Kinetic Energy. Kinetic Energy. Potential Energy

Transcription

1 Kinetic Energy Kinetic energy is the energy associated with an object s motion. Doing work on an object increases its kinetic energy. Work done = change in kinetic energy KE = 1 2 mv 2 Kinetic Energy Negative work is the work done by a force acting in a direction opposite to the object s motion. For example, a car skidding to a stop What force is acting to slow the car? Potential Energy If work is done but no kinetic energy is gained, we say that the potential energy has increased. For example, if a force is applied to lift a crate, the gravitational potential energy of the crate has increased. The work done is equal to the force (mg) times the distance lifted (height). The gravitational potential energy equals mgh. Work is done on a large crate to tilt the crate so that it is balanced on one edge, rather than sitting squarely on the floor as it was at first. Has the potential energy of the crate increased? a) Yes b) No Yes. The weight of the crate has been lifted slightly. If it is released it will fall back and convert the potential energy into kinetic energy. 1

2 Potential Energy The term potential energy implies storing energy to use later for other purposes. For example, the gravitational potential energy of the crate can be converted to kinetic energy and used for other purposes. Potential Energy An elastic force is a force that results from stretching or compressing an object. Elastic potential energy is the energy gained when work is done to stretch a spring. The spring constant, k, is a number describing the stiffness of the spring. Potential Energy The increase in elastic potential energy is equal to the work done by the average force needed to stretch the spring. PE = work done = average force distance Conservative forces are forces for which the energy can be completely recovered. Gravity and elastic forces are conservative. Friction is not conservative. average force = 1 2 kx PE = 1 2 kx 2 2

3 Conservation of Energy Conservation of energy means the total energy (the kinetic plus potential energies) of a system remain constant. Energy is conserved if there are no forces doing work on the system. If W = 0, then TME = KE+PE Energy Transformation for a Pendulum Total Mechanical Energy A lever is used to lift a rock. Will the work done by the person on the lever be greater than, less than, or equal to the work done by the lever on the rock? a) Greater than b) Less than c) Equal to d) Unable to tell from this graph Work done in pulling a sled up a hill produces an increase in potential energy of the sled and rider. This initial energy is converted to kinetic energy as they slide down the hill. The work done by the person can never be less than the work done by the lever on the rock. If there are no dissipative forces they will be equal. This is a consequence of the conservation of energy. 3

4 Any work done by frictional forces is negative. That work removes mechanical energy from the system. A sled and rider with a total mass of 40 kg are perched at the top of the hill shown. Suppose that 2000 J of work is done against friction as the sled travels from the top (at 40 m) to the second hump (at 30 m). Will the sled make it to the top of the second hump if no kinetic energy is given to the sled at the start of its motion? a) yes b) no c) It depends. Yes. The difference between the potential energy at the first point and the second point, plus loss to friction is less than the kinetic energy given at the start of the motion. A sled and rider with a total mass of 40 kg are perched at the top of the hill shown. Suppose that 2000 J of work is done against friction as the sled travels from the top (at 40 m) to the second hump (at 30 m). What is the maximum height that the second hump could be in order for the sled to reach the top? a) 10 m b) 35 m c) 32 m d) 40 m e) 30 m Energy Transformation on a Roller Coaster 35 m. This additional height would allow the body to reach this point just as it has lost all of its kinetic energy. If W = 0, then TME = KE+PE 4

5 DISSIPATIVE forces acting on Downhill Skiing If W = 0, then TME = KE+PE But in this case W 0 KE +W Internal W Internal + W work PE -W Work done by external forces = TME Work done by external forces TME = PE + KE Energy and Oscillations KE +W Internal W Internal + W work PE -W Work done by external forces Work done by external forces Why does a swinging pendant return to the same point after each swing? TME = KE + PE ± W my system ext 5

6 Energy and Oscillations The force does work to move the ball. This increases the ball s energy, affecting its motion. Simple Machines, Work, and Power A simple machine multiplies the effect of an applied force. For example, a lever : A small force applied to one end delivers a large force to the rock. The small force acting through a large distance moves the rock a small distance. Simple Machines, Work, and Power A simple machine multiplies the effect of an applied force. For example, a pulley : A small tension applied to one end delivers twice as much tension to lift the box. The small tension acting through a large distance moves the box a small distance. The mechanical advantage of a simple machine is the ratio of the output force to the input force. For the pulley example, the mechanical advantage is 2. Work is equal to the force applied times the distance moved. Work = Force x Distance: W = F d Work output = Work input units: 1 joule (J) = 1 Nm 6

