Question: A transverse wave on a string is
A transverse wave on a string is described by
Plot the displacement y and the velocity vy versus t for one complete cycle of the point x = 0 on the string.
> In Fig. 17.13, why is the person touching the dome of the van de Graaff generator not electrocuted even though there may be a potential difference of hundreds of thousands of volts between him and the ground?
> Under favorable conditions, the human eye can detect light waves with intensities as low as 2.5 × 10−12 W/m2. (a) At this intensity, what is the average power incident on a pupil of diameter 9.0 mm? (b) If this light is produced by an isotropic source 1
> At what time is energy stored in the inductor 0.10 times its initial value?
> Another example of motional emf is a rod attached at one end and rotating in a plane perpendicular to a uniform magnetic field. We can analyze this motional emf using Faraday’s law. (a) Consider the area that the rod sweeps out in each
> A uniform string of length 10.0 m and weight 0.25 N is attached to the ceiling. A weight of 1.00 kN hangs from its lower end. The lower end of the string is suddenly displaced horizontally. How long does it take the resulting wave pulse to travel to the
> If we know the potential at a single point, what (if anything) can we say about the magnitude of the electric field at that same point?
> It takes a flea 1.0 × 10−3 s to reach a peak speed of 0.74 m/s. (a) If the mass of the flea is 0.45 × 10−6 kg, what is the average power required? (b) Insect muscle has a maximum output of 60 W/kg. If 20% of the flea’s weight is muscle, can the muscle
> A lens is placed at the end of a bundle of optical fibers in an endoscope. The purpose of the lens is to make the light rays parallel before they enter the fibers (in other words, to put the image at infinity). What is the advantage of using a lens with
> A 6.2 cm by 2.2 cm parallel plate capacitor has the plates separated by a distance of 2.0 mm. (a) When 4.0 × 10−11 C of charge is placed on this capacitor, what is the electric field between the plates? (b) If a dielectric with dielectric constant of 5
> An axon has the outer part of its membrane positively charged and the inner part negatively charged. The membrane has a thickness of 4.4 nm and a dielectric constant κ = 5. If we model the axon as a parallel plate capacitor whose area is 5 µm2, what is i
> Show that the amplitudes of the graphs you made in Problem 89 satisfy the equation A′ = 2A cos (ωt), where A′ is the amplitude of the wave you plotted and A is 5.0 cm, the amplitude of the waves that were added together.
> A converging lens made from dense flint glass is placed into a container of transparent glycerin. Describe what happens to the focal length.
> Why must a blood pressure cuff be wrapped around the arm at the same vertical level as the heart?
> An electron is placed in a uniform electric field of strength 232 N/C. If the electron is at rest at the origin of a coordinate system at t = 0 and the electric field is in the positive x-direction, what are the x- and y-coordinates of the electron at t
> During a thunderstorm, some cows gather under a large tree. One cow stands facing directly toward the tree. Another cow stands at about the same distance from the tree, but it faces sideways (tangent to a circle centered on the tree). Which cow do you th
> The ball is released from rest when the thread makes an angle of 32° with the vertical. How fast is it moving when the thread is vertical?
> Calculate the kinetic energy of the alpha particle in Problem 25. This time, do not assume that the / nucleus is at rest after the reaction. Start by figuring out the ratio of the kinetic energies of the alpha particle and the / nucleus.
> A photoelectric experiment illuminates the same metal with six different ultraviolet sources. Both the wavelength and the intensity vary from one source to another. Rank the six situations in order of the stopping potential, largest to smallest. (a) λ =
> A curve in a stretch of highway has radius 610 m. The road is banked at angle 5.8° to the horizontal. The coefficient of static friction between the tires and road is 0.50. What is the fastest speed that a car can travel through the curve without skiddin
> The voltage across an inductor and the current through the inductor are related by vL = L Δi/Δt. Suppose that i(t) = I sin ωt. (a) Sketch a graph of i(t), showing at least one full cycle. (b) Using a small-angle approximation (Appendix A.9), find the s
> Suppose that an ideal capacitor and an ideal inductor are connected in series in an ac circuit. (a) What is the phase difference between vC(t) and vL(t)? [Hint: Since they are in series, the same current i(t) flows through both.] (b) If the rms voltage
> If an object is traveling at a constant velocity, is it necessarily traveling in a straight line? Explain.
> Repeat Problem 22, but now the copper washer and the steel bolt are both raised to the same temperature. At what temperature will the washer fit on the bolt?
> What are some of the advantages of a UV microscope over a visible light microscope? What are some of the disadvantages?
