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physics
university physics
University Physics with Modern Physics 13th edition Hugh D. Young, Roger A. Freedman, A. Lewis Ford - Solutions
A certain heat engine operating on a Carnot cycle absorbs 150 J of heat per cycle at its hot reservoir at 135°C and has a thermal efficiency of 22.0%. (a) How much work does this engine do per cycle? (b) How much heat does the engine waste each cycle? (c) What is the temperature of
An average sleeping person metabolizes at a rate of about 80 W by digesting food or burning fat. Typically, 20% of this energy goes into bodily functions, such as cell repair, pumping blood, and other uses of mechanical energy, while the rest goes to heat. Most people get rid of all this excess
Digesting fat produces 9.3 food calories per gram of fat, and typically 80% of this energy goes to heat when metabolized. (One food calorie is 1000 calories and therefore equals 4186 J.) The body then moves all this heat to the surface by a combination of thermal conductivity and motion of the
A large cylindrical tank contains 0.750 m3 of nitrogen gas at 27oC and 7.50 × 103 (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m3 and the temperature is increased to 157oC?
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2atmosphere), and Saturn€™s moon Titan (where the
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m3. If the temperature remains constant, what is
Helium gas with a volume of 2.60 L, under a pressure of 0.180 atm and at a temperature of 41.0oC, is warmed until both pressure and volume are doubled.a. What is the final temperature?b. How many grams of helium are there? The molar mass of helium is 4.00 g/mol.
A 20.0-L tank contains 4.86 × 10–4 of helium at 18.0oC. The molar mass of helium is 4.00 g/mol.(a) How many moles of helium are in the tank?(b) What is the pressure in the tank, in pascals and in atmospheres?
A person who has skin of surface area and temperature 30.0°C is resting in an insulated room where the ambient air temperature is 20.0°C. In this state, a person gets rid of excess heat by radiation. By how much does the person change the entropy of the air in this room each second?(Recall that
You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0°C) and the other end at the surface of your skin, at 30.0°C. (a) What is the maximum efficiency of such a heat engine? Would it be a very useful
“Freeze-drying” food involves the same process as “freezer burn,” referred to in Discussion Question 18.6. For freeze-drying, the food is usually frozen first, and then placed in a vacuum chamber and irradiated with infrared radiation. What is the purpose of the vacuum? The radiation? What
Unwrapped food placed in a freezer experiences dehydration, known as “freezer burn.” Why?
The coolant in an automobile radiator is kept at a pressure higher than atmospheric pressure. Why is this desirable? The radiator cap will release coolant when the gauge pressure of the coolant reaches a certain value, typically 15 lb/in.2 or so. Why not just seal the system completely?
When a car is driven some distance, the air pressure in the tires increases. Why? Should you let out some air to reduce the pressure? Why or why not?
On a chilly morning you can “see your breath.” Can you really? What are you actually seeing? Does this phenomenon depend on the temperature of the air, the humidity, or both? Explain.
In the ideal-gas equation, could an equivalent Celsius temperature be used instead of the Kelvin one if an appropriate numerical value of the constant R is used? Why or why not?
Section 18.1 states that ordinarily, pressure, volume, and temperature cannot change individually without one affecting the others. Yet when a liquid evaporates, its volume changes, even though its pressure and temperature are constant. Is this inconsistent? Why or why not?Section 18.1A 20.0-L tank
A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat of frequency 3 Hz, which increases to 4 Hz when she tightens her violin string slightly.(a) What was the frequency of the
(a) By how much would the body temperature of the bicyclist in the preceding problem increase in an hour if he were unable to get rid of the excess heat?(b) Is this temperature increase large enough to be serious? To find out, how high a fever would it be equivalent to, in °F? (Recall that the
(a) The average normal body temperature measured in the mouth is 310 K. What would Celsius and Fahrenheit thermometers read for this temperature?(b) During very vigorous exercise, the body’s temperature can go as high as 40oC. What would Kelvin and Fahrenheit thermometers read for this
Suppose that both ends of the rod in Fig. 17.23a are kept at a temperature of 0oC, and that the initial temperature distribution along the rod is given by T = (100oC) sin πx/L where x is measured from the left end of the rod. Let the rod be copper, with length L = 0100 and
In the northern hemisphere, June 21 (the summer solstice) is both the longest day of the year and the day on which the sun’s rays strike the earth most vertically, hence delivering the greatest amount of heat to the surface. Yet the hottest summer weather usually occurs about a month or so later.