7 Only forces parallel to the motion do work. Power is the rate of doing work Power = Work divided by Time: P = W / t units: 1 watt (W) = 1 J / s A string is used to pull a wooden block across the floor without accelerating the block. The string makes an angle to the horizontal. Does the force applied via the string do work on the block? a) Yes, the force F does work. b) No, the force F does no work. c) Only part of the force F does work. d) You can t tell from this diagram. Only the part of the force that is parallel to the distance moved does work on the block. This is the horizontal part of the force F. If there is a frictional force opposing the motion of the block, does this frictional force do work on the block? Does the normal force of the floor pushing upward on the block do any work? a) Yes, the frictional force does work. b) No, the frictional force does no work. c) Only part of the frictional force does work. d) You can t tell from this diagram. Since the frictional force is antiparallel to the distance moved, it does negative work on the block. a) Yes, the normal force does work. b) No, the normal force does no work. c) Only part of the normal force does work. d) You can t tell from this diagram. Since the normal force is perpendicular to the distance moved, it does no work on the block. 7

8 A force of 50 N is used to drag a crate 4 m across a floor. The force is directed at an angle upward from the crate as shown. What is the work done by the horizontal component a) 120 J b) 160 J c) 200 J d) 280 J e) 0 J The horizontal component of force is 40 N and is in the direction of motion: W = F d = (40 N) (4 m) = 160 J. of the force? What is the work done by the vertical component of the force? a) 120 J b) 160 J c) 200 J d) 280 J e) 0 J The vertical component of force is 30 N but isn t in the direction of motion: W = F d = (30 N) (0 m) = 0 J. What is the total work done by the 50-N force? a) 120 J b) 160 J c) 200 J d) 280 J e) 0 J Only the component of force in the direction of motion does work: W = F d = (40 N) (4 m) = 160 J. What are temperature and heat? Are they the same? What causes heat? 8

9 What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its Measurement If two objects are in contact with one another long enough, the two objects have the same temperature. This begins to define temperature, by defining when two objects have the same temperature. When the physical properties are no longer changing, the objects are said to be in thermal equilibrium. Two or more objects in thermal equilibrium have the same temperature. This is the zeroth law of thermodynamics. The first widely used temperature scale was devised by Gabriel Fahrenheit. Another widely used scale was devised by Anders Celsius. The Celsius degree is larger than the Fahrenheit degree: the ratio of Fahrenheit degrees to Celsius degrees is 180/100, or 9/5. T C = 5 9 ( T 32) F T F = 9 5 T C + 32 The zero point on the Fahrenheit scale was based on the temperature of a mixture of salt and ice in a saturated salt solution. The zero point on the Celsius scale is the freezing point of water. Both scales go below zero. Is there such a thing as absolute zero? They are both equal at

10 What is absolute zero? If the volume of a gas is kept constant while the temperature is increased, the pressure will increase. This can be used as a means of measuring temperature. A constant-volume gas thermometer allows the pressure to change with temperature while the volume is held constant. The difference in height of the two mercury columns is proportional to the pressure. We can then plot the pressure of a gas as a function of the temperature. The curves for different gases or amounts are all straight lines. When these lines are extended backward to zero pressure, they all intersect at the same temperature, C. Since negative pressure has no meaning, this suggests that the temperature can never get lower than C, or 0 K (kelvin). T K = T C Can anything ever get colder than 0 K? No. Can absolute zero ever be reached? No. T K = T C Heat and Specific Heat Capacity What happens when objects or fluids at different temperatures come in contact with one another? The colder object gets hotter, and the hotter object gets colder, until they both reach the same temperature. What is it that flows between the objects to account for this? We use the term heat for this quantity. 10