> An old highway is built out of concrete blocks of equal length. A car traveling on this highway feels a little bump at the joint between blocks. The passengers in the car feel that the ride is uncomfortable at a speed of 45 mi/h, but much smoother at spe
> Your friend balances a package with mass m = 10 kg on top of his head while standing. The mass of his upper body is M = 55 kg (about 65% of his total mass). Because the spine is vertical rather than horizontal, the force exerted by the sacrum on the spin
> A solenoid with 8500 turns per meter has radius 65 cm. The current in the solenoid is 25.0 A. A circular loop of wire with 100 turns and radius 8.00 cm is put inside the solenoid. The current in the circular loop is 2.20 A. What is the maximum possible m
> If a piece of white cardboard is placed at the location of a virtual object, what (if anything) would be seen on the cardboard?
> Estimate the minimum total kinetic energy of the 2H and 3H nuclei necessary to allow the fusion reaction of Eq. (29-49) to take place.
> A horizontal segment of pipe tapers from a cross-sectional area of 50.0 cm2 to 0.500 cm2. The pressure at the larger end of the pipe is 1.20 × 105 Pa, and the speed is 0.040 m/s. What is the pressure at the narrow end of the segment?
> The charge on a capacitor doubles. What happens to its capacitance?
> Four people sit in a car. The masses of the people are 45 kg, 52 kg, 67 kg, and 61 kg. The car’s mass is 1020 kg. When the car drives over a bump, its springs cause an oscillation with a frequency of 2.00 Hz. What would the frequency be if only the 45 kg
> You are hiking through a lush forest with some of your friends when you come to a large river that seems impossible to cross. However, one of your friends notices an old metal barrel sitting on the shore. The barrel is shaped like a cylinder and is 1.20
> You will be hiking to a lake with some of your friends by following the trails indicated on a map at the trail-head. The map says that you will travel 1.6 mi directly north, then 2.2 mi in a direction 35° east of north, then finally 1.1 mi in a direction
> A sphere of copper is subjected to 100 MPa of pressure. The copper has a bulk modulus of 130 GPa. By what fraction does the volume of the sphere change? By what fraction does the radius of the sphere change?
> A light wave passes through a hazy region in the sky. If the electric field vector of the emerging wave is one quarter that of the incident wave, what is the ratio of the transmitted intensity to the incident intensity?
> In Fig. 20.2, the distance between the rails is L = 5.0 cm. The metal rod is sliding to the right at v = 16 cm/s and the magnetic field has magnitude B = 0.75 T. The rod and rails have negligible resistance compared with the resistor (R = 180 Ω). Find (
> 1. Which of these statements are postulates of Einstein's special relativity? (1) The speed of light is the same in all inertial reference frames. (2) Moving clocks run slow. (3) Moving objects are contracted along the direction of motion. (4) The laws o
> An above-ground swimming pool is filled with water (total mass M) to a height h. Explain why the gravitational potential energy of the water (taking U = 0 at ground level) is /. Where does the factor of / come from? How much work must be done to fill t
> When we talk about the potential difference between the plates of a capacitor, shouldn't we really specify two points, one on each plate, and talk about the potential difference between those points? Or doesn't it matter which points we choose? Explain.
> A uniform magnetic field of 0.50 T is directed to the north. At some instant, a particle with charge +0.020 μC is moving with velocity 2.0 m/s in a direction 30° north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b
> A gold wire of 0.50 mm diameter has 5.90 × 1028 conduction electrons per cubic meter. If the drift speed is 6.5 µm/s, what is the current in the wire?
> Color printers always use at least three different colors of ink or toner. Televisions and computer monitors have pixels of at least three different colors. Why are at least three necessary? [Hint: See Fig. 24.9.]
> Sheena can row a boat at 3.00 mi/h in still water. She needs to cross a river that is 1.20 mi wide with a current flowing at 1.60 mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0°
> A circular metal loop carries a current I as shown. The points are all in the plane of the page and the loop is perpendicular to the page. Sketch the loop, and draw vector arrows at the points A, B, C, D, and E to show the direction of the magnetic field
> Finola has a circuit with a 4.00 kΩ resistor, a 0.750 H inductor, and a capacitor of unknown value connected in series to a 440.0 Hz ac source. With an oscilloscope, she measures the phase angle to be 25.0°. (a) What is the value of the unknown capacito
> At a point due south of the transmitter, what is the direction of the wave’s magnetic field?
> A constant force, acting for 3.6 × 104 s (10 h), brings a spaceship of mass 2200 kg from rest to speed 0.70c. (a) What is the magnitude of the force? [Hint: Use the impulse-momentum theorem.] (b) What is the initial acceleration of the spaceship? Comme
> Why does a mirror hanging in a vertical plane seem to interchange left and right but not up and down? [Hint: Refer to Fig. 23.28. Instead of calling Grant's hands left and right, call them east and west. In Grant's image, are the east and west hands reve
> Point P is at a potential of 500.0 kV, and point S is at a potential of 200.0 kV. The space between these points is evacuated. When a charge of +2e moves from P to S, by how much does its kinetic energy change?
