The graph shows potential energy (in J) vs. position (in m) for an object moving along the x-axis. The mechanical energy is 20 J. Assume the mechanical energy is conserved. The object moves to the right starting from x = 0 m. Over which interval does the kinetic energy decrease by the smallest amount?
A magnetic field is passing through a loop of wire whose area is 0.014 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.19 T/s. (a) Determine the magnitude of the emf induced in the loop. (b) Suppose the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m^2/s) should the area be changed at the instant when B = 1.4 T if the induced emf is to be zero? Use a minus sign if the area is to be shrunk. (a) Number Units (b) Number Units
If this 40−kg thin disk with a 0.75−m radius and a radius of gyration of k = 0.64 m is released from rest at A, find the speed of the disk's center when it reaches B. The height h = 3.2 meters. Assume that the object rolls without slipping. vB = 6.47 m/s vB = 7.04 m/s vB = 6.03 m/s vB = 5.14 m/s
Suppose you wish to make a solenoid whose self-inductance is 1.6 mH. The inductor is to have a cross-sectional area of 1.4×10−3 m2 and a length of 0.074 m. How many turns of wire are needed? Number Units
A 4.2 kg mess kit sliding on a frictionless surface explodes into two 2.1 kg parts, one moving at 2.0 m/s, due north, and the other at 6.8 m/s, 29∘ north of east. What is the original speed of the mess kit? Number Units
In New England, the horizontal component of the Earth's magnetic field has a magnitude of 1.3×10−5 T. An electron is shot vertically straight up from the ground with a speed of 3.4×106 m/s. What is the magnitude of the acceleration caused by the magnetic force? Ignore the gravitational force acting on the electron. Number Units
In the figure, the particles have charges q1 = −q2 = 680 nC and q3 = −q4 = 91 nC, and distance a = 6.2 cm. What are the (a) x and (b) y components of the net electrostatic force on particle 3? (a) Number Units (b) Number Units
(a) What is the angular speed ω about the polar axis of a point on Earth's surface at a latitude of 34∘N? (Earth rotates about that axis. ) (b) What is the linear speed v of the point? What are (c) ω and (d) v for a point at the equator? (Note: Earth radius equals 6370 km and let one day be 24 hours) (a) Number Units (b) Number Units (c) Number Units (d) Number Units
In 99 days the number of radioactive nuclei decreases to one-eighth the number present initially. What is the half-life (in days) of the material? Number Units
An empty capacitor has a capacitance of 5.57 μF and is connected to a 12−V battery. A dielectric material (k = 4.5) is inserted between the plates of this capacitor. What is the magnitude of the surface charge on the dielectric that is adjacent to either plate of the capacitor? (Hint: The surface charge is equal to the difference in charge on the plates with and without the dielectric.) Number Units
The electric field has a constant value of 3.3×104 V/m and is directed downward. The field is the same everywhere. The potential at a point P within this region is 110 V. Find the potential at the following points: (a) 8.1×10−3 m directly above P, (b) 3.2×10−3 m directly below P, (c) 4.3×10−3 m directly to the right of P. (a) Number Units (b) Number Units (c) Number Units
When the moment is applied to the wheel as shown and the wheel rolls without slipping, what is true regarding the friction force between the wheel and the surface? The friction force's direction is to the right. The friction force's magnitude is zero. The friction force's direction is to the left. The friction force's direction is to the upward.
