Question: A horizontal block – spring system with the

> An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00 g is 1.60 m long and has a 3.00 - kg object suspended from it. A pulse requires 3

> Before beginning a long trip on a hot day, a driver inflates an automobile tire to a gauge pressure of 1.80 atm at 300. K. At the end of the trip, the gauge pressure has increased to 2.20 atm. (a) Assuming the volume has remained constant, what is the te

> Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A 5.00 - m length of string with a total mass of 0.060 0 kg is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the ten

> A student taking a quiz finds on a reference sheet the two equations f = 1/t and v = √T/μ She has forgotten what T represents in each equation. (a) Use dimensional analysis to determine the units required for T in each equation. (b) Explain how you can i

> A piano string of mass per unit length 5.00 x 10-3 kg/m is under a tension of 1350 N. Find the speed with which a wave travels on this string.

> Workers attach a 25.0 - kg mass to one end of a 20.0 - m long cable and secure the other end to the top of a stationary crane, suspending the mass in midair. If the cable has a mass of 12.0 kg, determine the speed of transverse waves at (a) The middle an

> A biologist hangs a sample of mass 0.725 kg on a pair of identical, vertical springs in parallel and slowly lowers the sample to equilibrium, stretching the springs by 0.200 m. Calculate the value of the spring constant of one of the springs.

> An ethernet cable is 4.00 m long and has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cable. The pulse makes four trips down and back along the cable in 0.800 s. What is the tension in the cable?

> Ocean waves are traveling to the east at 4.0 m/s with a distance of 20.0 m between crests. With what frequency do the waves hit the front of a boat (a) When the boat is at anchor and (b) When the boat is moving westward at 1.0 m/s?

> Orchestra instruments are commonly tuned to match an A-note played by the principal oboe. The Baltimore Symphony Orchestra tunes to an A-note at 440 Hz while the Boston Symphony Orchestra tunes to 442 Hz. If the speed of sound is constant at 343 m/s, fin

> A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 60.0 x 103 Hz and the speed of sound in air is 343 m/s, what is the smallest insect

> A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

> A liquid with a coefficient of volume expansion of β just fills a spherical flask of volume V0 at temperature Ti (Fig. P10.61). The flask is made of a material that has a coefficient of linear expansion of a. The liquid is free to expand into

> The distance between two successive minima of a transverse wave is 2.76 m. Five crests of the wave pass a given point along the direction of travel every 14.0 s. Find (a) The frequency of the wave and (b) The wave speed.

> Light waves are electromagnetic waves that travel at 3.00 x 108 m/s. The eye is most sensitive to light having a wavelength of 5.50 x 10-7 m. Find (a) The frequency of this light wave and (b) Its period.

> An object attached to a spring vibrates with simple harmonic motion as described by Figure P13.42. For this motion, find (a) The amplitude, (b) The period, (c) The angular frequency, (d) The maximum speed, (e) The maximum acceleration, and (f) An equatio

> The sinusoidal wave shown in Figure P13.41 is traveling in the positive x - direction and has a frequency of 18.0 Hz. Find the (a) Amplitude, (b) Wavelength, (c) Period, and (d) Speed of the wave. Figure P13.41:

> A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What

> A spring is hung from a ceiling, and an object attached to its lower end stretches the spring by a distance d = 5.00 cm from its un-stretched position when the system is in equilibrium as in Figure P13.4. If the spring constant is 47.5 N/m, determine the

> The free - fall acceleration on Mars is 3.7 m/s2. (a) What length of pendulum has a period of 1.0 s on Earth? (b) What length of pendulum would have a 1.0 - s period on Mars? An object is suspended from a spring with force constant 10.0 N/m. Find the mas

> A coat hanger of mass m = 0.238 kg oscillates on a peg as a physical pendulum as shown in Figure P13.38. The distance from the pivot to the center of mass of the coat hanger is d = 18.0 cm and the period of the motion is T = 1.25 s. Find the moment of in

> A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g = 9.800 m/s2. The pendulum bob has length L = 0.2482 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes p

> A “seconds” pendulum is one that moves through its equilibrium position once each second. (The period of the pendulum is 2.000 s.) The length of a second’s pendulum is 0.9927 m at Tokyo and 0.9942 m at Cambridge, England. What is the ratio of the free -

> A 20.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.50 x 105 Pa and temperature of 19.0°C. (a) Calculate the temperature of the gas in Kelvin. (b) Use the ideal gas law to calculate the number of moles of gas in the tank. (c) Use the periodic

> A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) The period of the pendulum and (b) The value of g at the location of the pendulum.

