## Solutions for Principles of Physics: A Calculus-Based Text

# Browse All Chapters of This Textbook

Chapter 1 - Introduction And VectorsChapter 1.2 - Dimensional AnalysisChapter 1.3 - Conversion Of UnitsChapter 1.7 - Vectors And ScalarsChapter 1.8 - Some Properties Of VectorsChapter 1.9 - Components Of A Vector And Unit VectorsChapter 2 - Motion In One DimensionChapter 2.1 - Average VelocityChapter 2.2 - Instantaneous VelocityChapter 2.4 - Acceleration

Chapter 2.5 - Motion DiagramsChapter 2.7 - Freely Falling ObjectsChapter 3 - Motion In Two DimensionsChapter 3.1 - The Position, Velocity, And Acceleration VectorsChapter 3.3 - Projectile MotionChapter 3.4 - Analysis Model: Particle In Uniform Circular MotionChapter 3.5 - Tangential And Radial AccelerationChapter 4 - The Laws Of MotionChapter 4.1 - The Concept Of ForceChapter 4.4 - Newton’s Second LawChapter 4.5 - The Gravitational Force And WeightChapter 4.6 - Newton’s Third LawChapter 4.7 - Analysis Models Using Newton’s Second LawChapter 5 - More Applications Of Newton’s LawsChapter 5.1 - Forces Of FrictionChapter 5.2 - Extending The Particle In Uniform Circular Motion ModelChapter 5.3 - Nonuniform Circular MotionChapter 5.4 - Motion In The Presence Of Velocity-dependent Resistive ForcesChapter 6 - Energy Of A SystemChapter 6.2 - Work Done By A Constant ForceChapter 6.3 - The Scalar Product Of Two VectorsChapter 6.4 - Work Done By A Varying ForceChapter 6.5 - Kinetic Energy And The Work–kinetic Energy TheoremChapter 6.6 - Potential Energy Of A SystemChapter 6.8 - Relationship Between Conservative Forces And Potential EnergyChapter 7 - Conservation Of EnergyChapter 7.1 - Analysis Model: Nonisolated System (energy)Chapter 7.2 - Analysis Model: Isolated System (energy)Chapter 7.4 - Situations Involving Kinetic FrictionChapter 8 - Momentum And CollisionsChapter 8.1 - Linear MomentumChapter 8.3 - Analysis Model: Nonisolated System (momentum)Chapter 8.4 - Collisions In One DimensionChapter 8.6 - The Center Of MassChapter 8.7 - Motion Of A System Of ParticlesChapter 9 - RelativityChapter 9.4 - Consequences Of Special RelativityChapter 9.5 - The Lorentz Transformation EquationsChapter 9.7 - Relativistic EnergyChapter 10 - Rotational MotionChapter 10.1 - Angular Position, Speed, And AccelerationChapter 10.2 - Analysis Model: Rigid Object Under Constant Angular AccelerationChapter 10.3 - Relations Between Rotational And Translational QuantitiesChapter 10.4 - Rotational Kinetic EnergyChapter 10.5 - Torque And The Vector ProductChapter 10.7 - Analysis Model: Rigid Object Under A Net TorqueChapter 10.9 - Analysis Model: Nonisolated System (angular Momentum)Chapter 10.10 - Analysis Model: Isolated System (angular Momentum)Chapter 10.12 - Rolling Motion Of Rigid ObjectsChapter 11 - Gravity, Planetary Orbits, And The Hydrogen AtomChapter 11.1 - Newton’s Law Of Universal Gravitation RevisitedChapter 11.3 - Kepler’s LawsChapter 11.4 - Energy Considerations In Planetary And Satellite MotionChapter 11.5 - Atomic Spectra And The Bohr Theory Of HydrogenChapter 12 - Oscillatory MotionChapter 12.1 - Motion Of An Object Attached To A SpringChapter 12.2 - Analysis Model: Particle In Simple Harmonic MotionChapter 12.4 - The Simple PendulumChapter 12.5 - The Physical PendulumChapter 13 - Mechanical WavesChapter 13.1 - Propagation Of A DisturbanceChapter 13.2 - Analysis Model: Traveling WaveChapter 13.3 - The Speed Of Transverse Waves On StringsChapter 13.5 - Rate Of Energy Transfer By Sinusoidal Waves On StringsChapter 13.7 - The Doppler Eff EctChapter 14 - Superposition And Standing WavesChapter 14.1 - Analysis Model: Waves In InterferenceChapter 14.2 - Standing WavesChapter 14.3 - Analysis Model: Waves Under Boundary ConditionsChapter 14.4 - Standing Waves In Air ColumnsChapter 14.5 - Beats: Interference In TimeChapter 15 - Fluid MechanicsChapter 15.1 - PressureChapter 15.2 - Variation Of Pressure With DepthChapter 15.4 - Buoyant Forces And Archimedes’s PrincipleChapter 15.6 - Streamlines And The Continuity Equation For FluidsChapter 15.7 - Bernoulli’s EquationChapter 16 - Temperature And The Kinetic Theory Of GasesChapter 16.2 - Thermometers And Temperature ScalesChapter 16.3 - Thermal Expansion Of Solids And LiquidsChapter 16.4 - Macroscopic Description Of An Ideal GasChapter 16.5 - The Kinetic Theory Of GasesChapter 16.6 - Distribution Of Molecular SpeedsChapter 17 - Energy In Thermal Processes: The First Law Of ThermodynamicsChapter 17.2 - Specific HeatChapter 17.3 - Latent HeatChapter 17.5 - The First Law Of ThermodynamicsChapter 17.6 - Some Applications Of The First Law Of ThermodynamicsChapter 17.7 - Molar Specifi C Heats Of Ideal GasesChapter 17.10 - Energy Transfer Mechanisms In Thermal ProcessesChapter 18 - Heat Engines, Entropy, And The Second Law Of ThermodynamicsChapter 18.1 - Heat Engines And The Second Law Of ThermodynamicsChapter 18.3 - The Carnot EngineChapter 18.4 - Heat Pumps And RefrigeratorsChapter 18.6 - EntropyChapter 18.7 - Entropy And The Second Law Of ThermodynamicsChapter 18.8 - Entropy Changes In Irreversible ProcessesChapter 19 - Electric Forces And Electric FieldsChapter 19.2 - Properties Of Electric ChargesChapter 19.3 - Insulators And ConductorsChapter 19.4 - Coulomb’s LawChapter 19.5 - Electric FieldsChapter 19.6 - Electric Field LinesChapter 19.9 - Gauss’s LawChapter 20 - Electric Potential And CapacitanceChapter 20.1 - Electric Potential And Potential Diff ErenceChapter 20.2 - Potential Diff Erence In A Uniform Electric FieldChapter 20.3 - Electric Potential And Potential Energy Due To Point ChargesChapter 20.4 - Obtaining The Value Of The Electric Field From The Electric PotentialChapter 20.7 - CapacitanceChapter 20.8 - Combinations Of CapacitorsChapter 20.9 - Energy Stored In A Charged CapacitorChapter 20.10 - Capacitors With DielectricsChapter 21 - Current And Direct Current CircuitsChapter 21.1 - Electric CurrentChapter 21.2 - Resistance And Ohm’s LawChapter 21.5 - Energy And Power In Electric CircuitsChapter 21.7 - Resistors In Series And ParallelChapter 21.9 - Rc CircuitsChapter 22 - Magnetic Forces And Magnetic FieldsChapter 22.2 - The Magnetic FieldChapter 22.3 - Motion Of A Charged Particle In A Uniform Magnetic FieldChapter 22.5 - Magnetic Force On A Current-carrying ConductorChapter 22.7 - The Biot–savart LawChapter 22.8 - The Magnetic Force Between Two Parallel ConductorsChapter 22.9 - Ampère’s LawChapter 22.10 - The Magnetic Field Of A SolenoidChapter 23 - Faraday’s Law And InductanceChapter 23.1 - Faraday’s Law Of InductionChapter 23.2 - Motional EmfChapter 23.3 - Lenz’s LawChapter 23.4 - Induced Emfs And Electric FieldsChapter 23.6 - Rl CircuitsChapter 23.7 - Energy Stored In A Magnetic FieldChapter 24 - Electromagnetic WavesChapter 24.1 - Displacement Current And The Generalized Form Of Ampère’s LawChapter 24.4 - Energy Carried By Electromagnetic WavesChapter 24.6 - The Spectrum Of Electromagnetic WavesChapter 24.7 - Polarization Of Light WavesChapter 25 - Reflection And Refraction Of LightChapter 25.3 - Analysis Model: Wave Under ReflectionChapter 25.4 - Analysis Model: Wave Under RefractionChapter 25.5 - Dispersion And PrismsChapter 25.7 - Total Internal Refl EctionChapter 26 - Image Formation By Mirrors And LensesChapter 26.1 - Images Formed By Flat MirrorsChapter 26.2 - Images Formed By Spherical MirrorsChapter 26.4 - Images Formed By Thin LensesChapter 26.5 - The EyeChapter 27 - Wave OpticsChapter 27.3 - Analysis Model: Waves In InterferenceChapter 27.5 - Interference In Thin FilmsChapter 27.6 - Diff Raction PatternsChapter 27.7 - Resolution Of Single-slit And Circular AperturesChapter 27.8 - The Diff Raction GratingChapter 28 - Quantum PhysicsChapter 28.1 - Blackbody Radiation And Planck’s TheoryChapter 28.2 - The Photoelectric Eff EctChapter 28.5 - The Wave Properties Of ParticlesChapter 28.6 - A New Model: The Quantum ParticleChapter 28.10 - A Particle In A BoxChapter 28.13 - Tunneling Through A Potential Energy BarrierChapter 29 - Atomic PhysicsChapter 29.2 - The Hydrogen Atom RevisitedChapter 29.4 - Physical Interpretation Of The Quantum NumbersChapter 29.5 - The Exclusion Principle And The Periodic TableChapter 29.6 - More On Atomic Spectra: Visible And X-rayChapter 30 - Nuclear PhysicsChapter 30.1 - Some Properties Of NucleiChapter 30.3 - RadioactivityChapter 30.4 - The Radioactive Decay ProcessesChapter 31 - Particle PhysicsChapter 31.2 - Positrons And Other AntiparticlesChapter 31.5 - Conservation LawsChapter 31.9 - Quarks