A parallel-plate air-filled capacitor having area 37 cm2 and plate spacing 0.82 mm is charged to a potential difference of 670 V. Find (a) the capacitance, (b) the magnitude of the charge on each plate, (c) the stored energy, (d) the electric field between the plates, (e) the energy density between the plates. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
A heart defibrillator passes 11.9 A through a patient's torso for 5.00 ms in an attempt to restore normal beating. (a) How much charge passed? (b) What voltage was applied if 473 J of energy was dissipated? kV (c) What was the path's resistance? kΩ (d) Find the temperature increase caused in the 8.00 kg of affected tissue. The specific heat of tissue is 3500 J/(kg⋅∘C). ∘C
At a given instant the current and self-induced emf in an inductor are directed as indicated in the figure. (a) Is the current increasing or decreasing? (b) The induced emf is 14 V and the rate of change of the current is 30 kA/s; find the inductance. (a) (b) Units
Three displacement vectors of a croquet ball are shown in the figure, where |A→| = 22.0 units, |B→| = 35.0 units, and |C→| = 10.0 units. (a) Find the resultant in unit-vector notation. R→ = units (b) Find the magnitude and direction of the resultant displacement. magnitude unit(s) direction counterclockwise from the +x-axis
When a resistor is connected across the terminals of an ac generator (114 V) that has a fixed frequency, there is a current of 0.343 A in the resistor. When an inductor is connected across the terminals of the same generator, there is a current of 0.420 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, what is (a) the impedance of the series combination and (b) the phase angle between the current and the voltage of the generator? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. Circuit 1 Circuit 2 Circuit 3 (a) Number Units (b) Number Units
Review Conceptual Example 5 before attempting this problem. Then refer to the drawing, in which the generator delivers 6.00 times as much current at very low frequencies as it does at very high frequencies. Find the ratio R2/R1 of the resistances. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. Number Units
The current in the 8.00−Ω resistor in the drawing is 0.610 A. Find the current in (a) the 20.0−Ω resistor and in (b) the 9.00−Ω resistor. (a) Number Units (b) Number Units
In a series circuit, a generator (1300 Hz, 11.0 V) is connected to a 13.0−Ω resistor, a 4.20−μF capacitor, and a 4.80−mH inductor. Find the voltages across (a) the resistor, (b) the capacitor, and (c) the inductor. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. (a) Number Units (b) Number Units (c) Number Units
A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the n = 3 excited state. The atom returns to the ground state by emitting two photons, one in dropping to n = 2 state, and one in further dropping to the ground state. What are the photon wavelengths of (a) the first and (b) the second transitions? (a) Number Units (b) Number Units
Remove the capacitor from the circuit in the figure and set R = 152 Ω, L = 341 mH, fd = 60.0 Hz, and εm = 42.0 V. What are (a) Z , (b) φ, and (c) I? (a) Number Units (b) Number Units (c) Number Units
x = (2.2 m)cos[(4πrad/s)t + π/4 rad] gives the simple harmonic motion of a body. At t = 8.5 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
In a series circuit, a generator (1200 Hz, 18.0 V) is connected to a 16.0−Ω resistor, a 4.40−μF capacitor, and a 5.10−mH inductor. Find the voltages across (a) the resistor, (b) the capacitor, and (c) the inductor. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. (a) Number Units (b) Number Units (c) Number Units
The dark fringe for m = 0 in a Young's double-slit experiment is located at an angle of θ = 14∘. What is the angle that locates the dark fringe for m = 1? Double slit Screen
The ac generator in the figure supplies 120 V at 60.0 Hz . With the switch open as in the diagram, the current leads the generator emf by 22.3∘. With the switch in position 1, the current lags the generator emf by 11.5∘. When the switch is in position 2, the current amplitude is 2.10 A. What are (a) R, (b) L, and (c) C? (a) Number Units (b) Number Units (c) Number Units
In the figure, a long, straight copper wire (diameter 2.56 mm and resistance 0.944 Ω per 270 m) carries a uniform current of 24.0 A in the positive x direction. For point P on the wire's surface, calculate the magnitudes of (a) the electric field E→, (b) the magnetic field B→, and (c) the Poynting vector S→, and (d) determine the direction of S→ (a) Number Units (b) Number Units (c) Number Units (d)
The drawing shows an electron entering the lower left side of a parallel plate capacitor and exiting at the upper right side. The initial speed of the electron is 3.62×106 m/s. The capacitor is 2.00 cm long, and its plates are separated by 0.150 cm. Assume that the electric field between the plates is uniform everywhere and find its magnitude. Number Units
Consider the circuit shown in the diagram below. The potential difference across the points a and b is ΔV = 120.0 V and the capacitors have the following values: C1 = 11.0 μF, C2 = 2.00 μF, C3 = 9.00 μF, and C4 = 18.0 μF. Initially the capacitors are all uncharged. (a) What is the total charge that has to flow through meter A for the capacitors to go from the initial uncharged state to the final state when they are fully charged? mC (b) What is the charge on each fully charged capacitor? Q1 = mc Q2 = mc Q3 = mc Q4 = mc
