Type of Force and its Symbol Description of Force Normal Force Fnorm The normal force is the support force exerted upon an object which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasion, a normal force is exerted horizontally between two objects which are in contact with each other. Friction Force Ffrict The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. The friction force opposes the motion of the object. For example, if a book moves across the surface of a desk, the desk exerts a friction force in the direction opposite to the motion of the book. Friction results when two surfaces are pressed together closely, causing attractive intermolecular forces between the molecules of the two different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. The friction force can be calculated using the equation on a previous slide.

Type of Force and its Symbol Description of Force Air Resistance Force Fair Air resistance is a special type of frictional force which acts upon objects as they travel through the air. Like all frictional forces, the force of air resistance always opposes the motion of the object. This force will frequently be ignored due to its negligible magnitude. It is most noticeable for objects which travel at high speeds (e.g., a skydiver or a downhill skier) or for objects with large surface areas. Tensional Force Ftens Tension is the force which is transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end. The tensional force is directed along the wire and pulls equally on the objects on either end of the wire. Spring Force Fspring The spring force is the force exerted by a compressed or stretched spring upon any object which is attached to it. This force acts to restores the object, which compresses or stretches a spring, to its rest or equilibrium position. For most springs (specifically, for those said to obey "Hooke's Law"), the magnitude of the force is directly proportional to the amount of stretch or compression.

Mass vs. Weight The force of gravity is a source of much confusion to many students of physics. The mass of an object refers to the amount of matter that is contained by the object; the weight of an object is the force of gravity acting upon that object. Mass is related to "how much stuff is there" and weight is related to the pull of the Earth (or any other planet) upon that stuff. The mass of an object (measured in kg) will be the same no matter where in the universe that object is located. Mass is never altered by location, the pull of gravity, speed or even the existence of other forces. For example, a 2-kg object will have a mass of 2 kg whether it is located on Earth, on the moon, or on Jupiter; its mass will be 2 kg whether it is moving or not (at least for purposes of this study); and its mass will be 2 kg whether it is being pushed or not.

On the other hand, the weight of an object (measured in Newtons) will vary according to where in the universe the object is. Weight depends upon which planet is exerting the force and the distance the object is from the planet. Weight, being equivalent to the force of gravity, is dependent upon the value of g (acceleration of gravity). On Earth's surface, g is 9.8 m/s2 (often approximated to 10 m/s2). On the moon's surface, g is 1.7 m/s2. Go to another planet, and there will be another g value. In addition, the g value is inversely proportional to the distance from the center of the planet. So if g were measured at a distance of 400 km above the earth's surface, you would find the value of g to be less than 9.8 m/s2. (The nature of the force of gravity will be discussed in detail in in a later chapter of Conceptual Physics.) Always be cautious of the distinction between mass and weight. It is the source of much confusion for many students of physics.

You must thoroughly understand the meaning of each of these forces if you are to successfully proceed through this unit. Ultimately, you must be capable of reading the description of a physical situation and knowing enough about these forces to recognize their presence (or absence) and to construct a free-body diagram which illustrates their relative magnitudes and directions.

Free-body diagrams for four situations are shown below Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Depress the mouse to view the answers. Situation A: Net Force = Situation B: Net Force = Situation C: Net Force = Situation D: Net Force = 0 Newtons 5 Newtons left 0 Newtons 15 Newtons upward

6.5 Applying Force -- Pressure The amount of force per unit area is called pressure. For a constant force, an increase in the area of contact will result in a decrease in the pressure. Pressure = force/area of application P = F/A Pressure = Newtons/Square Meter = Pascals (Pa)

6.6 Free Fall Explained Where F stands for the force (weight) Recall that mass (a quantity of matter) and weight (the force due to gravity) are proportional. In symbolic notation: F / m = F / m = g Where F stands for the force (weight) and m stands for the mass The ratio is the same for all objects

All freely falling objects fall with the same acceleration because the net force on an object is only its weight and ratio of weight to mass is the same for all objects. Since the cannon ball has both a greater weight and inertia (m) one offsets the other. Now the . accelerations of both are equal. Acceleration = g .

6.7 Falling and Air Resistance When the forces of gravity and air resistance act on a falling object, it is not in free fall. The air resistance force an object experiences depends on the object’s speed and area. Air resistance force ~ speed x frontal area Terminal Speed: Terminal speed is the speed at which the acceleration (g) of an object is zero because air friction balances the weight. Terminal Velocity is Terminal Speed & Direction