### Book Details

PRINCIPLES OF PHYSICS features a concise approach to traditional topics, an early introduction to modern physics, and integration of physics education research pedagogy, as well as the inclusion of contemporary topics throughout the text. This revision of PRINCIPLES OF PHYSICS also contains a new worked example format, two new Contexts features, a revised problem set based on an analysis of problem usage data from WebAssign, and a thorough revision of every piece of line art in the text.

# Sample Solutions for this Textbook

We offer sample solutions for Principles of Physics: A Calculus-Based Text homework problems. See examples below:

Chapter 1, Problem 1OQSection 1: To determine: The density of the aluminum sphere. Answer: The density of the aluminum...The figure 1 shows the vector sum of C→=A→+B→ and the vector difference of D→=A→−B→. Conclusion:...Write the expression for the given vector sum. A→+B→ (I) Conclusion: Substitute (3i^−2j^) for A→ and...Chapter 1, Problem 50PChapter 1, Problem 51PThe figure 1 shows the vector notation of the following magnitudes. Write the expression for the...Write the expression for person on the right pull with a force F→1. F→1=F1xcosθi^+F1ysinθj^ (I)...Chapter 1, Problem 69P

The figure 1 shows the geometry of the problem says to use the law of cosines to known sides and...Chapter 2, Problem 1OQGiven information: The following table contains the data of position of the car at various time...Chapter 2, Problem 12PChapter 2, Problem 13PWrite the kinematics equation. vf=vi+at Here, vf is the final speed, vi is the initial speed, a is...Chapter 2, Problem 40PChapter 2, Problem 46PInitially the rocket moves vertically upward with initial speed 80.0 m/s and acceleration 4.00 m/s2...Section 1: To determine: The acceleration of the Laura. Answer: The acceleration of the Laura is...Chapter 3, Problem 1OQSection 1: To determine: The position vector ri→ . Answer: The position vector ri→ is (3.00...Chapter 3, Problem 3PChapter 3, Problem 4PChapter 3, Problem 5PWrite the expression for the vertical final velocity of the basketball player. vyf2=vyi2+2a(yf−yi)...Chapter 3, Problem 19PChapter 3, Problem 54PThe snowballs are having denser medium than the surrounding air. Hence, it can be assumed that the...Chapter 4, Problem 4PFormula to calculate net force acts on a particle is, F→net=F→1+F→2 Here, F→net is the net force...Explanation: Given information: Three forces acting on a object are F→1=(−2.00i^+2.00j^) N ,...Chapter 4, Problem 7PChapter 4, Problem 42PWrite the equation for the position of the glider. x=(z2−h02)1/2 (I) Here, x is the position of the...The free body diagram for the system is given by figure 1. Write the expression for the net force...Consider the free body diagram given below. Figure I Here, a is the acceleration of hanging block...Chapter 5, Problem 1OQChapter 5, Problem 12PChapter 5, Problem 14PChapter 5, Problem 18PWrite the expression for drag force on the car. R=12DρAv2 (I) Here, R is the dray force, D is the...Chapter 5, Problem 43PThe free body diagram is the graphical illustration used to visualize the movements and forces...Assume that, the friction points up the incline, the net force is directed left towards the centre...The free body diagram of the top block is shown in Figure 1. The free diagram of the bottom block is...At the terminal velocity, the drag force is balanced by the force due to gravity. mg=arv+br2v2 (I)...Chapter 6, Problem 1OQGiven that A→=3.00 i^−2.00j^ and B→=4.00 i^−4.00 j^. Write the expression for dot product of A→ and...Given Information: The mass of the object is 5.75 kg , the x-component of velocity of the object at...Given Information: The mass of a bullet is 15.0 g , the final speed of the bullet is 780 m/s and the...Given info: The coordinates of point (C) is (5.00 m, 5.00 m) and the force acting on the body is...The work done by a conservative force on a particle moving between any two points is independent of...Write the expression for centripetal force of the mass m attached at the end of the spring. F=mv2r...Write the expression for force from Figure P6.67. F→1=(25.0 N)(cos35.0°i^+sin35.0°j^) Simplify the...Figure 1 represents two springs attached