A 140−mH inductor and a 5.50−Ω resistor are connected with a switch to a 6.00−V battery as shown in the figure below. (a) After the switch is first thrown to a (connecting the battery), what time interval elapses before the current reaches 220 mA? ms (b) What is the current in the inductor 10.0 s after the switch is closed? A (c) Now the switch is quickly thrown from a to b. What time interval elapses before the current in the inductor falls to 160 mA? ms
A 13.1-Ω resistor, a 9.57−μF capacitor, and a 15.2-mH inductor are connected in series with a 135−V generator. (a) At what frequency is the current a maximum? (b) What is the maximum value of the rms current? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. (a) Number Units (b) Number Units
A 12.0 V battery is connected into a series circuit containing a 20.0 Ω resistor and a 2.50 H inductor. (a) In what time interval (in s) will the current reach 50.0% of its final value? s (b) In what time interval (in s) will the current reach 90.0% of its final value? s What If? After a very long time, using a switch like that shown in the figure below, the battery is removed and the inductor is connected directly across the resistor. (i) (c) In what time interval (in s) will the current decrease to 50.0% of its initial value? S (d) In what time interval (in s) will the current decrease to 10.0% of its initial value? S
A 9.71-Ω resistor, a 13.5−μF capacitor, and a 17.0-mH inductor are connected in series with a 177−V generator. (a) At what frequency is the current a maximum? (b) What is the maximum value of the rms current? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. (a) Number Units (b) Number Units
Three capacitors are connected to form the capacitor network shown in the drawing. The potential difference between points a and b is ΔVab = 36.0 V a. What is the equivalent capacitance for the capacitor network? (4) b. What charge is stored on the 6 μF capacitor? (4) c. What is the potential difference across the 18 μF capacitor? (4)
In the figure how much charge is stored on the parallel-plate capacitors by the 11.0 V battery? One is filled with air, and the other is filled with a dielectric for which k = 1.80; both capacitors have a plate area of 8.70×10−3 m2 and a plate separation of 5.60 mm. Number Units
An inductor has an inductance of 0.057 H. The voltage across this inductor is 26 V and has a frequency of 510 Hz. What is the current in the inductor? Number Units
In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.61 V for a wavelength of 320 nm and a stopping potential of 0.792 V for a wavelength of 405 nm. From these data find (a) a value for the Planck constant, (b) the work function Φ for sodium, and (c) the cutoff wavelength λ0 for sodium. (a) Number Units (b) Number Units (c) Number Units
A charged particle with a charge-to-mass ratio of |q|/m = 5.7×108 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.50 T. How much time does it take for the particle to complete one revolution? t =
Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.42 s. What is the time constant when they are connected with the same resistor as in part b? (a) (b) Number Units
In the figure a charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance d = 7.60 mm. The plate potentials are V1 = −63.0 V and V2 = −51.0 V. The particle is slowing from an initial speed of 83.0 km/s at the left plate. (a) Is the particle an electron or a proton? (b) What is its speed just as it reaches plate 2?
A 3.5-μF capacitor has a voltage of 37 V between its plates. What must be the current in a 4.0−mH inductor, such that the energy stored in the inductor equals the energy stored in the capacitor? Number Units
The current in an inductor is 0.29 A, and the frequency is 600 Hz. If the inductance is 0.065 H, what is the voltage across the inductor? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.
An alternating source drives a series RLC circuit with an emf amplitude of 6.00 V, at a phase angle of +32.4∘. When the potential difference across the capacitor reaches its maximum positive value of +5.22 V, what is the potential difference across the inductor (sign included)? Number Units
Two electric charges are placed a distance 2 r apart, as shown in the diagram below: Which one of the following statements regarding the −1 μC electric charge, when it is placed at distance r, is correct? The electrostatic force experienced by the −1 μC electric charge will A. remain the same. B. be halved. C. be doubled. D. increase four times. E. decrease four times.
An electric heater is used to boil small amounts of water and consists of a 11-Ω coil that is immersed directly in the water. It operates from a 120-V socket. How much time is required for the heater to raise the temperature of 0.40 kg of water from 22∘C to the normal boiling point? Take the specific heat capacity of water to be 4186 J/(kg⋅C∘). Number Units
A 79-kg fisherman in a 116-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of vi = 4.1 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown. (skip units)
An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to 3 times the energy difference E76 between the levels n7 and n6? (c) Can a pair of adjacent levels have an energy difference equal to 6E76? (a) Number Units (b) Number Units (c)
An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to 7 times the energy difference E76 between the levels n7 and n6? (c) Can a pair of adjacent levels have an energy difference equal to 2E76? (a) Number Units (b) Number Units (c)
A diffraction grating has 2639 lines per centimeter, and it produces a principal maximum at θ = 29.1∘. The grating is used with light that contains all wavelengths between 410 and 660 nm. What are the two wavelengths of the incident light that could have produced this maximum? Give the longer wavelength as answer (a). (a) Number Units (b) Number Units