> A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 15.5 s. (a) How tall is the tower? (b) If this pendulum is taken to the Moon, where the free - fall a

> Given that x = A cos (ωt) is a sinusoidal function of time, show that v (velocity) and a (acceleration) are also sinusoidal functions of time.

> A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500 - kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the or

> A 2.00 - kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.00 m to the right from its equilibrium position and then released, initiating simple harmonic

> An object executes simple harmonic motion with an amplitude A. (a) At what values of its position does its speed equal half its maximum speed? (b) At what values of its position does its potential energy equal half the total energy?

> The force constant of a spring is 137 N/m. Find the magnitude of the force required to (a) Compress the spring by 4.80 cm from its un-stretched length and (b) Stretch the spring by 7.36 cm from its un-stretched length.

> A 326 - g object is attached to a spring and executes simple harmonic motion with a period of 0.250 s. If the total energy of the system is 5.83 J, find (a) The maximum speed of the object, (b) The force constant of the spring, and (c) The amplitude of t

> A harmonic oscillator is described by the function x(t) = (0.200 m) cos (0.350t). Find the oscillator’s (a) Maximum velocity and (b) Maximum acceleration. Find the oscillator’s (c) Position, (d) Velocity, and (e) Acceleration when t = 2.00 s.

> The position of an object connected to a spring varies with time according to the expression x = (5.2 cm) sin (8.0pt). Find (a) The period of this motion, (b) The frequency of the motion, (c) The amplitude of the motion, and (d) The first time after t =

> A flask made of Pyrex is calibrated at 20.0°C. It is filled to the 100-mL mark on the flask with 35.0°C acetone. (a) What is the volume of the acetone when both it and the flask cool to 20.0°C? (b) Would the temporary increase in the Pyrex flask’s volume

> Explain why a dielectric increases the maximum operating voltage of a capacitor even though the physical size of the capacitor doesn’t change.

> When four people with a combined mass of 320 kg sit down in a 2.0 x 103 - kg car, they find that their weight compresses the springs an additional 0.80 cm. (a) What is the effective force constant of the springs? (b) The four people get out of the car an

> A vertical spring stretches 3.9 cm when a 10. -g object is hung from it. The object is replaced with a block of mass 25 g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

> The period of motion of an object – spring system is T = 0.528 s when an object of mass m = 238 g is attached to the spring. Find (a) The frequency of motion in hertz and (b) The force constant of the spring. (c) If the total energy of the oscillating mo

> The wheel in the simplified engine of Figure P13.23 has radius A = 0.250 m and rotates with angular frequency ω = 12.0 rad/s. At t = 0, the piston is located at x = A. Calculate the piston’s (a) Position, (b) Velocity, and (c

> An object moves uniformly around a circular path of radius 20.0 cm, making one complete revolution every 2.00 s. What are (a) The translational speed of the object, (b) The frequency of motion in hertz, and (c) The angular speed of the object?