to mass m. Write the expression for force. F=−kx (I) Here,...Given Information: The data that represents the different loads on a spring and the different length...Chapter 7, Problem 1OQChapter 7, Problem 12PExplanation: Given information: An 80.0 kg sky diver jumps out of a balloon at an altitude of 1000 m...Write the equation for frictional force within an isolated system. ΔK+ΔU=−fkd (I) Here ΔK is the...Chapter 7, Problem 45PChapter 7, Problem 68PChapter 7, Problem 69PWrite down the equation of energy conservation. Ki+Ugi=Kf+Ugf (I) Here Ki is the initial kinetic...Given info: The mass of the person is 64.0 kg, height of the hot air balloon above the ground is...Chapter 7, Problem 81PConsider the needle is fired horizontally from a spring. Maximum speed occurs just after the needle...Write the expression for momentum, P=mv (I) Here, P is the momentum, m is the mass, and v is the...Assume equal firing speeds and equal forces required for the two bullets to push wood fibers apart....Given info: The mass of the fullback is 90.0 kg , the speed of the fullback is 5.00 m/s , the mass...The position vector shows the location of particle with respect to x and y axis in x-y plane. The...Chapter 8, Problem 46PChapter 8, Problem 48PWrite the expression for conservation of momentum for inelastic collision. mpvi=(mp+mc)vf (I) Here,...Given information: The mass of the object is 3 kg , the velocity of the object is 7j^ m/s and the...Given info: The force constant is 3.85 N/m , the spring is compressed by 8.00 cm . The mass of left...Given information: The masses of the particle are m and 3m . The initial speed of both the particle...Chapter 9, Problem 1OQWrite the Lorenz transformation equation for position. Δx′=γ(Δx−υΔt) (I) Here, Δx′ is the distance...Given info: The speed limit is 90.0 km/h and the fine for driving at 190 E is $80.0 . Write the...Given info: The kinetic energy of the electron and proton is 2.00 MeV , the rest energy of the...Isolated system is system which does not allow the flow of mass energy in our out. Here, the...The gravitational force acting on the satellite is equal centripetal force. Write the expression for...Given info: The first mass of first fragment is 1.00 MeVc2 , the momentum of the first fragment is...Consider the mass of the object is 1.00 kg , the rest energy of the object is mc2=9.00×1016 J . The...The formula to calculate the relative momentum is, p=mu1−(u/c)2 Here, m is the mass of the electric...Chapter 10, Problem 1OQTo have large energy storage the flywheel should have large moment of inertia. For this the flywheel...The vector A is given by. A→=−3i^+7j^−4k^ Vector B is given as. B→=6i^−10j^+9k^ Take the dot product...Chapter 10, Problem 28PChapter 10, Problem 40PChapter 10, Problem 45PChapter 10, Problem 66PChapter 10, Problem 67PChapter 10, Problem 72PChapter 10, Problem 73PChapter 10, Problem 81PThe total energy of the system is conserved. Since the skateboarder is starting from rest the...The air particles are attracted towards the earth’s atmosphere due to the gravitational acceleration...Write the expression for the force on the test object. Fg=mobjg (I) Here, Fg is the force on the...Write the expression for the centripetal force. Fc=mv2r (I) Here, Fc is the centripetal force, m is...Given info: The initial speed of the vehicle is vi , the escape speed of space vehicle is vesc and...Write the expression for the radius of the orbit in the hydrogen atom relating the Bohr radius....Explanation: Given information: The maximum distance from the Earth to the Sun is 1.521×1011 m and...The system of two planets are isolated, so the energy as well as the momentum is conserved. Write...Write the expression for the total energy of the earth-satellite system. E=K+U (I) Here, E is the...Explanation: Given information: A object of mass m is distance from the Earth’s center is 1.20×107 m...Chapter 12, Problem 1OQGiven information: The amplitude of the motion of the particle is 2.00 cm and the frequency of the...Given information: The initial position of the particle is 0.270 m , the velocity of the particle is...Write the expression to calculate the force constant of the spring. k=Fx (I) Here, k is spring force...A free falling