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Physics Chapter 5 Forces A team of skydivers can form beautiful patterns as they plummet toward Earth at high speeds of up to 120mph. How do the skydivers control their velocities? Bad news around 60 sky divers a year use the ground - Fatalities by Year due to sky diving accidents 2004 (70) 2006 (60) 2005 (62) 2007 (61) 2008 (61) updated http://adventure.howstuffworks.com/skydiving.htm 1 Chapters 3 and 4 were limited to a discussion of the study of how objects move, kinematics. Galileo devised many ingenious experiments that allowed him to effectively describe motions but not to explain them. Chapter 5 introduces the subject of dynamics. The study of why objects move as they do. Dynamics can answer such questions as, "Why do sky divers accelerate rather than fall at a constant rate?" The causes of acceleration were first studied by Sir Isaac Newton (1642-1727). The connection between acceleration and its cause can be summarized by three statements known, after the man who formulated them, as Newton's laws of motion. http://www.neatorama.com/2007/08/08/ten-strange-facts-about-newton/ (Ten strange facts about Newton) 5-1 LAWS OF MOTION Isaac Newton started work on his laws of motion in 1665, but did not publish them until 1687. More than three hundred years later, his three laws still summarize the relationship between acceleration, and its cause, force. Forces http://videos.howstuffworks.com/discovery/4867-physics-primal-forcesvideo.htm (Four forces of Matter) Video 4 number 1 forces What is a force? Force can be defined as a push or a pull. When you hang your jacket on a coat-hook, the hook pulls upward on your jacket. If you place a coin on your palm, the coin pushes downward on your hand. These forces occur when one object touches another. On the other hand, if you drop the coin, it will fall to the ground, pulled by a force called gravity. Gravity is a force that acts between objects even when they are not touching. Sometimes forces, like that of gravity on a coin, cause accelerations; other times forces stretch, bend, or squeeze an object. All forces are vectors - they not only have magnitude but they also have direction. in fact, we define "down" as the direction gravity pulls. Although you can think of hundreds of different forces, physicists group them all into just four kinds. The force that Newton first described, the gravitational force, is an attractive force that exists between all objects. The gravitational force of Earth on the moon holds the moon in its orbit. The gravitational force of the moon on Earth causes tides. Despite its effects on our daily lives, the gravitational force is the weakest of the four forces. The forces that give materials their strength, their ability to bend, squeeze, stretch, or shatter, are examples of the electromagnetic force. These forces result from a basic property of particles called electric charge. Charged particles at rest or in motion exert electric forces on each other. When charged particles are in motion they produce magnetic forces on each other. Electric and magnetic forces are both considered to be aspects of a single force, the electromagnetic force. It is 2 very large compared to the gravitational force. The two remaining forces are less familiar because they are evident mainly over distances the size of the nucleus of an atom. The third force is the strong nuclear force that holds the particles in the nucleus together. It is the strongest of the four forces - hundreds of times stronger than the electromagnetic force. But it only acts over distances the size of the nucleus. The fourth force is called the weak force. It is actually a form of electromagnetic force, and is involved in the radioactive decay of some nuclei (Boson). Scientists have discovered and used mathematical laws to describe forces each mathematical law works well in its own domain, but sometimes seem to contradict each other when dealing with different forces. For instance, in normal scales, gravity uses one law, but for very small objects, another law is needed. For this reason scientists have tried to develop a theory that could be used to describe all forces. Electricity and magnetism were unified into a single force in the 1870s. Recently the electromagnetic force has been linked with the weak force. This suggests to physicists that all forces are different aspects of a single force. They have constructed theories called Grand Unification Theories (GUTs) and Supersymmetric theories that try to demonstrate this unification. Latest model is the String Theory that shows the most promise of unifying a theory to describe all forces. String Theory describes matter as strings instead of individual particles like grains of sand. Based on 10 to 24 dimensions only see 4. At this time all theories that unify forces are incomplete and do not fully agree with experiments. Newton's First Law of Motion http://videos.howstuffworks.com/hsw/19126-roller-coaster-physics-the-thrill-of-it-all-video.htm Video 2 #1 Suppose you place a cart on the incline and let it gravity pull it down the incline onto a carpet. The carpet fibers push backwards on the cart wheels , and the cart will stop moving soon after it leaves the incline. If