> A horizontal spring attached to a wall has a force constant of k = 8.50 x 102 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P13.21. (a) The block is pulled to a position xi = 6.00

> A student stretches a spring, attaches a 1.00 - kg mass to it, and releases the mass from rest on a frictionless surface. The resulting oscillation has a period of 0.500 s and an amplitude of 25.0 cm. Determine (a) The oscillation frequency, (b) The spri

> A spring oriented vertically is attached to a hard horizontal surface as in Figure P13.2. The spring has a force constant of 1.46 kN/m. How much is the spring compressed when a object of mass m = 2.30 kg is placed on top of the spring and the system is a

> At an outdoor market, a bunch of bananas attached to the bottom of a vertical spring of force constant 16.0 N/m is set into oscillatory motion with an amplitude of 20.0 cm. It is observed that the maximum speed of the bunch of bananas is 40.0 cm/s. What

> A 0.40 - kg object connected to a light spring with a force constant of 19.6 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine (a) The maximum speed of the object, (b) The speed of t

> A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P10.58). (a) If n moles of an ideal gas are in the cylinder at a temperature of T, use Newton’s second law for equilibrium

> A block – spring system consists of a spring with constant k = 425 N/m attached to a 2.00 - kg block on a frictionless surface. The block is pulled 8.00 cm from equilibrium and released from rest. For the resulting oscillation, find the (a) Amplitude, (b

> A 0.250 - kg block attached to a light spring oscillates on a frictionless, horizontal table. The oscillation amplitude is A = 0.125 m and the block moves at 3.00 m/s as it passes through equilibrium at x = 0. (a) Find the spring constant, k. (b) Calcula

> An object – spring system moving with simple harmonic motion has an amplitude A. (a) What is the total energy of the system in terms of k and A only? (b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equa

> A 10.0 - g bullet is fired into, and embeds itself in, a 2.00 - kg block attached to a spring with a force constant of 19.6 N/m and having negligible mass. How far is the spring compressed if the bullet has a speed of 300. m/s just before it strikes the

> An automobile having a mass of 1.00 x 103 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 5.00 x 106 N/m and is compressed 3.16 cm as the car is brought to rest. What was the speed of the car before impact,

> A student pushes the 1.50 - kg block in Figure P13.11 against a horizontal spring, compressing it by 0.125 m. When released, the block travels across a horizontal surface and up an incline. Neglecting friction, find the block’s maximum

> An archer pulls her bowstring back 0.400 m by exerting a force that increases uniformly from zero to 230 N. (a) What is the equivalent spring constant of the bow? (b) How much work is done in pulling the bow?

> A block of mass m = 0.60 kg attached to a spring with force constant 130 N/m is free to move on a frictionless, horizontal surface as in Figure P13.1. The block is released from rest after the spring is stretched a distance A = 0.13 m. At that instant, f

> A diatomic ideal gas expands from a volume of VA = 1.00 m3 to VB = 3.00 m3 along the path shown in Figure P12.76. If the initial pressure is PA = 2.00 x 105 Pa and there are 87.5 mol of gas, calculate (a) The work done on the gas during this process, (b)

> Two sets of Christmas lights are available. For set A, when one bulb is removed, the remaining bulbs remain illuminated. For set B, when one bulb is removed, the remaining bulbs do not operate. Explain the difference in wiring for the two sets.

> An electrical power plant has an overall efficiency of 15%. The plant is to deliver 150 MW of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at 190°C, which drives the turbines. The steam is condensed into

> Hydrothermal vents deep on the ocean floor spout water at temperatures as high as 570°C. This temperature is below the boiling point of water because of the immense pressure at that depth. Because the surrounding ocean temperature is at 4.0°C, an organis

> Suppose you spend 30.0 minutes on a stair- climbing machine, climbing at a rate of 90.0 steps per minute, with each step 8.00 inches high. If you weigh 150. lb and the machine reports that 600. kcal have been burned at the end of the workout, what effici

> Two moles of molecular hydrogen (H2) react with 1 mole of molecular oxygen (O2) to produce 2 moles of water (H2O) together with an energy release of 241.8 kJ/mole of water. Suppose a spherical vessel of radius 0.500 m contains 14.4 moles of H2 and 7.2 mo

> A cylinder containing 10.0 moles of a monatomic ideal gas expands from â’¶ to â’· along the path shown in Figure P12.71. (a) Find the temperature of the gas at point A and the temperature at point â’·.