object is an object that is falling under the sole influence of gravity. Any object...Section 1: To determine: The amplitude of the motion. Answer: The maximum speed of the amplitude of...The general expression for the position of the object is given by, x=Acosωt (I) Here, x is the...Given information: Mass of the particle is 0.50 kg , the force constant of the spring is 50.0 N/m...Write the relation between force on spring and maximum static frictional force. kx=μsn Here, k is...Section 1: To determine: The angular frequency of the system. Answer: The angular frequency of the...All mechanical waves are the result of some kind of disturbance at a point in a medium. Waves carry...Chapter 13, Problem 3OQChapter 13, Problem 5PGiven information: The value of A is 8.0 cm , the value of λ is 80.0 cm , the value of f is 3.0 Hz...The wave is traveling in the negative x direction, amplitude of the wave is 20.0 cm, wavelength of...Chapter 13, Problem 14PWrite the expression for the maximum speed. vmax=ωA (II) Here, vmax is the maximum speed, ω is the...Given Info: The wave function for string is given as, y(x,t)=(A0e−bx)sin(kx−ωt) Formula to calculate...The free body diagram of the suspended object with rope is shown below. Figure (1) From free body...Chapter 13, Problem 69PChapter 13, Problem 71PChapter 14, Problem 1OQGiven information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0...Given information: The speed of the sound is 344 m/s , frequency generated by the loudspeakers is...Given info: The frequency of the concert A is 440 Hz , the frequency of concert G is 392 Hz , the...Write the expression for the wave function of a standing wave. y=2Asinkxcosωt (I) Here, A is the...Given info: The dimension of the shower stall is 86.0 cm×86.0 cm×210 cm . The range of frequencies...The well can be considered as a pipe open at one end and closed at the other end. The fundamental...Chapter 14, Problem 56PChapter 14, Problem 60PChapter 15, Problem 1OQWrite the equation for pressure on the bottom due to water. Pb=FbA Here, Pb is the pressure on the...Chapter 15, Problem 13PChapter 15, Problem 14PChapter 15, Problem 25PChapter 15, Problem 40PChapter 15, Problem 45PAn analysis model is a simplified version of any physical system that strips away the unnecessary...Write the condition for equilibrium. B=Fg (I) Here, B is the buoyant force and Fg is the weight of...Chapter 15, Problem 67PWrite the equation for the volume flow rate. Q=ΔVΔt (I) Here, Q is the volume flow rate, ΔV is the...Write the expression from the ideal gas law. P1V1T1=P2V2T2P2=P1V1T2T1V2=P1(V1V2)(T2T1) (I) In the...Given information:Initial temperature is 20.0 °C , inner diameter of the aluminium ring is 5.0000 cm...Write the expression for change in volume when the temperature rises by ΔT. ΔV=βViΔT (I) Here, ΔV is...Write the expression for ideal gas equation for the initial condition. PiVi=nRTi (I) Here, Pi is the...Given information:Temperature of the air is 300 K , atmospheric pressure of the air is 1.013×105 Pa...Given that, the expression for lapse rate. dTdy=γ−1γgMR (I) Here, dTdy is the lapse rate, γ is the...Given info: The density of the liquid is ρ , the change in the temperature is ΔT , the maximum...Given information:Value of average speed is vmp50.0 . Write the expression for the Maxwell-Boltzmann...Introduction: The Maxwell distribution curve is the graph between the distribution of speed and the...Consider the Figure shown below. Write the ideal gas equation for the initial and final state of the...Chapter 16, Problem 74PAn amount of energy is added to ice by heat and raise it temperature from −10°C to −5°C, the change...Given info: The mass of the calorimeter is 100 g , the mass of water in calorimeter is 250 g , the...Given info: The mass of the ice cube is 40.0 g , the temperature of the ice is −10.0 °C and the...Given info: The mass of one bullet is 12.0 g , mass of second bullet is 8.00 g , speed of one bullet...Chapter 17, Problem 32PGiven Info: Temperature of air is 300 K , Initial pressure is 2.00×105 Pa , Initial volume is 0.350...In this cycle, from C to A the pressure remains same, only the volume is changed. From A to B the...Chapter 17, Problem 48PWrite the expression for the work