(a) If the jogger in the preceding problem were not able to get rid of the excess heat, by how much would his body temperature increase above the normal 37°C in a half hour of jogging? The specific heat for a human is about 3500 J/kg ‧ K.(b) How high a fever (in °F) would this temperature
You have probably seen people jogging in extremely hot weather and wondered Why? As we shall see, there are good reasons not to do this! When jogging strenuously, an average runner of mass 68 kg and surface area 1.85 m2 produces energy at a rate of up to 1300 W, 80% of which is converted to heat.
The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 75-kg (165-lb) person of height 1.83 m (6 ft) has a body surface area of approximately 2.0 m2.(a) What is the net amount of heat this person could radiate per second into a room at 18°C (about
Animals in cold climates often depend on two layers of insulation: a layer of body fat (of thermal conductivity 0.20 W/m ‧ K) surrounded by a layer of air trapped inside fur or down. We can model a black bear (Ursus americanus) as a sphere 1.5 m in diameter having a layer of fat 4.0 cm thick.
A Styrofoam bucket of negligible mass contains 1.75 kg of water and 0.450 kg of ice. More ice, from a refrigerator at -15.0oC, is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0.868 kg. Assuming no heat exchange with the
A steel rod 0.450 m long and an aluminum rod 0.250 m long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by 60.0 Co. What is the stress in each rod?
(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ΔL when its temperature changes by ΔT, the stress is equal toWhere F is the tension on the rod, L0 is
On a cool (4.0oC) Saturday morning, a pilot fills the fuel tanks of her Pitts S-2C (a two-seat aerobatic airplane) to their full capacity of 106.0 L. Before flying on Sunday morning, when the temperature is again 4.0oC, she checks the fuel level and finds only 103.4 L of gasoline in the tanks. She
A surveyor’s 30.0-m steel tape is correct at a temperature of 20.0oC. The distance between two points, as measured by this tape on a day when its temperature is 5.00oC, is 25.970 m. What is the true distance between the points?
You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [β = 2.7 × 10–5 (Co)–1] that is filled with olive oil [β = 6.8 × 10–4 (Co)–1] to a height of 2.00 mm below the top of the cup. Initially, the cup and oil are at room temperature
The blood plays an important role in removing heat from the body by bringing this heat directly to the surface where it can radiate away. Never the-less, this heat must still travel through the skin before it can radiate away. We shall assume that the blood is brought to the bottom layer of skin at
Two rods, one made of brass and the other made of cop-per, are joined end to end. The length of the brass section is 0.200 m and the length of the copper section is 0.800 m. Each segment has cross-sectional area 0.00500 m2. The free end of the brass segment is in boiling water and the free end of
An insulated beaker with negligible mass contains 0.250 kg of water at a temperature of 75.0oC. How many kilograms of ice at a temperature of – 20.0oC must be dropped into the water to make the final temperature of the system 40.0oC?
A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at – 20.0oC. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 1.20 kg of ice and
In a container of negligible mass, 0.200 kg of ice at an initial temperature of – 40.0oC is mixed with a mass m of water that has an initial temperature of 80.0oC. No heat is lost to the surroundings. If the final temperature of the system is 20.0oC, what is the mass m of the water that was
If the air temperature is the same as the temperature of your skin (about 30°C), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70-kg person’s body produces energy at a rate of about
A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at a temperature of 20.0°C. A 0.250-kg block of iron at 85.0°C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings?
One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0°C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached 32.0°C. To treat a 70.0-kg patient, what is
A 15.0-g bullet traveling horizontally at 865 m/s passes through a tank containing 13.5 kg of water and emerges with a speed of 534 m/s. What is the maximum temperature increase that the water could have as a result of this event?
Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawbacks are that energy is wasted because the tank loses heat when it is not in use and that you can run out of hot water if you use too much. Some utility
A circular saw blade with radius 0.120 m starts from rest and turns in a vertical plane with a constant angular acceleration of 3.00 rev/s2. After the blade has turned through 155 rev, a small piece of the blade breaks loose from the top of the blade. After the piece breaks loose, it travels with a
(a) The range of audible frequencies is from about 20 Hz to 20,000 Hz. What is the range of the wavelengths of audible sound in air?(b) The range of visible light extends from 400 nm to 700 nm. What is the range of visible frequencies of light?(c) Surgeons can remove brain tumors by using a
A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s for the boat to travel from its highest point to its lowest, a total distance of 0.62 m. The fisherman sees that the wave crests are spaced 6.0 m apart.(a) How fast are
The upper end of a 3.80-m-long steel wire is fastened to the ceiling, and a 54.0-kg object is suspended from the lower end of the wire. You observe that it takes a transverse pulse 0.0492 s to travel from the bottom to the top of the wire. What is the mass of the wire?
One string of a certain musical instrument is 75.0 cm long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s.(a) To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that
A wave pulse on a string has the dimensions shown in Fig. E15.30 at t = 0. The wave speed is 40 cm/s.(a) If point O is a fixed end, draw the total wave on the string at t = 15 ms, 20 ms, 25 ms, 30 ms, 35 ms, 40 ms, and 45 ms.(b) Repeat part (a) for the case in which point O is a free end.Figure
A horizontal wire is stretched with a tension of 94.0 N, and the speed of transverse waves for the wire is 492 m s. What must the amplitude of a traveling wave of frequency 69.0 Hz be in order for the average power carried by the wave to be 0.365 W?
A light wire is tightly stretched with tension F. Trans-verse traveling waves of amplitude A and wavelength λ1 carry average power Pav,1 = 0.400 W. If the wavelength of the waves is doubled, so λ2 = 2λ1, while the tension F and amplitude A are not altered, what then is the average
A 1750-N irregular beam is hanging horizontally by its ends from the ceiling by two vertical wires (A and B), each 1.25 m long and weighing 0.360 N. The center of gravity of this beam is one-third of the way along the beam from the end where wire A is attached. If you pluck both strings at the same
You are designing a two-string instrument with metal strings 35.0 cm long, as shown in Fig. P15.58. Both strings are under the same tension. String S1has a mass of 8.00 g and produces the note middle C (frequency 262 Hz) in its fundamental mode.(a) What should be the tension in the string?(b) What
The lower end of a uniform bar of mass 45.0 kg is attached to a wall by a friction-less hinge. The bar is held by a horizontal wire attached at its upper end so that the bar makes an angle of 30.0o with the wall. The wire has length 0.330 m and mass 0.0920 kg. What is the frequency of the
You are exploring a newly discovered planet. The radius of the planet is 7.20 × 107 m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0600 s for a transverse pulse to travel from the lower end to the upper end
Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.38. For what frequencies does their sound at the speakers produce(a) Constructive interference and(b) Destructive interference?Figure
The motors that drive airplane propellers are, in some cases, tuned by using beats. The whirring motor produces a sound wave having the same frequency as the propeller.(a) If one single-bladed propeller is turning at 575 rpm and you hear a 2.0-Hz beat when you run the second propeller, what are the
Two swift canaries fly toward each other, each moving at 15.0 m/s relative to the ground, each warbling a note of frequency 1750 Hz.(a) What frequency note does each bird hear from the other one?(b) What wavelength will each canary measure for the note from the other one?
The siren of a fire engine that is driving northward at 30.0 m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m/s.(a) What is the frequency of the siren’s sound that the fire engine’s driver hears reflected from the back of the truck?(b)
A uniform 165-N bar is supported horizontally by two identical wires A and B (Fig. P16.62). A small 185-N cube of lead is placed three-fourths of the way from A to B. The wires are each 75.0 cm long and have a mass of 5.50 g. If both of them are simultaneously plucked at the center, what is the
A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 10.0 Hz?