> How much work is done by an applied force that moves two charges of 6.5 µC that are initially very far apart to a distance of 4.5 cm apart?
> If a uniform electric field exists in a region of space, is the potential the same at all points in the region? Explain.
> We can model some of the electrical properties of an unmyelinated axon as an electric cable covered with defective insulation so that current leaks out of the axon to the surrounding fluid. We assume the axon consists of a cylindrical membrane filled wit
> Four masses are arranged as shown. They are connected by rigid, massless rods of lengths 0.75 m and 0.50 m. What torque must be applied to cause an angular acceleration of 0.75 rad/s2 about the axis shown?
> (a) When ice floats in water at 0°C, what percent of its volume is submerged? (b) What is the specific gravity of ice?
> At a rock concert, the engineer decides that the music isn't loud enough. He turns up the amplifiers so that the amplitude of the sound, where you're sitting, increases by 50.0%. (a) By what percentage does the intensity increase? (b) How does the inte
> In a velocity selector, the electric and magnetic forces cancel if . Show that / must be in the same direction as / [Hint: Since is perpendicular to both and in a velocity selector, there are only two possibilities for the direction of /:
> A circular conducting loop with radius 3.40 cm is placed in a uniform magnetic field of 0.880 T with the plane of the loop perpendicular to the magnetic field, as shown. The loop is rotated 180° about the axis in 0.222 s. (a) As the loop begi
> Dash is standing on his frictionless skateboard with three balls, each with a mass of 100 g, in his hands. The combined mass of Dash and his skateboard is 60 kg. How fast should Dash throw the balls forward if he wants to move backward with a speed of 0.
> How many different hadrons are stable (as far as we know)?
> According to Maxwell, why is it impossible to have an electric wave without any magnetic component?
> Find the energy for a hydrogen atom in the stationary state n = 4.
> Stan and Ollie are standing next to a train track. Stan puts his ear to the steel track to hear the train coming. He hears the sound of the train whistle through the track 2.1 s before Ollie hears it through the air. How far away is the train?
> A stretched string has a fundamental frequency of 847 Hz. What is the fundamental frequency if the tension is increased by a factor of 3.0?
> You are bicycling along a straight north-south road. Let the x-axis point north. Describe your motion in each of the following cases. Example: ax > 0 and vx > 0 means you are moving north and speeding up. (a) ax > 0 and vx < 0. (b) ax = 0 and vx < 0.
> Under what special circumstances can kelvins or Celsius degrees be used interchangeably?
> At a point P, a distance R0 from a positive charge Q0, the electric field has a magnitude E0 = 100 N/C and the electric potential is V0 = 10 V. The charge is now increased by a factor of three, becoming 3Q0. (a) At what distance, RE, from the charge 3Q0
> An electroscope consists of a conducting sphere, conducting pole, and two metal foils (see Fig. 16.10). The electroscope is initially uncharged. (a) A positively charged rod is allowed to touch the conducting sphere and then is removed. What happens to
> The eyepiece of a Galilean telescope is a diverging lens. The focal points Fo and F′e coincide. In one such telescope, the lenses are a distance d = 32 cm apart and the focal length of the objective is 36 cm. A rhinoceros is viewed from
> An RC filter is shown. The filter resistance R is variable between 180 Ω and 2200 Ω and the filter capacitance is C = 0.086 µF. At what frequency is the output amplitude equal to times the input amplitude if R = (a
> A radio wave with a wavelength of 1200 m follows two paths to a receiver that is 25.0 km away. One path goes directly to the receiver and the other reflects from an airplane that is flying above the point that is exactly halfway between the transmitter a
> In tall buildings, the water supply system uses multiple pumping stations on different floors. At each station, water pumped up from below collects in a storage tank held at atmospheric pressure before it enters the pump. The storage tank supplies water
> A truck carrying explosive gases either has chains or straps that drag along the ground, or else it has special tires that conduct electricity (ordinary tires are good insulators). Explain why the chains, straps, or conducting tires are necessary.
> You are given two x-ray tubes, A and B. In tube A, electrons are accelerated through a potential difference of 10 kV. In tube B, the electrons are accelerated through 40 kV. What is the ratio of the minimum wavelength of x-rays in tube A to the minimum w
> Explain why electric field lines never cross.
> A fellow student says that there is never an electric field inside a conductor. Do you agree? Explain.