done on the gas, Wab=−∫VaVbPdV (I) Here, Wab is the work done on...Chapter 17, Problem 53PChapter 17, Problem 68PGiven info: The radius of copper disk is 28.0 m , thickness of copper disk is 1.20 m , the...Write the formula to find the work done by the engine Weng=|Qh|−|Qc| (I) Here, Weng is the work done...Given information:The rate of work output of the engine is 1.40 MW , thetemperature into the cooling...Given info: The efficiency of the two engine is e1 and e2 . The lower and higher temperature of the...Consider the first adiabatic process along D through A Write the equation for adiabatic process,...Given Info: The mass of the ice cube is 27.9 g , the value of cold temperature is −12 °C and the...Air conditioner removes its energy in the form of heat from the cold reservoir. Write the equation...Given info: The mass of the athlete and the water is 70 kg and 454 g respectively. The initial...Write the ideal gas equation and rearrange for VA and VC to determine the volume at point A and C....Chapter 18, Problem 63PChapter 19, Problem 1OQThe ionized hydrogen atom H+ is the loss of on electron from the hydrogen atom. Write the expression...Chapter 19, Problem 10PGiven info: The radius of the uniformly charged ring is 10.0 cm and the total charge on the ring is...Chapter 19, Problem 19PFigure 1 represents a proton is projected with an angle of θ with initial velocity vi, under an...Given info: The radius of solid sphere is 40.0 cm and the total positive charge on the sphere is...Consider the earth’s surface as a charged conducting plane. Write the expression for electric field...Figure 1 represents four charges of equal magnitude of 10.0 μC. Write the expression for angle θ...Chapter 19, Problem 68PChapter 19, Problem 75PChapter 20, Problem 1OQChapter 20, Problem 7PWrite the expression of standard equation for the potential difference. V=kqr (I) Here, V is the...Chapter 20, Problem 19PThe potential on each sphere will be same. Write the equation at same potential. V1=V2 (I) Here,...Given information: The radius of the spherical conductor is 14.00 cm and charge is 26 μC . In any...Given info: The radii of two conducting sphere is R1 and R2 . The total charge shared between them...Chapter 20, Problem 66PWrite the expression from conservation of momentum. P→i=P→f (I) Here, P→i is the initial momentum...Write the expression from conservation of momentum. P→i=P→f (I) Here, P→i is the initial momentum...The diagram for the system is given by figure 1. Write the expression total potential. V=V1−V2 (I)...Chapter 20, Problem 85PChapter 21, Problem 1OQWrite the expression for the resistivity. ρ=ρ0[1+α(T−T0)] (I) Here, ρ is the resistivity of the wire...Given Info: The cross-sectional area of iron wire is 5.00×10−6 m2 and the electric current is 30.0 A...Write the expression for the output power of the heater. P=QΔt (I) Here, P is the power output, Q is...Write the expression for the energy taken by the battery. Ein=PinΔtin (I) Here, Ein is the energy...Chapter 21, Problem 40PWrite the expression for the power delivered to the vacuum cleaner. P=IΔV (I) Here, P is the power...Chapter 21, Problem 47PChapter 21, Problem 50PThe switch is closed in the electric circuit and the current exists in a simple series circuit as...Given information: Area of cross section of gauge wire is 7.30×10−8 m2 , length of gauge wire 1 is...Write the formula for magnetic force (Lorentz force) F = qv×B=qvBsinθ (I) Here, F is the magnetic...Given Info: The accelerating voltage is 600 V , the outer radius is 0.350 m and the magnitude of...Chapter 22, Problem 20PThe Fleming left hand rule stats that, the thumb points in the direction of the force, the index...Write the formula for torque on a rotor. τ=INABsinθ (I) Here, τ is the torque, I is current on the...Chapter 22, Problem 33PFrom the figure 1 Write the expression to calculate the side of the square, x=a2+a2=2a (I) Write the...Write the expression for the magnetic field at the point A. B=μoi4π(l2)(cosθ−cos(180°−ϕ)) (I) Here,...Given info: The electric current in wire 1 is 1.50 A in upward direction and the electric current in...Write the expression of the magnetic field at the origin due to the current I1 ....Write the expression for the