you use a smooth wooden floor instead of the carpet, the smooth surface pushes back less, and the cart will roll farther. If you have an extremely smooth floor and wheels that produce very little resistance to motion, very little backward force is exerted on the wheels, and the cart may roll at almost constant speed for a long distance without any additional pushes from you. Galileo speculated that if a perfectly smooth object were on a perfectly smooth horizontal surface it might travel forever in a straight line. Air Hockey Table It was left to Newton, however, to develop Galileo's idea more fully. Imagine an 3 object with no force on it. If it is moving at constant speed in a straight line, it will continue to do so. If it is at rest, it will remain at rest, because rest is a special name for zero velocity. This behavior of objects is described in Newton's first law. The law states that an object with no force acting on it moves with constant velocity. This Referred to as Inertia. Turn corner with ball and cart Objects often have more than one force acting on them. The sum of all the forces acting on an object is known as the net force. Think of the rope used in a tug-ofwar. The members of one team pull the rope in one direction and the people on the other team pull it in the opposite direction. If the two teams pull with equal strength, the rope will experience no net force, even though there are obviously forces acting on it, it will not move. If one team pulls harder than the other a net force exists and the rope will begin to accelerate in the direction of the net force. To understand the effects of forces in two directions, we assign signs: positive for forces to the right, negative for forces to the left. All the forces pulling to the right combine to produce one large positive force. In the same way, forces to the left combine into a large negative force. If the team pulling to the right is stronger, the net force is positive. If the other team is stronger, the net force is negative. Thus, our method of finding the net force on an object is to sum all the forces, keeping track of signs. If the rope starts at rest, it does not begin to move if the net force is zero. It has a constant – zero - velocity. Thus, we state Newton's first law more carefully: an object with no net force acting on it remains at rest or moves with constant velocity in a straight line. (Law of Inertia) Newton's Second Law of Motion http://science.howstuffworks.com/newton-law-of-motion.htm/printable http://videos.howstuffworks.com/hsw/19113-exploring-motion-newtons-second-law-of-motion-video.htm Video 2 #2 Newton's first law states that if there is no net force on an object, there is no acceleration. In other words, the object moves at constant velocity. But how much will an object accelerate when there is a net force? Think about pushing a bowling ball. The harder you push, the faster the velocity of the ball will change. The larger the force, the larger the acceleration, the rate of change in velocity. Acceleration is found to be directly proportional to force. Acceleration also depends on the mass of an object. Masses of bowling balls vary; some are small, others large. If you exert the same force on a less massive ball, its acceleration will be larger. In fact, if the mass is half as much, the acceleration will be twice as large. The acceleration is inversely proportional to the mass. These relationships are true in general and are stated in Newton's second law: the acceleration of a body is directly proportional to the net force on it and inversely 4 proportional to its mass. Newton's second law may be summarized as a = F/m, or m = F/a or, more commonly, F = ma. If an object has a net force exerted on it, it will accelerate. Force and acceleration both have direction as well as size. The acceleration is in the same direction as the force causing it. If the force is in the positive direction, so will be the acceleration. Similarly, if the force is in the negative direction, so will be the acceleration. By reducing the mass of a racecar, car builders get maximum acceleration from the available force. The fastest top fuelers can attain terminal speeds of over 530 km/h (329 mph) while covering the quarter mile (402 m) distance in roughly 4.45 seconds. It is often related that Top Fuel dragsters are the fastest accelerating vehicles on Earth; quicker even than the space shuttle launch vehicle or catapult-assisted jet fighter According to Newton's second law, a net force on an object causes it to accelerate. In addition, the larger the mass of the object, the smaller the acceleration. For this reason, we say that a massive body has more inertia than a less massive body. The following simple experiment demonstrates Newton's second law. Lay an index card over a drinking glass. Place a penny on the card, centered over the glass. With the flick of a finger, give the card a quick horizontal push. The card moves away, but the penny drops into the glass. Why doesn't the penny accelerate with the card? The penny has more mass (we say it has more inertia), and a horizontal force is needed to accelerate it. The card is too smooth to exert much horizontal force on the penny. With very little horizontal force on it, the