A person leaning over a 125-m-deep well accidentally drops a siren emitting sound of frequency 2500 Hz. Just before this siren hits the bottom of the well, find the frequency and wavelength of the sound the person hears(a) Coming directly from the siren and(b) Reflected off the bottom of the
A turntable 1.50 m in diameter rotates at 75 rpm. Two speakers, each giving off sound of wavelength 31.3 cm, are attached to the rim of the table at opposite ends of a diameter. A listener stands in front of the turntable.(a) What is the greatest beat frequency the listener will receive from this
Two loudspeakers, A and B (see Fig. E16.33), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider point P between the speakers and along the line
You live on a busy street, but as a music lover, you want to reduce the traffic noise.(a) If you install special sound-reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity (in W/m2)?(b) If, instead, you reduce the intensity
Many opera singers (and some pop singers) have a range of about 2 ½ octaves or even greater. Sup-pose a soprano’s range extends from A below middle C (frequency 220 Hz) up to -flat above high C (frequency 1244 Hz). Although the vocal tract is quite complicated, we can model it as a resonating
(a) If two sounds differ by 5.00 dB, find the ratio of the intensity of the louder sound to that of the softer one.(b) If one sound is 100 times as intense as another, by how much do they differ in sound intensity level (in decibels)?(c) If you increase the volume of your stereo so that the
At point A, 3.0 m from a small source of sound that is emitting uniformly in all directions, the sound intensity level is 53 dB.(a) What is the intensity of the sound at A?(b) How far from the source must you go so that the intensity is one-fourth of what it was at A? (c) How far must you go
(a) Blue whales apparently communicate with each other using sound of frequency 17 Hz, which can be heard nearly 1000 km away in the ocean. What is the wavelength of such a sound in seawater, where the speed of sound is 1531 m/s?(b) One type of sound that dolphins emit is a sharp click of
A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB.(a) How much energy is transferred to her eardrums each second?(b) How fast would a 2.0-mg mosquito have to fly (in mm/s) to have this much kinetic energy? Compare the mosquito’s speed with that
Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans.(a) How much energy is delivered to the eardrum each second when someone whispers (20 dB) a secret in your ear?(b) To comprehend how
(a) Show that for a wave on a string, the kinetic energy per unit length of string is where is the mass per unit length of string is(b) Calculate for a sinusoidal wave given by Eq. (15.7).(c) There is also elastic potential energy in the string, associated with the work required to deform and
A deep-sea diver is suspended beneath the surface of Loch Ness by a 100-m-long cable that is attached to a boat on the surface (Fig. P15.84). The diver and his suit have a total mass of 120 kg and a volume of The cable has a diameter of 2.00 cm and a linear mass density of µ = 1.10
A large rock that weighs 164.0 N is suspended from the lower end of a thin wire that is 3.00 m long. The density of the rock is 3200 kg/m3. The mass of the wire is small enough that its effect on the tension in the wire can be neglected. The upper end of the wire is held fixed. When the rock is in
A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 70.0 Hz, amplitude 5.00 mm, and wavelength 0.600 m.(a) How long does it take the wave to travel a distance of 8.00 m along the length of
A 1.80-m-long uniform bar that weighs 536 N is suspended in a horizontal position by two vertical wires that are attached to the ceiling. One wire is aluminum and the other is cop-per. The aluminum wire is attached to the left-hand end of the bar, and the copper wire is attached 0.40 m to the left
For a string stretched between two supports, two successive standing-wave frequencies are 525 Hz and 630 Hz. There are other standing-wave frequencies lower than 525 Hz and higher than 630 Hz. If the speed of transverse waves on the string is 384 m/s, what is the length of the string? Assume that
(a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequency as the note that is sung. If someone sings the note B flat, which has a frequency of 466 Hz, how much time does it take the person’s vocal cords to vibrate through one complete
An object is undergoing SHM with period 0.900 s and amplitude 0.320 m. At t = 0 the object is at x = 0.320 m and is instantaneously at rest. Calculate the time it takes the object to go(a) From x = 0.320 m to x = 0.160 m and(b) From x = 0.160 m to x = 0?
A small block is attached to an ideal spring and is moving in SHM on a horizontal, friction less surface. When the block is at x = 0.280 m, the acceleration of the block is –5.30 m/s2. What is the frequency of the motion?