11 Heat and Specific Heat Capacity Heat flow is a form of energy transfer between objects. One-hundred grams of room-temperature water is more effective than 100 grams of room-temperature steel shot in cooling a hot cup of water. Steel has a lower specific heat capacity than water. The specific heat capacity of a material is the relative amount of heat needed to raise its temperature. The specific heat capacity of a material is the quantity of heat needed to change a unit mass of the material by a unit amount in temperature. For example, to change 1 gram by 1 Celsius degree. It is a property of the material, determined by experiment. The specific heat capacity of water is 1 cal/g C : it takes 1 calorie of heat to raise the temperature of 1 gram of water by 1 C. We can then calculate how much heat must be absorbed by a material to change its temperature by a given amount: Q = mc T where Q = quantity of heat m = mass c = specific heat capacity T = change in temperature When two objects at different temperatures are placed in contact, heat will flow from the object with the higher temperature to the object with the lower temperature. Heat added increases temperature, and heat removed decreases temperature. Heat and temperature are not the same. Temperature is a quantity that tells us which direction the heat will flow. Phase Changes and Latent Heat When an object goes through a change of phase or state, heat is added or removed without changing the temperature. Instead, the state of matter changes: solid to liquid, for example. The amount of heat needed per unit mass to produce a phase change is called the latent heat. The latent heat of fusion of water corresponds to the amount of heat needed to melt one gram of ice. The latent heat of vaporization of water corresponds to the amount of heat needed to turn one gram of water into steam. 11

12 If the specific heat capacity of ice is 0.5 cal/g C, how much heat would have to be added to 200 g of ice, initially at a temperature of -10 C, to raise the ice to the melting point? If the specific heat capacity of ice is 0.5 cal/g C, how much heat would have to be added to 200 g of ice, initially at a temperature of -10 C, to completely melt the ice? a) 1,000 cal b) 2,000 cal c) 4,000 cal d) 0 cal m = 200 g c = 0.5 cal/g C T = -10 C Q = mc T = (200 g)(0.5 cal/g C )(10 C) = 1,000 cal (heat required to raise the temperature) a) 1,000 cal b) 14,000 cal c) 16,000 cal d) 17,000 cal L f = 80 cal/g Q = ml f = (200 g)(80 cal/g) = 16,000 cal (heat required to melt the ice) Total heat required to raise the ice to 0 C and then to melt the ice is: 1,000 cal + 16,000 cal = 17,000 cal = 17 kcal Joule s Experiment and the First Law of Thermodynamics Rumford noticed that cannon barrels became hot during drilling. Joule performed a series of experiments showing that mechanical work could raise the temperature of a system. In one such experiment, a falling mass turns a paddle in an insulated beaker of water, producing an increase in temperature. Joule s Experiment and the First Law of Thermodynamics Joule s experiments led to Kelvin s statement of the first law of thermodynamics. Both work and heat represent transfers of energy into or out of a system. If energy is added to a system either as work or heat, the internal energy of the system increases accordingly. The increase in the internal energy of a system is equal to the amount of heat added to a system minus the amount of work done by the system. U = Q - W 12

13 Joule s Experiment and the First Law of Thermodynamics This introduced the concept of the internal energy of a system. An increase in internal energy may show up as an increase in temperature, or as a change in phase, or any other increase in the kinetic and/or potential energy of the atoms or molecules making up the system. Internal energy is a property of the system uniquely determined by the state of the system. The internal energy of the system is the sum of the kinetic and potential energies of the atoms and molecules making up the system. A hot plate is used to transfer 400 cal of heat to a beaker containing ice and water; 500 J of work are also done on the contents of the beaker by stirring. What is the increase in internal energy of the ice-water mixture? a) 900 J b) 1180 J c) 1680 J d) 2180 J W = -500 J Q = 400 cal = (400 cal)(4.19 J/cal) = 1680 J U = Q - W = 1680 J - (-500 J) = 2180 J A hot plate is used to transfer 400 cal of heat to a beaker containing ice and water; 500 J of work are also done on the contents of the beaker by stirring. How much ice melts in this process? Gas Behavior and The First Law Consider a gas in a cylinder with a movable piston. If the piston is pushed inward by an external force, work is done on the gas, adding energy to the system. a) g b) g c) 6.5 g d) g L f = 80 cal/g = (80 cal/g)(4.19 J/cal) = 335 J/g U = ml f m = U / L f = (2180 J) / (335 J/g) = 6.5 g The force exerted on the piston by the gas equals the pressure of the gas times the area of the piston: F = PA The work done equals the force exerted by the piston times the distance the piston moves: W = Fd = (PA)d = P V 13