magnetic field on a wire. B=μ0I2πr (I) Here, B is the magnetic field,...Chapter 22, Problem 76PWrite the equation for the induced emf in the coil. ε=−NΔϕΔt (I) Here, N is the number of turns in...Write the equation for the emf generated in the coil. ε=−dϕBdt (I) Here, ϕB is the magnetic flux...Chapter 23, Problem 12PWrite the equation for the current in the circuit. I=εR Here, I is the current in the circuit when...Write the equation for the change in current in the circuit. I=εR(1−e−t/τ) (I) Here, I is the...The rate of deliver of energy is the power of the battery. Write the equation for the power of the...Write the equation for the magnetic field at the center of the coil. Bcenter= μ0I2a (I) Here, μ0 is...Write the equation for the current in the bulb in term of the emf. I= εR (I) Here, ε is the emf in...Figure.1 shows the flow of currents in the circuit. From figure.1, I1 is the current through the...Write the equation for the emf induced in the loop. ε=−NdϕBdt (I) Here, N is the number of turns in...Chapter 23, Problem 73PElectromagnetic wave is the coupled propagation of electric field and magnetic field at right...Given info: The linear density of the rod is 35.0 nC/m and the speed is 1.50×107 m/s . The value of...The formula to calculate the wavelength is, λ=cf (1) Here, c is the speed of light. f is the...Write the expression for the separation distance. d=Nλ2 (I) Here, d is the separation distance, N is...Given info: The diameter of the space mirror is 200 m and the intensity of the sunlight is 1370 W/m2...Given info: The diameter of the circular mirror is 1.00 m , the radius of the absorbing plate is...Given info: The weight of the black cat is 5.50 kg , the weight of the kittens is 0.800 kg , the...Chapter 24, Problem 72PChapter 24, Problem 73PGiven info: The equation of the electromagnetic power is p=q2a26πε∘c3 . The formula to calculate the...Write the expression for critical angle. θc=sin−1(n2n1) (I) Here, θc is the critical angle, n2 is...Given info: The wavelength of sound wave is 589 nm and angle of incidence is 13.0° . The speed of...Write the expression for Snell’s law of refraction at the air-silica flint glass interface....Chapter 25, Problem 25PGiven info: The index of refraction of glass is 1.55 and the angle of incidence is 30° . From, law...Given info: The distance h between the atmosphere and the surface of earth is 100 km , the index of...Figure 1 represent the path of the ray before the container is filled. From the Figure 1, write the...Let θ be the angle between the dashed line and reflected beam in the Figure P25.59. From the Figure,...The path of the ray in the quarter circle is shown in the Figure. Consider the triangle OPQ from the...When human eyes are larger than normal, the image is not formed in retina. Image is formed before...Given info: The height of the following car is 1.50 m . The distance between the observer’s eyes and...Chapter 26, Problem 38PConsider the mirror and write the equation for radius of curvature 2R=1p1+1q1 (I) Here, R is the...Given info: The distance between the candle and the wall is 1.50 m . The distance by which the lens...Write the mirror equation for the first pass through the lens. 1f1=1p1+1q1 (I) Here p1 is the object...Write the equation for intensity I=PA (I) Here I is the intensity, P is the power and A is the area...Given info: The focal length of the left and right lenses are f1=5.00 cm and f2=10.0 cm . The object...Write the mirror equation. 1f=1p1+1q1 (I) Here, f is the focal length, p1 is the object distance and...Chapter 26, Problem 72PWrite the equation for power P=IA (I) Here P is the power, I is the intensity and A is the area of...Chapter 27, Problem 1OQChapter 27, Problem 7PGiven info: The separation of the slit is 2.40×10−4 m , the distance between the screen and the slit...Write the equation to find the wavelength of wave produced by oscillator in speaker. λ=cf Here, λ is...Given Information: The refractive index of the oil film is 1.45 , thickness of the film is 280 nm ....Draw the diagram of spectral lines as per the given data. Write the equation to find the grating...Given info: Temperature of air is 20.0 °C , spacing between centre is 1.30 cm and frequency of array...Given