The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t = 0 its position and velocity components are +1.1 cm –15 cm/s. and respectively.(a) Find the acceleration component of the needle at t = 0.(b) Write equations giving the position, velocity,
A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.70 s to travel from x = 0.090 to x = – 0.090 m. If the amplitude is doubled, to 0.180 m, how long does it take the block to
In February 2004, scientists at Purdue University used a highly sensitive technique to measure the mass of a vaccinia virus (the kind used in smallpox vaccine). The procedure involved measuring the frequency of oscillation of a tiny sliver of silicon (just 30 nm long) with a laser, first without
For the oscillating object in Fig. E14.4, what are(a) Its maximum speed and(b) Its maximum acceleration?Figure E14.4: х (ст) 10.0 t (s) A0.0 15.0 5.0 -10.0
A small block is attached to an ideal spring and is moving in SHM on a horizontal, friction-less surface. The amplitude of the motion is 0.120 m. The maximum speed of the block is 3.90 m s. What is the maximum magnitude of the acceleration of the block?
A mass m is attached to a spring of force constant 75 N m and allowed to oscillate. Figure E14.34 shows a graph of its velocity as a function of time t. Find(a) The period,(b) The frequency,(c) The angular frequency of this motion.(d) What is the amplitude (in cm), and at what times does the mass
A small block is attached to an ideal spring and is moving in SHM on a horizontal, friction-less surface. The amplitude of the motion is 0.250 m and the period is 3.20 s. What are the speed and acceleration of the block when x = 0.160 m?
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
A 2.50-kg rock is attached at the end of a thin, very light rope 1.45 m long. You start it swinging by releasing it when the rope makes an 11° angle with the vertical. You record the observation that it rises only to an angle of 4.5° with the vertical after swings.(a) How much energy has this
The motion of an under-damped oscillator is described by Eq. (14.42). Let the phase angle ɸ be zero.(a) According to this equation, what is the value of x at t = 0?(b) What are the magnitude and direction of the velocity at t = 0? What does the result tell you about the slope of the graph of x
A mass is vibrating at the end of a spring of force constant 225 N/m. Figure E14.62 shows a graph of its position x as a function of time t.(a) At what times is the mass not moving?(b) How much energy did this system originally contain?(c) How much energy did the system lose between and t = 4.0 s?
A sinusoidally varying driving force is applied to a damped harmonic oscillator.(a) What are the units of the damping constant b?(b) Show that the quantity ˆškm has the same units as b.(c) In terms of Fmax and k, what is the amplitude for ωd = ˆšk/m when (i) b =
Four passengers with combined mass 250 kg compress the springs of a car with worn-out shock absorbers by 4.00 cm when they get in. Model the car and passengers as a single body on a single ideal spring. If the loaded car has a period of vibration of 1.92 s, what is the period of vibration of the
A child with poor table manners is sliding his 250-g dinner plate back and forth in SHM with an amplitude of 0.100 m on a horizontal surface. At a point 0.060 m away from equilibrium, the speed of the plate is 0.400 m/s.(a) What is the period?(b) What is the displacement when the speed is 0.160
Tarzan spies a 35-kg chimpanzee in severe danger, so he swings to the rescue. He adjusts his strong, but very light, vine so that he will first come to rest 4.0 s after beginning his swing, at which time his vine makes a 12° angle with the vertical.(a) How long is Tarzan’s vine, assuming that he
A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper corner (Fig. P14.79). If it is rotated slightly to the left and then released, at what frequency will it swing back and forth?Figure
Two uniform solid spheres, each with mass and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end attached to the wall and the other end attached to a
A rifle bullet with mass 8.00 g and initial horizontal velocity 280 m/s strikes and embeds itself in a block with mass 0.992 kg that rests on a friction-less surface and is attached to one end of an ideal spring. The other end of the spring is attached to the wall. The impact compresses the spring
The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the
An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0 m/s. If nothing is
The asteroid Toro has a radius of about 5.0 km. Consult Appendix F as necessary.(a) Assuming that the density of Toro is the same as that of the earth (5.5 g/cm3), find its total mass and find the acceleration due to gravity at its surface.(b) Suppose an object is to be placed in a circular orbit
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