penny has little 5 sideways acceleration. As soon as the card is no longer under it, however, the upward force of the card is removed. There is mostly a net downward force, the force of gravity, so the penny accelerates downward, falling into the glass. Beakers of water paper pull - Table cloth and dishes inertia and second law combined. The Unit of Force Newton's second law gives us a way to define the unit of force. A force that causes a mass of one kilogram to accelerate at a rate of one meter per second squared is defined as one newton (N). That is F = ma = (1.00 kg)(1.00 m/s2) = 1.00 N. N = kgxm/s2 Newton's Second Law of Motion The Unit of Force Example Problem - Using Newton's Second Law to Find the Net Force on an Accelerating Object What net force is required to accelerate a 1500-kg racecar at +3.00 m/s2? Example Problem - Finding Force When Acceleration Must Be Calculated An artillery shell has a mass of 55.0 kg. The shell is fired from a cannon, leaving the barrel with a velocity of + 770.0 m/s. The cannon barrel is 1.50 m long. Assume that the force, and thus the acceleration, of the shell is constant while the shell is in the cannon barrel. What is the force on the shell while it is in the cannon barrel? Do Practice Problems 5-1 Newton’s Third Law of Motion http://videos.howstuffworks.com/hsw/19114-exploring-motion-newtons-third-law-of-motion-video.htm Video 4 #4 and #5 If you try to accelerate a bowling ball by kicking it, you may become painfully aware of Newton's third law. As you kick the ball, your toes will feel the equal force the ball is exerting on you. If you exert a force on a baseball to stop it, the ball also exerts a force on you. These are examples of the forces described in Newton's third law: When one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude but opposite in direction. According to Newton's third law, if you exert a small force on the ball, it exerts a small force on you. The larger the force you exert on the ball, the stronger its force is on you. The magnitudes are always equal. These two forces are often called action-reaction forces. 6 By analyzing the forces, using Figure 5-6, involved when you pick up a bowling ball up from the ground. When the ball is resting on the ground – the gravitational force between the ball and the Earth pull the ball toward the center of the earth – when the ball is in contact with the ground the upward force of the ground is equal to the downward force of gravity - your hand exerts a force on the ball, the ball exerts a force on your hand that is the same size, but in the opposite direction. These two forces are action-reaction forces. As you examine the diagram, note the two equal but opposite forces acting on two different objects, your hand and the ball, the ball and Earth. Why does the ball accelerate upward? After all, the force your hand exerts on the ball is the same magnitude as the force the ball exerts on your hand. Where is the net upward force that causes the acceleration? To answer that question, we need to isolate the bowling ball and examine only the forces that act on it. There are two forces acting on the ball, the force of your hand directed upward and the force of gravity pulling downward. When you lift the ball, the force exerted by your hand is greater than the force of gravity, so the ball accelerates upward. Only the forces on the ball determine its acceleration. Do Concept Review 5-1 5.2 USING NEWTON'S LAWS http://videos.howstuffworks.com/hsw/19112-exploring-motion-newtons-firstlaw-of-motion-video.htm review 1st law and friction A track can only exert force on a car through the tires. This force will be transmitted only if there is enough friction between track and tires. If you have ever tried to accelerate a car on icy or wet roads, you know that the existence of friction is not guaranteed. Among the applications of Newton's laws we will explore 7 in this section is friction. Drag racers "smoke" their tires before a race to increase the friction between the tires and the track. They rev the engine just enough to get the tires spinning, then let the tires spin for about 5 seconds just long enough to smoke the tires over. That's long enough because the purpose of the burnout is to clean off the surface, and to put heat in them for traction. Some racers mistakenly boil the tires off, or spin the tires for 15-20 seconds. This destroys the tires, and makes them slicker, not stickier, because overheating the tires draws the oils and resins to the tread surface. Mass and Weight While walking on the sidewalk at Old Fashion Days, you see a box and you give it a good kick. If the box goes sailing, you know it has a small mass. If the box hardly accelerates at all, it must have a large mass. Suppose you pick up the box and then let it drop. It will accelerate downward. Thus, Earth must be exerting a downward force on it. The gravitational force exerted by a large body, usually Earth, is called weight. Weight is measured in newtons like all other forces. A medium-sized apple weighs about one newton. The weight of an object can be found using Newton's second law of motion. On the surface of Earth, objects that have only the force of gravity acting on them fall downward with an acceleration of 9.80 m/s2. This