14 If the gas is being compressed, the change in volume is negative, and the work done is negative. Work done on the system is negative. Negative work increases the energy of the system. If the gas is expanding, positive work is done by the gas on its surroundings, and the internal energy of the gas decreases. An ideal gas is a gas for which the forces between atoms are small enough to be ignored. For an ideal gas, absolute temperature is directly related to the average kinetic energy of the molecules of the system. Most gases behave approximately as ideal gases. If the process is adiabatic, no heat flows into or out of the gas. Even though no heat is added, the temperature of a gas will increase in an adiabatic compression, since the internal energy increases. In an isothermal process, the temperature does not change. The internal energy must be constant. The change in internal energy, U, is zero. If an amount of heat Q is added to the gas, an equal amount of work W will be done by the gas on its surroundings, from U = Q - W. In an isobaric process, the pressure of the gas remains constant. The internal energy increases as the gas is heated, and so does the temperature. The gas also expands, removing some of the internal energy. Experiments determined that the pressure, volume, and absolute temperature of an ideal gas are related by the equation of state: PV = NkT where N is the number of molecules and k is Boltzmann s constant. What process makes a hot-air balloon rise? When gas is heated in a hotair balloon, the pressure, not the temperature, remains constant. The gas undergoes an isobaric expansion. Since the gas has expanded, the density has decreased. The balloon experiences a buoyant force because the gas inside the balloon is less dense than the surrounding atmosphere. 14

15 The Flow of Heat There are three basic processes for heat flow: Conduction Convection Radiation In conduction, heat flows through a material when objects at different temperatures are placed in contact with one another. (Conduction Contd.) The rate of heat flow depends on the temperature difference between the objects. It also depends on the thermal conductivity of the materials, a measure of how well the materials conduct heat. For example, a metal block at room temperature will feel colder than a wood block of the exact same temperature. The metal block is a better thermal conductor, so heat flows more readily from your hand into the metal. Since contact with the metal cools your hand more rapidly, the metal feels colder. In convection, heat is transferred by the motion of a fluid containing thermal energy. Convection is the main method of heating a house. It is also the main method heat is lost from buildings. 15

16 In radiation, heat energy is transferred by electromagnetic waves. The electromagnetic waves involved in the transfer of heat lie primarily in the infrared portion of the spectrum. Unlike conduction and convection, which both require a medium to travel through, radiation can take place across a vacuum. For example, the evacuated space in a thermos bottle. The radiation is reduced to a minimum by silvering the facing walls of the evacuated space. What process makes a car s interior heat up when parked in the sun? Why are houses insulated with material in the walls instead of just empty space? Why is this insulated material often foil-backed? Is a light-colored roof or a darkcolored roof more energy efficient? What heat-flow processes are involved in solar collectors? What heat-flow processes are involved in the greenhouse effect? 16

17 floating objects and moving fluids Pressure explains... Pressure and Pascal s Principle Why does a small woman wearing high-heel shoes sink into soft ground more than a large man wearing large shoes? Pressure The man weighs more, so he exerts a larger force on the ground. The woman weighs less, but the force she exerts on the ground is spread over a much smaller area. Pressure takes into account both force and the area over which the force is applied. Pressure is the ratio of the force to the area over which it is applied: Units: 1 N/m 2 = 1 Pa (pascal) Pressure is the quantity that determines whether the soil will yield. Pascal s Principle What happens inside a fluid when pressure is exerted on it? Does pressure have a direction? Does it transmit a force to the walls or bottom of a container? P = F A 17