info: Angles of spectral lines are 10.1° , 13.7° and 14.8° , Slits on the grating are 3600...Given info: The number of grooves per mm in the diffraction grating is 400, the incident wavelength...Write the Equation to find the wavelength. λ=cf Here, c is the speed of light in vaccum, f is the...In 1905 it was Einstein who suggested the concept of light having a wave particle duality. In a...The momentum of the photon before scattering is given by, p0=hλ0 (I) Here, p0 is the momentum before...The momentum of the photon before scattering is given by, p0=hλ0 (I) Here, p0 is the momentum before...The diameter of the beam of laser is 1.75 mm. The laser delivers 2.00×1018 photons/s. The wavelength...The initial height of the pellet is H, its mass is m and let the target be the origin Write the...The length of the box is 0.100 nm. Write the expression for energy of one dimensional box...Write the Schrodinger’s equation. −ℏ22md2Ψdx2+UΨ=EΨ (I) Here, ℏ is the reduced Planck’s constant, m...Write the Schrodinger’s equation. −ℏ22md2Ψdx2+UΨ=EΨ (I) Here, ℏ is the reduced Planck’s constant, m...Write the equation for the expectation value of x. 〈x〉=∫0LΨ2∗xΨ2dx (I) Here, 〈x〉 is the expectation...Write the expression for the allowed energy levels of the electron is given by,...Write the given wave function of the electron. ψ(x)={Ae−αx for x>0Ae+αx for x<0 (I) Here, ψ(x)...In this case, the principal quantum number, n=3 . Write the expression for the orbital quantum...Write the equation for acceleration according to Newton’s second law. a=Fm (I) Here, F is the force,...The longest wavelength of the photon implies lowest frequency and smallest energy. The electron...Write the equation for uncertainty principle. ΔxΔp ≥ ℏ2 Here, Δx is the uncertainty in position,...Write the general expression for the energy levels of one electron atoms. En=−μke2q12q222ℏ2n2 Here,...Write the condition for the normalization. ∫0∞|ψ1s(r)|2dV=1 (I) Here, dV is the elemental volume of...Write the expression for orbital angular momentum. L=l(l+1)ℏ Here, L is the orbital angular...The figure 1 shows the transitions from higher levels N shell down to K shell. The K series includes...Write the expression for the energy of the ground state. E1=−hcλseries limit (I) Here, E1 is the...In the decay of radioactive nucleus, the daughter nucleus has the same number of nucleon as the...Write the expression for the binding energy of the nucleus. Eb(MeV)=[ZM(H)+Nmn−M(ZAX)]×931.494 MeV/u...Let N10 be the number of parent nuclei at time t=0, N1(t) be the number of parent nuclei at any...Write the equation to find the number of carbon atoms. N=mMCNava Here, N is the number of carbon...Write the expression for the mass of water. mH2O=ρV (I) Here, mH2O is the mass of water, ρ is the...Write the expression for the average kinetic energy of the carbon atom. Kavg=32kBT (I) Here, Kavg is...Write the expression for the kinetic energy to overcome the columbic repulsion barrier in the...Write the expression for the radius of the 612C nucleus. r=aA1/3 (I) Here, r is the radius of the...Write the equation to find the number of nuclie in the given mass. n=NavaMPum Here, n is the number...Write the equation for volume of a cube. V=l3 (I) Here, V is the volume of a cube and l is the edge...In the given decay process, muon decays into an electron, electron antineutrino and a muon neutrino....Write the expression for the energy released in the reaction. (ΔE)=(mn−mp−me)c2 (I) Here, (ΔE) is...Check for the charge conservation. C:0+0→1+−1 Thus, charge is conserved. Check for Baryon number...Write the reaction. Ξ−→Λ0+μ−+νμ Check the conservation of baryon number for the reaction on both...Write the expression for the momentum. p=mv (I) Here, p is the momentum, m is the mass, v is the...Write the expression from the conservation of energy. Emin+m2c2=(m3c2)2+(p3c)2 (I) Here, Emin is the...Write the expression for the number of protons. Np=V(NAm)(np) (I) Here, Np is the number of proton,...Write the expression for velocity from Hubble’s law. v=HR (I) Here, v is the velocity, H is the...At threshold point, photon and a proton colliding head on to produce a proton and a pion at rest....

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