acceleration is so important that we give it a special symbol and write g = 9.80 m/s2 in the downward direction. The force of gravity on an object is present whether the object is falling, resting on the ground, or being lifted. Earth still pulls downward on it. The force of gravity is given by the equation F = mg. This force is called the weight of an object and is given the symbol W. Therefore, we write W = mg since g is acting downward (-) W is (-) On the surface of Earth, the weight of an object with a 1.00-kg mass is - 9.80 N. The weight of any object is proportional to its mass. Weight is a vector quantity 8 pointed toward the center of Earth. If we assign "up" to be the positive direction, then weight would be negative. More often we will use the word "down" instead of a minus sign (-) when direction is needed. Example Problem - Calculating Weight Find the weight of a 2.26-kilogram bag of sugar. Do practice problems 5-2 You do not really "feel" your weight. What you do feel are the forces exerted on you by objects that touch you. When standing, you don't feel the force you exert on the floor, you feel the force the floor exerts on you. The larger your weight, the larger the force exerted by the floor will be on you. When sitting, you feel the force of the chair. If you do a pull-up, you feel the force of the bar on your hands. When you are at rest, or moving at constant velocity, these forces are equal in magnitude to your weight, but in the opposite direction. Gravity is the force pulling you down the normal force pushes back against you. (-) W and (+) FN Mass and weight are not the same. Weight depends on the acceleration due to gravity, and thus may vary from location to location. A person weighs a very small amount less on top of a high mountain, even though he or she has the same mass. A bowling ball with a mass of 7.3 kg weighs 71 N on Earth, but only 12 N on the moon, where the acceleration due to gravity is 1.6 m/s2. If you tried to kick a bowling ball across the surface of the moon, however, it would be just as hard to accelerate as on Earth because its mass would be the same. Two Kinds of Mass We discussed one way of determining mass by measuring the amount of force necessary to accelerate it, that is, its inertia. The inertial mass of an object is the ratio of the net force exerted on the object and its acceleration, m = F/a A second method of finding mass is to compare the gravitational forces exerted on two objects, one with an unknown mass, and the other with a known mass. The object with the unknown mass is placed on one pan of a beam balance. The object with the known mass is placed on the pan at the other end of the beam. When the pans balance, the force of gravity is the same on each pan. Then the masses of the objects on either side of the balance must be the same. The mass measured this way is called the gravitational mass. Suppose you apply the same force to two different objects and find that the acceleration of one object is twice that of the other. You would conclude that the mass of the first object is half that of the second. If you put the same objects on a pan balance, you would find the gravitational force on the first object is half the gravitational force on the second. Very precise experiments indicate that inertial 9 mass and gravitational mass of objects are equal within the accuracy of the experiments . In 1916 Albert Einstein (1879-1955) used the equality of inertial and gravitational masses as one foundation for his general theory of relativity. http://www.jca.umbc.edu/~george/html/courses/glossary/mass_inertial_vs_grav.ht ml A body's Inertial Mass is is measure of how strongly the body is accelerated (by A) by a given force. It is the mi in Newton's 2nd-law: Force = mi A A body's Gravitational Mass is is measure of how strongly the body is affected by the force of Gravity It is the mg in Newton's universal law of gravitation when the body is a distance R from another body of mass M: Force = G mg M R-2 The inertial mass mi determines how the body accelerates as a results of the application of any force. The gravitational mass mg determines how the body "feels" a gravitational force (and how much of a gravitational force it generates). The fact that: mi A =G mgM r2 if mi equals mg then it is apparent that the acceleration (due to the force of gravity) is independent of mass. Simply put, gravitational mass is that property of an object that causes it to attract other massive objects. An objects inertial mass is its resistance to changes in motion. http://www.exploratorium.edu/ronh/weight/ your weight on other planets Friction Slide your hand across a tabletop. The force you feel opposing the movement of your hand is called friction. It acts when brakes slow a bike or car, when a sailboat moves through water, and when a skydiver falls through the air. If there were no friction, whenever you tried to walk, you would slip as if you were on ice. Without friction, tires would spin and cars would not move. An eraser could not grip your homework paper and remove a mistake. Friction is the force that opposes the motion between two surfaces that are in contact. The direction of the force is parallel to the surface and in a direction that opposes the slipping of the two surfaces. To understand the cause of friction, you must recognize that on a microscopic scale, all surfaces are rough. When two surfaces rub, the high points of one surface temporarily bond to the high points of the other. The electromagnetic force causes this bonding. 