> Two strings, each 15.0 m long, are stretched side by side. One string has a mass of 78.0 g and a tension of 180.0 N. The second string has a mass of 58.0 g and a tension of 160.0 N. A pulse is generated at one end of each string simultaneously. (a) On w
> (a) What is the density of an object that is 14% submerged when floating in water at 0°C? (b) What percentage of the object will be submerged if it is placed in ethanol at 0°C?
> The speed of waves on a lake depends on frequency. For waves of frequency 1.0 Hz, the wave speed is 1.56 m/s; for 2.0 Hz waves, the speed is 0.78 m/s. The 2.0 Hz waves from a speedboat's wake reach you 120 s after the 1.0 Hz waves generated by the same b
> Simon wishes to display a double-slit experiment for his class. His coherent light source has a wavelength of 510 nm, and the slit separation is d = 0.032 mm. He must set up the light on a desk 1.5 m away from the screen that is only 10 cm wide. How many
> Bruce is trying to remove an eyelash from the surface of his eye. He looks in a shaving mirror to locate the eyelash, which is 0.40 cm long. If the focal length of the mirror is 18 cm and he puts his eye at a distance of 11 cm from the mirror, how long i
> An electric device has the current-voltage (I-V) graph shown. What is its resistance at (a) point 1 and (b) point 2? [Hint: Use the definition of resistance.]
> When the muscles of the eye remain tensed for a significant period of time, eyestrain results. How much is this a concern for a person using (a) a microscope, (b) a telescope, and (c) a simple magnifier?
> The instantaneous sinusoidal emf from an ac generator with an rms emf of 4.0 V oscillates between what values?
> The K0 meson can decay to two pions: K0 → π+ + π−. The rest energies of the particles are: K0 = 497.7 MeV, π+ = π− = 139.6 MeV. If the K0 is at rest before it decays, what are the kinetic energies of the π+ and the π− after the decay?
> The length of a spring increases by 7.2 cm from its relaxed length when a mass of 1.4 kg is hanging in equilibrium from the spring. (a) What is the spring constant? (b) How much elastic potential energy is stored in the spring? (c) A different mass is
> Due to the similarity between Newton’s law of gravity and Coulomb’s law, a friend proposes this hypothesis: perhaps there is no gravitational interaction at all. Instead, what we call gravity might be electric forces acting between objects that are almos
> An airplane is flying at constant speed 740 km/h in a horizontal circle of radius 4.1 km. The lift force on the wings due to the air is perpendicular to the wings. At what angle to the vertical must the wings be banked to fly in this circle?
> While an elevator of mass 832 kg moves downward, the tension in the supporting cable is a constant 7730 N. Between t = 0 and t = 4.00 s, the elevator's displacement is 5.00 m downward. What is the elevator's speed at t = 4.00 s?
> A Compton scattering experiment is performed using an aluminum target. The incident photons have wavelength λ. The scattered photons have wavelengths λ′ and energies E that depend on the scattering angle θ. (a) At what angle θ are scattered photons with
> Are entropy changes always caused by the flow of heat? If not, give some other examples of processes that increase entropy.
> Why are heat pumps more often used in mild climates than in areas with severely cold winters?
> The pull cord of a lawnmower engine is wound around a drum of radius 6.00 cm. While the cord is pulled with a force of 75 N to start the engine, what magnitude torque does the cord apply to the drum?
> A discus thrower moves the discus in 1.5 complete revolutions in 1.4 s (starting from rest). The radius of the circular path of the discus is 0.90 m, and the mass of the discus is 2.0 kg. Assume a constant torque is applied to the discus by the athlete.
> Two spaceships are observed from Earth to be approaching each other along a straight line. Ship A moves at 0.40c relative to the Earth observer, and ship B moves at 0.50c relative to the same observer. What speed does the captain of ship A report for the
> Two steel wires (of the same length and different radii) are connected together, end to end, and tied to a wall. An applied force stretches the combination by 1.0 mm. How far does the midpoint move?
> A 2010 kg elevator moves with an upward acceleration of 1.50 m/s2. What is the tension in the cable that supports the elevator?
> Rank the flywheels in order of the linear speed at the rim, largest to smallest. Explain.
> No currents flow in the circuit diagrammed before the switch is closed. Consider all the circuit elements to be ideal. (a) At the instant the switch is closed, what are the values of the currents I1 and I2, the potential differences across the resistors
> Two blocks, one with mass m1 = 0.050 kg and one with mass m2 = 0.030 kg, are connected to each other by a string. The inner block is connected to a central pole by another string as shown in the figure with r1 = 0.40 m and r2 = 0.75 m. When the blocks ar