> Every second at Niagara Falls, approximately 5.00 x 103 m3 of water falls a distance of 50.0 m. What is the increase in entropy per second due to the falling water? Assume the mass of the surroundings is so great that its temperature and that of the wate

> One mole of neon gas is heated from 300. K to 420. K at constant pressure. Calculate (a) The energy Q transferred to the gas, (b) The change in the internal energy of the gas, and (c) The work done on the gas. Note that neon has a molar specific heat of

> An ideal gas initially at pressure P0, volume V0, and temperature T0 is taken through the cycle described in Figure P12.68. (a) Find the net work done by the gas per cycle in terms of P0 and V0. (b) What is the net energy Q added to the system per cycle?

> A 1.0 x 102-kg steel support rod in a building has a length of 2.0 m at a temperature of 20.0°C. The rod supports a hanging load of 6.0 x 103 kg. Find (a) The work done on the rod as the temperature increases to 40.0°C, (b) The energy Q added to the rod

> When a gas follows path 123 on the PV diagram in Figure P12.66, 418 J of energy flows into the system by heat and -167 J of work is done on the gas. (a) What is the change in the internal energy of the system? (b) How much energy Q flows into the system

> If electrical power is transmitted over long distances, the resistance of the wires becomes significant. Why? Which mode of transmission would result in less energy loss: high current and low voltage or low current and high voltage? Discuss.

> A substance undergoes the cyclic process shown in Figure P12.65. Work output occurs along path AB while work input is required along path BC, and no work is involved in the constant volume process CA. Energy transfers by heat occur during each process in

> A Carnot engine operates between 100°C and 20°C. How much ice can the engine melt from its exhaust after it has done 5.0 x 104 J of work?

> A 1500-kW heat engine operates at 25% efficiency. The heat energy expelled at the low temperature is absorbed by a stream of water that enters the cooling coils at 20.°C. If 60. L flows across the coils per second, determine the increase in temperature o

> A Carnot engine operates between the temperatures Th = 1.00 x 102°C and Tc = 20.0°C. By what factor does the theoretical efficiency increase if the temperature of the hot reservoir is increased to 5.50 x 102°C?

> Suppose a highly trained athlete consumes oxygen at a rate of 70.0 mL/(min · kg) during a 30.0-min workout. If the athlete’s mass is 78.0 kg and their body functions as a heat engine with a 20.0% efficiency, calculate (a) Their metabolic rate in kcal/min

> A woman jogging has a metabolic rate of 625 W. (a) Calculate her volume rate of oxygen consumption in L/s. (b) Estimate her required respiratory rate in breaths/min if her lungs inhale 0.600 L of air in each breath and air is 20.9% oxygen.

> Sweating is one of the main mechanisms with which the body dissipates heat. Sweat evaporates with a latent heat of 2430 kJ/kg at body temperature, and the body can produce as much as 1.5 kg of sweat per hour. If sweating were the only heat dissipation me

> A weightlifter has a basal metabolic rate of 80.0 W. As he is working out, his metabolic rate increases by about 650 W. (a) How many hours does it take him to work off a 450-Calorie bagel if he stays in bed all day? (b) How long does it take him if he’s

> On a typical day, a 65-kg man sleeps for 8.0 h, does light chores for 3.0 h, walks slowly for 1.0 h, and jogs at moderate pace for 0.5 h. What is the change in his internal energy for all these activities?

> When a metal bar is temporarily connected between a hot reservoir at Th and a cold reservoir at Tc, the energy transferred by heat from the hot reservoir to the cold reservoir is Qh. In this irreversible process, find expressions for the change in entrop

> A short circuit is a circuit containing a path of very low resistance in parallel with some other part of the circuit. Discuss the effect of a short circuit on the portion of the circuit it parallels. Use a lamp with a frayed line cord as an example.