18 Pascal s Principle Fluid pushes outward uniformly in all directions when compressed. Any increase in pressure is transmitted uniformly throughout the fluid. Pressure exerted on a piston extends uniformly throughout the fluid, causing it to push outward with equal force per unit area on the walls and the bottom of the cylinder. This is the basis of Pascal s Principle: Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid. How does a hydraulic jack work? A force applied to a piston with a small area can produce a large increase in pressure in the fluid because of the small area of the piston. This increase in pressure is transmitted through the fluid to the piston with the larger area. The force exerted on the larger piston is proportional to the area of the piston: F = PA. Applying the same pressure to the larger area of the second piston results in a larger force on the second piston. A force of 10 N is applied to a circular piston with an area of 2 cm 2 in a hydraulic jack. The output piston for the jack has an area of 100 cm 2. What is the pressure in the fluid? What is the force exerted on the output piston by the fluid? a) Pa b) 5 Pa c) 10 Pa d) 50 kpa F 1 = 10 N A 1 = 2 cm 2 = m 2 P = F 1 / A 1 = 10 N / m 2 = 50,000 N/m 2 = 50 kpa a) 50 N b) 500 N c) 5,000 N d) 50,000 N P = 50 kpa A 2 = 100 cm 2 = 0.01 m 2 F 2 = PA 2 = (50,000 N/m 2 )(0.01 m 2 ) = 500 N The mechanical advantage is 500 N / 10 N = 50. E5, E6 18

19 Buoyant force Buoyant force F B = W T Archimedes Principle Pressure Archimedes Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. F F F B B B = weight of water displaced = mass of water displaced g = ρ water V g 19

20 Atmospheric Pressure and the Behavior of Gases Living on the surface of the earth, we are at the bottom of a sea of air. This sea of air is thinner at higher altitudes. It is also thinner during certain weather conditions. We describe this property by atmospheric pressure: the pressure of the layer of air that surrounds the earth. At sea level, the atmospheric pressure is 100 kpa, or 14.7 pounds per square inch, but it decreases with altitude. Pascal principle: Application with hydraulic jack Torricelli invented the barometer, a device for measuring atmospheric pressure, in an attempt to explain why water pumps could pump water to a height of only 32 feet. He filled a tube with mercury and inverted it into an open container of mercury. Mercury worked well because it is much denser than water. Density is the mass of an object divided by its volume. Air pressure acting on the mercury in the dish supported a column of mercury, of height proportional to the atmospheric pressure. Otto von Guericke performed a famous experiment to demonstrate the effects of air pressure. He designed two bronze hemispheres that could be smoothly joined together at their rims. He pumped the air out of the sphere formed from the two hemispheres. Two eight-horse teams were unable to pull the hemispheres apart. 20

21 In other experiments on variations in atmospheric pressure, Pascal sent his brother-in-law to the top of a mountain with a barometer and a partially inflated balloon. The balloon expanded as the climbers gained elevation. This was evidence of a decrease in the external atmospheric pressure. Variations in the volume and density of a gas that accompanies changes in pressure were studied by Boyle and Mariotte. The density of a column of air decreases as altitude increases because air expands as pressure decreases. Boyle s Law Boyle s Law Boyle s Law: PV = constant Boyle discovered that the volume of a gas is inversely proportional to the pressure. Boyle s Law: PV = constant If the pressure increases, the volume decreases. The density of a column of air decreases as altitude increases because air expands as pressure decreases. P 1 V 1 = P 2 V 2 In Boyle s experiment, adding mercury to the open side of the bent tube caused a decrease in the volume of the trapped air in the closed side. This law is only valid if the gas is kept at constant temperature while the pressure and volume change. 21

22 A fixed quantity of gas is held in a cylinder capped at one end by a movable piston. The pressure of the gas is initially 1 atmosphere (101 kpa) and the volume is initially 0.3 m 3. What is the final volume of the gas if the pressure is increased to 3 atmospheres at constant temperature? a) 0.1 m 3 b) 0.3 m 3 c) 1 m 3 d) 3 m 3 P 1 = 1 atm P 2 = 3 atm V 1 = 0.3 m 3 V 2 =? V 2 = P 1 V 1 / P 2 = (1 atm)(0.3 m 3 ) / 3 atm = 0.1 m 3 E9 Archimedes Principle Why do some things float while others do not? Is floating determined by the weight of the object? Archimedes Principle The key is: DENSITY. Objects that are denser than the fluid they are immersed in will sink those less dense will float. Not a matter of the total weight of the object. What is the key then? What is DENSITY? It is MASS divided by VOLUME. MASS (m) is measured in kg (SI) VOLUME (V) is measured in m 3 (SI) DENSITY (ρ) is measured in kg/m 3 in the international system of units, but very often it is also given in g/cm 3 22