10 If you try to push a heavy box along the floor, you will find it very hard to start it from rest, Figure 5-11. If two objects are not in relative motion, static friction is the force that opposes the start of motion. Static friction forces have maximum values. When the magnitude of your push on the box is greater than the maximum value of the static friction between the floor and the box, the box starts moving. When the box starts to move, the force of friction will decrease. The force between surfaces in relative motion is called sliding friction. The force of sliding friction is less than that of static friction. Thus, a car will stop faster if the wheels are not skidding. (anti-lock brakes) How large is the force of sliding friction? Slide your book across the desk. It slows down. To keep it moving at constant velocity, you must exert a constant force that is just the same size as the frictional force, but in the opposite direction. See Figure 5-12. (No net force if no acceleration so FA = Ff) By measuring the force you exert, called the applied force, FA , you can find the force of friction, Ff. Ff = FA Experimentally it has been found that the force of friction depends primarily on the force pushing the surfaces together, FN, and on the nature of the surfaces in contact. This result can be expressed as Ff = FN. 11 In this equation (mu), called the coefficient of friction, is a constant that depends on the two surfaces in contact. FN is the force pushing the surfaces together. It is called the normal force, where "normal" means perpendicular. In the example above, the normal force on the book is the force exerted by the table, perpendicular to its surface. When the book is resting on a horizontal surface, the normal force of the table on the book is numerically equal to the weight of the book (W). The normal force of the table on the book is also equal to the force of the book on the table, since they are action-reaction forces. If you use your hands to exert an extra force, F, down on the book, the force of the book on the table increases to W + F. By Newton's third law, the normal force of the table upward on the book also increases to W + F. W + F. = FN Notice that when we are studying the friction between two objects, such as a book lying on a horizontal table, there are two sets of forces. The first set is parallel to the surfaces that are touching. This set consists of the force that moves the object and the opposing frictional force. The second set of forces acts perpendicular to the two surfaces. The downward force may be just the object's weight, the downward force of gravity. Often, though, other forces are exerted on the object. A person might push the object down, or perhaps lift up on it. A second object might be placed on top of the first. The sum of all vertical forces is the total downward force. The other force in this set is the equal but upward force exerted on the object by the table. That force is the normal force on the object. In many cases, the coefficient of sliding friction for two surfaces in contact is very nearly independent of the amount of surface area in contact and the velocity of motion. The problems we solve will make this assumption. PROBLEM SOLVING STRATEGY When solving problems involving more than one force on an object: 1. Always start by sketching a neat drawing of the object. 2. Then draw arrows representing all the forces acting on the object. 3. Label each force with the cause of the force. Be specific. Examples are "weight," "force of string," "normal force exerted by table," "force of friction." Evaluate your drawing and compare all the forces to determine the magnitude and direction of the NET FORCE because that is the force that will cause acceleration. Example Problem - Static and Sliding Friction A smooth 40.0N wooden block is placed on a smooth wooden tabletop. You put a force sensor hook to your lab quest and observe that a force of 18.0N must be applied to start the block in motion, once it starts to move at a constant velocity the force applied drops to 14.0N. a. What is the coefficient of static friction and sliding friction for the block and table? b. If a 20.0-N brick is placed on the block, 12 what force will be required to keep the block and brick moving at constant velocity? Do practice problems 5-3 While this general description of friction known as the standard model has practical utility, it is by no means a precise description of friction. Friction is in fact a very complex phenomenon, which cannot be represented by a simple model. Almost every simple statement you make about friction can be countered with specific examples to the contrary. Saying that rougher surfaces experience more friction sounds safe enough - two pieces of coarse sandpaper will obviously be harder to move relative to each other than two pieces of fine sandpaper. But if two pieces of flat metal are made progressively smoother, you will reach a point where the resistance to relative movement increases. If you make them very flat and smooth, and remove all surface contaminants in a vacuum, the smooth flat surfaces will actually adhere to each other, making what is called a "cold weld". But like in most cases in basic, introductory physics we simplify to gain a general understanding of nature. The standard model can be used if the following assumptions are made: The frictional force is independent of area of contact The frictional force is independent of the velocity of motion The frictional force is proportional to the normal force. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html The Net Force Causes Acceleration 13 In Newton's second law of motion, F = ma, the force, F, that causes the mass to accelerate is the net force acting on the mass. In Figure 5-14a, a 10 kg mass rests on a frictionless, horizontal surface. A + 100-N force is exerted horizontally on the mass. The resulting acceleration is +100 N a = F/m = +100N/10kg = +10m/s2 If the same mass rests on a rough surface, friction will oppose the motion. In Figure 5-14b, the frictional force is -20 N. The negative sign indicates that the force acts in a direction opposite the positive applied force. The acceleration of any object is the result of the net force acting on it. The net force is the vector sum of the applied and frictional forces. When you sum forces, which are vectors, you must pay attention to the signs. That is, Fnet = Fapplied + Ff +100 N + (-20 N) = +80 N, and the resulting acceleration is given by a = Fnet/m = +80N/10kg =+8.0 m/s2 The direction of the acceleration is positive, in the direction of the applied force. Other forces besides friction act on objects. Consider a 10.0-kg stone lying on the ground. The stone is at rest; the net force on it is zero. The weight of the stone, W, is 98.0 N in a downward direction. The ground exerts an equal and opposite force, 98.0 N, upward. The net force is Fnet = Fground + W = +98.0 N + (- 98.0 N) =0N How can the stone be given an upward acceleration? Suppose a person exerts a 148-N upward force on the stone. The net force is Fnet = Fperson + W = +148.0 N + (-98.0 N) = +50.0 N. The net force acting on the stone is 50 N upward. The acceleration of the stone 14 can now be found from Newton's second law: a = f/m = +50 N/10 kg = +5 m/s2 The stone will be accelerated upward at +5 mIs2. Example Problem - Forces on an Accelerating Object A spring scale hangs from the ceiling of an elevator. It supports a package that weighs 25.0 N. a. What upward force does the scale exert when the elevator is not moving? b. What force must the scale exert when the elevator and object accelerate upward at + 1.50 mIs2? Use Figure 5-16. That is, the scale exerts a larger force and thus indicates a larger weight when the elevator accelerates upward. If you ride an elevator, you "feel" your inertial mass. When the elevator accelerates upward, you feel the added force of the floor on your feet, accelerating 15 you up. You also feel the forces your muscles exert on your stomach; these forces may make your stomach feel strange. Do Practice Problems 5-4 The Fall of Bodies in the Air Astronauts on the surface of the moon dropped a hammer and a feather together. These objects hit the surface at the same time. Without any air, all objects fall with the same acceleration. On Earth, the acceleration is 9.80 m/s2; on the moon it is 1.60 m/s2. In air, however, an additional force acts on moving bodies. Try this experiment. Take two pieces of notebook paper. Crumple one into a ball. Now hold them side by side and drop them at the same time. The two pieces of paper obviously do not accelerate at the same rate. The flat paper encounters much more air resistance than the ball. Air resistance, sometimes called the drag force, is a friction-like force. As an object moves through the air, it collides with air molecules that exert a force on it. The force depends on the size and shape of the object, the density of the air, and the speed of motion. (Through air knuckle ball) Suppose you drop a ping-pong ball. Just after you drop it, it has very little velocity, and thus very small drag force. The downward force of gravity is larger than the upward drag force and the ball accelerates downward. As its velocity increases, so does the drag force. At some later time the drag force equals the force of gravity. The net force is now zero, and the velocity of the ball becomes constant. This constant velocity is called the terminal velocity. The terminal velocity of a ping-pong ball in air is only 9 m/s (20mph). A basketball has a terminal velocity of 20 m/s (45mph) as does a penny, while a baseball can fall as fast as 42m/s (94mph). Skiers increase their terminal velocities by decreasing drag force. They hold their bodies in an "egg" shape and wear very smooth clothing and streamlined helmets. A skydiver can control terminal velocity by changing body shape. A spread-eagle position gives the slowest terminal velocity, about 60 m/s (134mph). By opening the parachute, The skydiver has become part of a very large object with a correspondingly large drag force. The terminal velocity is now about 5 m/s 11mph. http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html freefall with air and without 16