> Prepare a table for the following occurrence: You toss four coins into the air simultaneously and record all the possible results of the toss in terms of the numbers of heads and tails that can result. (For example, HHTH and HTHH are two possible ways in

> When an aluminum bar is temporarily connected between a hot reservoir at 725 K and a cold reservoir at 310 K, 2.50 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. In this irreversible process, calculate the change in ent

> The surface of the Sun is approximately at 5.70 x 103 K, and the temperature of the Earth’s surface is approximately 290. K. What entropy change occurs when 1.00 x 103 J of energy is transferred by heat from the Sun to the Earth?

> A sealed container holding 0.500 kg of liquid nitrogen at its boiling point of 77.3 K is placed in a large room at 21.0°C. Energy is transferred from the room to the nitrogen as the liquid nitrogen boils into a gas and then warms to the room’s temperatur

> A 70.0-kg log falls from a height of 25.0 m into a lake. If the log, the lake, and the air are all at 300. K, find the change in entropy of the Universe during this process.

> What is the change in entropy of 1.00 kg of liquid water at 100.°C as it changes to steam at 100.°C?

> A freezer is used to freeze 1.0 L of water completely into ice. The water and the freezer remain at a constant temperature of T = 0°C. Determine (a) The change in the entropy of the water and (b) The change in the entropy of the freezer.

> A 65-g ice cube is initially at 0.0°C. (a) Find the change in entropy of the cube after it melts completely at 0.0°C. (b) What is the change in entropy of the environment in this process? Hint: The latent heat of fusion for water is 3.33 x 105 J/kg.

> A Styrofoam cup holding 125 g of hot water at 1.00 x 102°C cools to room temperature, 20.0°C. What is the change in entropy of the room? (Neglect the specific heat of the cup and any change in temperature of the room.)

> A heat engine operates in a Carnot cycle between 80.0°C and 350°C. It absorbs 21000 J of energy per cycle from the hot reservoir. The duration of each cycle is 1.00 s. (a) What is the mechanical power output of this engine? (b) How much energy does it ex

> Given three light-bulbs and a battery, sketch as many different circuits as you can.

> A certain nuclear power plant has an electrical power output of 435 MW. The rate at which energy must be supplied to the plant is 1420 MW. (a) What is the thermal efficiency of the power plant? (b) At what rate is thermal energy expelled by the plant?

> A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency

> In one cycle a heat engine absorbs 500 J from a high-temperature reservoir and expels 300 J to a low- temperature reservoir. If the efficiency of this engine is 60% of the efficiency of a Carnot engine, what is the ratio of the low temperature to the hig

> Two heat engines are operated in series so that part of the energy expelled from engine A is absorbed by engine B with |QhB| = 0.750|QcA|. Engines A and B have efficiencies eA = eB = 0.250 and engine A performs work WA = 275 J. Find the overall efficienc

> A freezer has a coefficient of performance of 6.30. The freezer is advertised as using 457 kW-h/y. (a) On average, how much energy does the freezer use in a single day? (b) On average, how much thermal energy is removed from the freezer each day? (c) Wha

> A heat pump has a coefficient of performance of 3.80 and operates with a power consumption of 7.03 x 103 W. (a) How much energy does the heat pump deliver into a home during 8.00 h of continuous operation? (b) How much energy does it extract from the out

> An engine absorbs 1.70 kJ from a hot reservoir at 277°C and expels 1.20 kJ to a cold reservoir at 27°C in each cycle. (a) What is the engine’s efficiency? (b) How much work is done by the engine in each cycle? (c) What is the power output of the engine i

> A lawnmower engine ejects 1.00 x 104 J each second while running with an efficiency of 0.200. Find the engine’s horsepower rating, using the conversion factor 1 hp = 746 W.

> One of the most efficient engines ever built is a coal-fired steam turbine engine in the Ohio River valley, driving an electric generator as it operates between 1870°C and 430°C. (a) What is its maximum theoretical efficiency? (b) Its actual efficiency i

> In each cycle of its operation, a heat engine expels 2400 J of energy and performs 1800 J of mechanical work. (a) How much thermal energy must be added to the engine in each cycle? (b) Find the thermal efficiency of the engine.