23 This is the definition of density: ρ = m V This is the definition of density: ρ = m V Density of interstellar space kg/m 3 Density of air 1.21 kg/m 3 Density of styrofoam 100 kg/m 3 Density of water 1000 kg/m 3 Density of iron 7900 kg/m 3 Density of mercury kg/m 3 Density of the Earth (average) 5500 kg/m 3 Density of the Sun (average) 1400 kg/m 3 (core) kg/m 3 What if, in a problem, I have the density and the volume, but don t know the mass. How do I calculate the mass? m = ρ V Archimedes: a little bit of history Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the Gods and replacing it with another, cheaper alloy. Archimedes knew that the irregular shaped wreath could be smashed into a cube or sphere, where the volume could be calculated more easily when compared with the weight; the king did not approve of this. Baffled, Archimedes went to take a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek for "I have found it!"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment. This story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. What have you learnt so far from the story? To find the volume of an object, you can measure the volume of water displaced, and that will be the volume of the object you are searching for. This is particularly useful for irregular objects (like the wreath). Another way of determining volume is by measuring the dimensions of the object and calculating the volume mathematically. 23

24 Archimedes Principle Is it hard to submerge in water a large block of wood or a rubber inner tube filled with air? They keep popping back to the surface, don t they? The upward force that pushes such objects back toward the surface is called the BUOYANT FORCE (F B ). Archimedes Principle Legend has it that Archimedes was sitting in the public baths observing floating objects when he realized what determines the strength of the BUOYANT FORCE. When an object is submerged, its volume takes up space occupied by water: it DISPLACES the water, in other words. The more water displaced by the object as you push downward, the greater the upward buoyant force. Initial level of water final level of water Block of wood water F B W Archimedes Principle Archimedes Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. Aluminium (Al) Density (near r.t.) 2.70 g cm 3 Copper (Cu) Density (near r.t.) 8.96 g cm 3 Tin Density (near r.t.)(white) g cm 3 Exercises E10, 11, 12 F F F B B B = weight of water displaced = mass of water displaced g = ρ water V g 24

25 The source of the buoyant force is the increase in pressure that occurs with increasing depth in a fluid. Atmospheric pressure is greater near the surface of the earth than at higher altitudes. The pressure near the bottom of a pool is larger than near the surface. The weight of the fluid above contributes to the pressure that we experience. Water emerging from a hole near the bottom of a can filled with water has a larger horizontal velocity than water emerging from a hole near the top. Weight = mg = Vdg Volume = Ah W dgah Excess Pressure P = = = dgh A A For example, consider a block submerged in water, suspended from a string. The pressure of the water pushes on the block from all sides. Because the pressure increases with depth, the pressure at the bottom of the block is greater than at the top. There is a larger force (F = PA) pushing up at the bottom than there is pushing down at the top. The difference between these two forces is the buoyant force. The buoyant force is proportional to both the height and the crosssectional area of the block, and thus to its volume. The volume of the fluid displaced is directly related to the weight of the fluid displaced. What forces act on a floating object? For the block shown, the weight W is balanced by the string s tension T and the buoyant force. If there are no strings attached or other forces pushing or pulling on the object, only the weight of the object and the buoyant force determine what happens. The weight is proportional to the density and volume of the object, and the buoyant force depends on the density of the fluid and the volume of the fluid displaced by the object. What happens if the density of the object is: greater than that of the fluid? less than that of the fluid? the same as that of the fluid? How does an airplane wing work? The shape and tilt of the wing cause the air to move faster across the top than across the bottom. This causes a lower pressure on the top of the wing. The pressure difference produces a net upward force, or lift, acting on the wing. When the lift balances the airplane s weight, the airplane will fly. 25

26 How can a ball be suspended in mid-air? Why does a curveball curve? A ball is suspended in an upwardmoving column of air produced by a hair dryer. The air pressure is smallest in the center of the column, where the air is moving the fastest. The whirlpool of air created by the spin of the ball causes the air to move more rapidly on one side than the other. The difference in pressure produces a force toward the lowerpressure, higher-airspeed side. 26